Class 10th Mathematics Gujarat Board Solution
Exercise 15.1- Find the mean of the following frequency
- Find the mean wage of 200 workers of a factory where wages are classified as…
- Marks obtained by 140 students of class X out of 50 in mathematics are given in…
- Find the mean of the following frequency distribution by step-deviation…
- Find the mean for the following frequency
- A survey conducted by a student of B.B.A. for daily income of 600 families is…
- The number of shares held by a person of various companies are as follows. Find…
- The mean of the following frequency distribution of 100 observations is 148.…
- The table below gives the percentage of girls in higher secondary science…
- The following distribution shows the number of out door patients in 64…
Exercise 15.2- Find the mode for the following frequency
- The data obtained for 100 shops for their daily profit per shop are as…
- Daily wages of 90 employees of a factory are as follows:Daily wages (in…
- Find the mode for the following
- Find the mode for the following
- The following data gives the information of life of 200 electric bulbs (in…
Exercise 15.3- Find the median for the following:Value of
- Find the median for the following frequency
- Find the median from following frequency
- The following frequency distribution represents the deposits (in thousand…
- The median of the following frequency distribution is 38. Find the value of a…
- The median of 230 observations of the following frequency distribution is 46.…
- The following table gives the frequency distribution of marks scored by 50…
Exercise 15- In a retail market, a fruit vendor was selling apples kept in packed boxes.…
- The daily expenditure of 50 hostel students are as follows:Daily expenditure…
- The mean of the following frequency distribution of 200 observations is 332.…
- Find the mode of the following frequency
- Find the mode of the following
- The mode of the following frequency distribution of 165 observations is 34.5.…
- Find the mode of the following frequency
- Find the median of the following frequency
- The median of the following data is 525. Find the value of x and y, if the sum…
- For some data, if Z = 25 and bar {x} = 25, then M = Select a proper option…
- For some data Z — M = 2.5. If the mean of the data is 20, then Z = Select a…
- If bar {x} — Z = 3 and bar {x} + Z = 45, then M = Select a proper option…
- If Z = 24, bar {x} = 18, then M= Select a proper option (a), (b), (c) or…
- If M = 15, bar {x} = 10, then Z= Select a proper option (a), (b), (c) or (d)…
- (6) If M = 22, Z = 16, then bar {x} = Select a proper option (a), (b), (c)…
- (7) If bar {x} = 21.44 and Z = 19.13, then M = Select a proper option (a),…
- If M = 26, bar {x} =36, then Z = Select a proper option (a), (b), (c) or…
- (9) The modal class of the frequency distribution given below
- The cumulative frequency of class 20-30 of the frequency distribution given…
- The median class of the frequency distribution given in (9) is …. Select a…
- Find the mean of the following frequency
- Find the mean wage of 200 workers of a factory where wages are classified as…
- Marks obtained by 140 students of class X out of 50 in mathematics are given in…
- Find the mean of the following frequency distribution by step-deviation…
- Find the mean for the following frequency
- A survey conducted by a student of B.B.A. for daily income of 600 families is…
- The number of shares held by a person of various companies are as follows. Find…
- The mean of the following frequency distribution of 100 observations is 148.…
- The table below gives the percentage of girls in higher secondary science…
- The following distribution shows the number of out door patients in 64…
- Find the mode for the following frequency
- The data obtained for 100 shops for their daily profit per shop are as…
- Daily wages of 90 employees of a factory are as follows:Daily wages (in…
- Find the mode for the following
- Find the mode for the following
- The following data gives the information of life of 200 electric bulbs (in…
- Find the median for the following:Value of
- Find the median for the following frequency
- Find the median from following frequency
- The following frequency distribution represents the deposits (in thousand…
- The median of the following frequency distribution is 38. Find the value of a…
- The median of 230 observations of the following frequency distribution is 46.…
- The following table gives the frequency distribution of marks scored by 50…
- In a retail market, a fruit vendor was selling apples kept in packed boxes.…
- The daily expenditure of 50 hostel students are as follows:Daily expenditure…
- The mean of the following frequency distribution of 200 observations is 332.…
- Find the mode of the following frequency
- Find the mode of the following
- The mode of the following frequency distribution of 165 observations is 34.5.…
- Find the mode of the following frequency
- Find the median of the following frequency
- The median of the following data is 525. Find the value of x and y, if the sum…
- For some data, if Z = 25 and bar {x} = 25, then M = Select a proper option…
- For some data Z — M = 2.5. If the mean of the data is 20, then Z = Select a…
- If bar {x} — Z = 3 and bar {x} + Z = 45, then M = Select a proper option…
- If Z = 24, bar {x} = 18, then M= Select a proper option (a), (b), (c) or…
- If M = 15, bar {x} = 10, then Z= Select a proper option (a), (b), (c) or (d)…
- (6) If M = 22, Z = 16, then bar {x} = Select a proper option (a), (b), (c)…
- (7) If bar {x} = 21.44 and Z = 19.13, then M = Select a proper option (a),…
- If M = 26, bar {x} =36, then Z = Select a proper option (a), (b), (c) or…
- (9) The modal class of the frequency distribution given below
- The cumulative frequency of class 20-30 of the frequency distribution given…
- The median class of the frequency distribution given in (9) is …. Select a…
Exercise 15.1
Question 1.Find the mean of the following frequency distribution:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoQAAADFCAYAAADNLOOvAAAACXBIWXMAAAsTAAALEwEAmpwYAAAgAElEQVR4Xu3dCdQ015zH8YTYY9/XJAQHsQYnthDM4MjMIJjMEeRgjCUcZEQwZIZYhwmJwyDOeRDMjGAGybHLZieSiERseQWxk0Ts4Z3f703dN/etVHffevrf9fTt+t5z/t7q6upb//u51d3/rqonttuOhgACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAJjEdi+YKCbC7ZhEwQQQAABBBBAAIEVFqAgXM7JXaV5WaWxLOJowSdGFUccYwRieuF4xDFGIKaXzZeJ6YdeEEAAAQQQQAABBGoVoCCsdebIGwEEEEAAAQQQCBKgIAyCpBsEEEAAAQQQQKBWAQrCWmeOvBFAAAEEEEAAgSABCsIgSLpBAAEEEEAAAQRqFaAgrHXmyBsBBBBAAAEEEAgSoCAMgqQbBBBAAAEEEECgVgEKwlpnjrwRQAABBBBAAIEgAQrCIEi6QQABBBBAAAEEahWgIKx15sgbAQQQQAABBBAIEqAgDIKkGwQQQAABBBBAoFYBCsJaZ468EUAAAQQQQACBIAEKwiBIukEAAQQQQAABBGoVoCCsdebIGwEEEEAAAQQQCBKgIAyCpBsEEEAAAQQQQKBWAQrCWmeOvBFAAAEEEEAAgSABCsIgSLpBAAEEEEAAAQRqFaAgrHXmyBsBBBBAAAEEEAgSoCAMgqQbBBBAAAEEEECgVgEKwlpnjrwRQAABBBBAAIEgAQrCIEi6QQABBBBAAAEEahWgIKx15sgbAQQQQAABBBAIEqAgDIKkGwQQQAABBBBAoFYBCsJaZ468EUAAAQQQQACBIAEKwiBIukEAAQQQQAABBGoVoCCsdebIGwEEEEAAAQQQCBKgIAyCpBsEEEAAAQQQQKBWAQrCWmeOvBFAAAEEEEAAgSABCsIgSLpBAAEEEEAAAQRqFaAgrHXmyBsBBBBAAAEEEAgSoCAMgqQbBBBAAAEEEECgVgEKwlpnjrwRQAABBBBAAIEgAQrCIEi6QQABBBBAAAEEahWgIKx15sgbAQQQQAABBBAIEqAgDIKkGwQQQAABBBBAoFYBCsJaZ468EUAAAQQQQACBIIGNKAgPVO4/UGxW7B00DrpBIFrgfurw+4qjojtecH87qf8TFX6PLUO7n5LAcRlmghwQQACBOQVcuJW222rDNcV3FT9U/ExxvOKFil0Uqe2qBQrCDGQdi6Xzcg31/VbFWYozFccoblm4vyO1nffTjtd1vP42WvdRxRmKbyreqLhqx3Zdq0rGchO9sJ1Heuwx5m2eMV9OHb1ccbriN4ppBWHpmOfJx+Mq8fF2+yo2Kb6jmFYQlubjH4zPU3hOT1N8SfFgRUkrdewzr/Pk45wjHYfK+0HK+wMKv3+/pvA8HKS4ggfUakPMq3dZ4ribtnuTwp85ztvHkD8TbuAOWm2IvEsdh5pXE0Q6DpX3fZX32xU+Dk9R+LP+3Yqbe0CtNsS8epcljrfQdq9VnNyE8/6UYq9Wzn44RN6ljkPNq8dd4li2kTp7lMJfoD4DeBX3rnZ5xWMVv1b8sVnnfygIM4x1LpZM3vbq+wTFsQp/gfjxqxQu1q9bsF8XhIco9mvF7q3X3lCPf6p4UbP+Svr3OMXHWttNelgyFr8xTlW0c/FjFx+pzTtmf3H4i8tj+LliUkFYOuZ58/G4Snw8v8cpbqY4WjGpIOyTz6Hq5xzFjRVuD1X4fewPs1mt1LF0Xr2/efLx6yMdh8jbX0zO+d8U6WrOnbV8geK9HlDWhppX77LE0cWCP3eu1uToz5uvKM5W7Nis8z9D5N3HcYh5TcOPdBwqb3+2fFyR5vXqWvYVCZ8EumIa2EDz2sfxAG18rsK1h9tlFYcpfq+4fbPO/wxxPHo/pY5DzatzKjkeizbymcHfKV7sXjva47Tuomw9BWEHUs9VJZP3cPXp7fxrPTW/ac9XuDCc1Y7UBnvM2kjPv17xY8UO2bb30LL3/ZCC15eMxW+MjxT0Ne+Y/UGR2rSCsHTM8+bjXEp8/EGWioZpBWFpPj6T8weFP0jz5rPAX2it63pY6lg6r/Pm4xwjHYfI24XMLxXtW3uOaMbiHFIbal69vxJHF4R3yvLz4j7Nax+TrR8i7z6OQ8xrGn6k41B5+8eJP9vztl8zr3cfeF77OPo4e2orb5t5DnzGPbUhjkfvq9RxqHl1TpvbHzSZS6/Fg7W1vwD8QdXV/kcr/6/riWydB/4WxakKn9b1B8q/KtqXRu6vdZ9ptvFp6w8r9lak5lPXvsTifr6q8LbPueTpUS35A9iX7X35MzX/Ivqsws9FNfflM5EXZR26aPAZ48j9lOQ775j/XLKTZlwlY543n8J0tnyw/aVg49J8/J7yGX5fVsmbH/uDPy9GWptseVjq2PXarnXz5tPVZ9e6Useu13atmyfv89ShC+H2vPpMh5sLndSGmtdsl1MXfYz4MzxvKe9rZiuHyLuP49RBZU/OM6+l+/B2pY6lfc6b9yHa0edaO0tnC3+RrR9iXkvH7O1cE/gWhrylvH+erRwq71LHVsoTH847r1s6jioIfV/RNxS/mpCui5BZhYF/Te6muKfiLoo9FfdTuJJO7fpa+JDipQpv49d4vwds3WK77Vx8et0dFXdWvFrxsuz5MS3eQYM9u2PAXufCOV3a79hk66onaMmXBM5Q+IPgmYr8uLmWHvuSYns//hI7R+Ecopr38x6F72XzPVXvVPjsdN4ixtzq8lIP+4x5iHwuleCUFaX5pHlrz2t6vBHz6mENkc8Uvm2eKj0e58k7v9Um7fxWWvAZeb8HUlu2eZ2Ut/M9fgPynpRP29GpDTGvGcHUxUl5tx03Im9flfDZQp8Q8hUn37uc2rIdj1lqWxZ3URyu8I/6d2VPbkTe0xyd2mDHY0RBeGUl7PtD/Maap/lD4u8UPqvk5vtk/IX/pOax//G1fu/vu806Fx2vUbj6d/O9ZC4U8y8Nn5l8ZfP82P65jgZsx3bzOh+ELmymtV/rSf968v1gt1O8UOFfNu/IXuR9uE3az7WzbedZTGecPN93a2Kz/v2iwsV/avOOOetq4mKfMQ+Rz8REO54ozcfb+YyvbwXJW5rnjZjXIfLpIOtc1ed4jMzb8/IIhe/X/VOW2bLNaxvNnzf/qPCX79eWIO9Jjhs1r22vSY8nOQ6dty/7+7vB39v+PnhxK+FlPR5vqTx9f7VrCH+WPVrhW2NSGzrvWY6DzmtEQZgg/eU8T3Mh+PcKX2r0maVNChdy/uK5msLNl4HPV3xS8VzFTgoXom/2k2r+gPy84jDFfyh2v3j1NmcZm1X80wj4vj9fekqRnzV8tta/QPFbhefXlwv/XeGDONlqcZD2I+3FPwh8Y7qb38xPUfjN7D826NvyMV+974vZfqvAjlrKLfN7B0uYoue1ZJ8R20TnXeLoz+u3Kj6oODJiEAP28Szty8fJ0xe8z3kdo+c1eriTHKPznuXowt7fzbsp7qvw967nd9nbt5Sgb3dx7j9R+MfJXReY9LyO0fM6dagRBaGLBf9S8L0u8zQXHi7kXqJwobezwgWJm+9lcvP9cL6nwgWhz1RtUvgXSn6GyH/E8DrFvoovK76p8K+AMTbPS9d/+sUFtgu8XyoeqPhVFu+bAZX+oGCPZjvvw23SfvL7SmZ03ftpH3unK1Iu7qBkzFfUdvmY/cHQp/UZc0k+ffY977al+Xg7/1iwVd7Sj7M0r5/Qk7mlz97O2ybNa0k+8+57ntfPk3eJ4+uVnK+CPKEjyeh57djFulf58/dpigcr/IM+b9F5z+vYNch55rWrv/Wum+bY1ec8eZc4ep/+ft1P4duzDsqSiJ7XrvHNs87ffQcofGLh8AXmPa9j1xjnmdeu/rauiygI3dmxitsoJp1p8S+HvRXXnJKNzzqdpDhGMe1sow/A/RUuQH052ffT+C8fU9HoD5wXKm6qcHHox/+luJNibO00DfjmHYPeRet8ytxnZf3L7j5ZHNhs7zM91+p4bTqFnc4E+Y31Q0V7Pz62bqZwDhHNx1aa47w/55OflSoZs88q5mO+f88E+4y5JJ+eu59r89J80ry159XHjlt6/slazi2/3jO7PvPqrmfl03P36948Ou9ZjocpU9vvo/CVkHaLntd2/+t97HxfqniAwpfq2i0673kdo+e1Pd71Pp7lGJ33JEffstVu39OK8xT5VaPoeW3vs+/jK+kFvtyeN393+AzhXbKV0XnP6xg9ry2C/g+nFWept1trwVXr8yd0/wqtP0eRvtB31bL7dZGY2re18OnssRf9i8Pb+bq+270Uvg8lb0/QA29zY4XPXhzeet5fIH7eBecqtZJ5eUQzdt//l9oVtOA376tmYOys57s+wH3W1vu+d/Z6m/vUdl6Y+aydt3NRPquVjGVNnfgHQN48lp8q/CsstXnGvE3neuBfuUe1VzaPS8cckU+JT57m0XrQNXfepjQf/+By4dy+xPcRrUtnifN9Tlue5rimF5bMa0Q+kY5D5u3bXz6s8PGems9u5J+fQ85rqaNzOkvhH4ap3UMLh2SPh8y7xHFNuS3b8VjiOETeO8jG3/PtH+b+3nVx9e4NmteS4/Ek5ZZ/Z6VUv6yFcwfOu4/jmnJbquOxBNueD1NcoHiGIl1m8r8+43Sh4oHeqGm76l/3m3+g+RfwRYq03c5a9i8Pb5cKwkdq+WzFjRRuLkDepvhG89jb+dfzns1j/7O/wjfGt88sZJtUuVgyL/5FdILCZ13Tm9jFud8A150x6p31vPfxPEX6ZeV7+Fz4+Yxs3m6oBy7MfGbWzb/GPq34ePN41j8lY1lTJz47vFPTmefel9Da8z3PmNt5TitkSscckU+JT577tIKwTz6HqlO/B9P7zcX9HxX3bUPNeDzNcU2vLZlX72LefCIdh8r7tRq331tPVPjSXIoPaXl/RWpDzmuJo4sYf+6+QJHn/Wo9Xrsk7a3/IeCSz6h55r/U0bkt0/FY6jhE3i5kPPf+3E0/TnzG8CiFPxfygmvZjseTlJ+/C6+nSM21iseTX+oeIu8+jmvKb5mOxy1gpe222tAHx9mKTYrvKPyr4Y5ZBy4Qf6Bwvz9RHNE85z9meKPixwoDuOjwm9jb+eyiC86bKN6g8H1jpyh8eeq9ilTs+f6aFym+0jx/mv49UbGXYtVa6bz4cv2RCpueqfDl/VsVYLiAfLLikwo7u+j+luJlChd87ea5/5jiDIX35f/m01XbG014XDIWF6Oee5/i97x+X+FjpOtX33rHnNLzeDcp/KvXP2a87GOz3UrHPG8+JT7OzT+ONil8K4B/XHn5ZEW7leZzGb3wYIWPG5v713TJGd+0vxLHPvM6bz6RjkPkna5uOO+u2D9BN/8ONa8ljv7M7srZ69YGzruP4xDzmoYf6ThU3i7uXbz7c/5UhT8b3q+4W2tO/XCZjkd/T6wp/JnkvJ2/C8RHKdptiLxLHYeaVxuUHI9lG7VFebxwgaLJW3gWMTtYpbHEiGzbCz4xqjjiGCMQ0wvHI44xAjG9hP0/lcSkQy8IIIAAAggggAACgwv4EgwNAQQQQAABBBBAYMQCFIQjnnyGjgACCCCAAAIIWICCkOMAAQQQQAABBBAYuQAF4cgPAIaPAAIIIIAAAghQEHIMIIAAAggggAACIxegIBz5AcDwEUAAAQQQQAABCkKOAQQQQAABBBBAYOQCFIQjPwAYPgIIIIAAAgggQEHIMYAAAggggAACCIxcgIJw5AcAw0cAAQQQQAABBCgIOQYQQAABBBBAAIGRC1AQjvwAYPgIIIAAAggggAAFIccAAggggAACCCAwcgEKwpEfAAwfAQQQQAABBBCgIOQYQAABBBBAAAEERi5AQTjyA4DhI4AAAggggAACFIQcAwgggAACCCCAwMgFKAhHfgAwfAQQQAABBBBAgIKQYwABBBBAAAEEEBi5AAXhyA8Aho8AAggggAACCFAQcgwggAACCCCAAAIjF6AgHPkBwPARQAABBBBAAAEKQo4BBBBAAAEEEEBg5AIUhCM/ABg+AggggAACCCBAQcgxgAACCCCAAAIIjFyAgnDkBwDDRwABBBBAAAEEKAg5BhBAAAEEEEAAgZELUBCO/ABg+AgggAACCCCAAAUhxwACCCCAAAIIIDByAQrCkR8ADB8BBBBAAAEEEKAg5BhAAAEEEEAAAQRGLkBBOPIDgOEjgAACCCCAAAIUhBwDCCCAAAIIIIDAyAUoCEd+ADB8BBBAAAEEEECAgpBjAAEEEEAAAQQQGLkABeHIDwCGjwACCCCAAAIIUBByDCCAAAIIIIAAAiMX2L5g/JsLtmETBBBAAAEEEEAAgRUWoCBczsldpXlZpbEs4mjBJ0YVRxxjBGJ64XjEMUYgppfNXDKOgaQXBBBAAAEEEECgWgEKwmqnjsQRQAABBBBAAIEYAQrCGEd6QQABBBBAAAEEqhWgIKx26kgcAQQQQAABBBCIEaAgjHGkFwQQQAABBBBAoFoBCsJqp47EEUAAAQQQQACBGAEKwhhHekEAAQQQQAABBKoVoCCsdupIHAEEEEAAAQQQiBGgIIxxpBcEEEAAAQQQQKBaAQrCaqeOxBFAAAEEEEAAgRgBCsIYR3pBAAEEEEAAAQSqFaAgrHbqSBwBBBBAAAEEEIgRoCCMcaQXBBBAAAEEEECgWgEKwmqnjsQRQAABBBBAAIEYAQrCGEd6QQABBBBAAAEEqhWgIKx26kgcAQQQQAABBBCIEaAgjHGkFwQQQAABBBBAoFoBCsJqp47EEUAAAQQQQACBGAEKwhhHekEAAQQQQAABBKoVoCCsdupIHAEEEEAAAQQQiBGgIIxxpBcEEEAAAQQQQKBaAQrCaqeOxBFAAAEEEEAAgRgBCsIYR3pBAAEEEEAAAQSqFaAgrHbqSBwBBBBAAAEEEIgRoCCMcaQXBBBAAAEEEECgWgEKwmqnjsQRQAABBBBAAIEYAQrCGEd6QQABBBBAAAEEqhWgIKx26kgcAQQQQAABBBCIEaAgjHGkFwQQQAABBBBAoFoBCsJqp47EEUAAAQQQQACBGAEKwhhHekEAAQQQQAABBKoVoCCsdupIHAEEEEAAAQQQiBGgIIxxpBcEEEAAAQQQQKBaAQrCaqeOxBFAAAEEEEAAgRgBCsIYR3pBAAEEEEAAAQSqFaAgrHbqSBwBBBBAAAEEEIgRoCCMcVz2XnZSgicqfrDsiRbkt0pjKRgumyBQtQDv16qnj+THJBBREF5XYC40fqPY3Cz7cR4X6PE/jwl2ica6r3I5XnGjGTldQ8+/VXGW4kzFMYpbznjN0E+XjOUmSsrHYVd4jKvabqGBvVZxchPf1L+fUuzVMeAa5roj7UFW7aa9vEnh98DXFGco3qi4QcfecexAyVbxfp3uU/rsHtrwowofiz4mv6h4VOmL2W6LQJ/3NWRTBPzFWtKO1Ea/n7DhoVpPQTgBZ52rS+blCur7OMXNFEcrJp0h3F7PnaA4VuHX+PGrFD9UuOBfdIsciwvCUxX7dcTlFj2QBfVf4nOA9n2uYtcmh8vq38MUfk/ePstro+d6QURF3ZY4nqKe/D64WtOjj/+vKM5W7JjtBcfp5KWfPav4fp0uc8mzJcejf5RfqPCPknQC54la9mv/tnRHK75diWPp+3rFqaYOr8Rxy4FX0qYVhP5CunVJJ2xTLFAyL/7SSh8i0wrCh2s79+dfUaldUQvnK1wYLrpFjsVfMB9ZdMID91/i4zl8aiuvdLb0oGz9Rs/1wHTb7K7E0V8cd2oluY8e+7WPwXGLQIlj6WfPKr5fW4fPxIcljs9pvHdp9fJTPX7XxJ7H9USJY+n7elxy2452c8Ql42mA/kX9c4VPc/tS5FMUnjyHv7xeovCB7ccuWNz8y9y/hjYpfNnLl8C6fgm5L2/jS9VfUuypcD+/Uvhy5wMUPiPmdc9SuLlvr/ujYu3iVVv/d9Z+27m/Qq/0vnwW7V9affmhx364YpPiNIUNjlD4DM4HFc7BZ2+cz5UVbr7Pz+Ox2b2bdfP847H/paADf+H9THF6tq1z+6zCzy1DKx3LMuS6ETl8QDv1pc68pbNcPp5Sq2GuW8MY9OHdtTd/eeTNZ17drpmtxHEboks94P16KZJ1rbioedUOrVf7CsCf19XjOF9U+r4ep06PUfuNXdK6zhCmgjC9/qpa8JlC9+lC7xCFzx66cHJB6IP8Mwp/IKcPX3/w+sB/sCI13z/hPg5U+EyWT6uf1Kw7YOtWFy/kBWF6yv2vZduV7DfP/ct67bMVzv3lCu/jPq3+fAnWl5rSOHbSsovHg5vtfL+ei7DLZa/zogtH/2qe1UrnJfVj30mXjF2wfqFjhy7MXVBepeO5yFWRY7GdDd+j8A8F/xB5p+K2kQkP3FdfH6fnMwqfUByv8OW71DZ6rrNUBl9cj6OTfLzCr80vveNYPn3TPntW8f1aKlNyPF5LnX1L4bOBV1L4JM7zFOcp7ly6oxXfrsSxi6Drfd213VjWFTkWbSQxF4Teth352QnDuoDzNh/OlH2fjgu+VOj5slbeXOx9PlvxdS1/tbXNg/TY/a6nICzdb8rdH3CpuZj0PR4vztY9UsvOZe9snRdfoEj3UvoMoLd5WLbN3bT88dZrJj0snZf0+mkfyj4D0rXfVzY53nRSEkHrI8dyQ+XkgnD3JjefJXuHwnN0x6B8h+6mj49/HKUz4+/X8vVbyW70XA9tl++vj2N6nS99+vPnKBy3CvR1nPbZs4rv19JjvNTR94Afp/id4hcKF4j3LN3JCLYrdcwpJr2vR8A1cYjhl4z/oF0ZOoXPqk1qPhOYms+U+b4vX+Z186XKvLn48ylf9+cveJ/t+dy2m2w5G7feVrLfvG+feUrNZy9/pMi/eB/YPJlv51U+m/ia5jl/yXxX8bjmsf/ZX/H27DGL/QU8Fz6Tk46HC7Tsy/0+Ng/t3111r/CXhc+6XFvxE4WL47tWN4rlSdi3m1xD8fTlSWmlMhn7+3XWZO6mDXz1xp9nPg598uSlCp/9z08mzOqH57cV4H3dcUTs0LEucpXvh5t0qc7337XbdZoV7cuXPjPnL/YbKNJ9j+3X+xT6elvJfn+ddX5+a0cuCn2mMLXU3y9nJORLmc9X+Mvb/T9U8dwZr1nE0z6L21W8u/j2r69Z41hETpF9/ladna7YI7LTJe/Lc+az5X+l8C0Z6YzCqs915LQ8Wp09TbGXov2exzFSetu+xvh+naTpkwhuBynSPYO+4vEPiv9U/O/FT/O/PQSmva97dLN6my66IHQx4T8aKW3+kHW7g8IFYFdzkeLmeyvy5l9PXc33wPmMZd52bD0u2W9X35PWpf58/+C08fuN7UvN+yp+rPi0wh+GQzffD/XXHTvdRet8FtOFfS3t6krUl1b8Rzt5axfttYynNE/fX+Q/BMovn3jMPkP4kKyTVZrrUpv1bLePXuQzMb564Evw7YZjW2R9j8f6fi3V8tWO7yhSMZhe5z+49G1WvjLlKwG0MoFZ7+uyXlZ0q0X/lXFftnQfmwvCvPks41uaFS4Uz1Dco7XNpBtsXZClM3Z+ic+Etf9oo2S/rd1NfejT+W7tS3XP1DqfEUzNxZYvnT9esb9ioy4Xv1/79qWI26XE9K//EMHG78vW1bD4eiWZX4Z3zh7LboqTaxjAOnP0MXyvjtf6/s/8DO8qzXXHcENWPUK9+MyMz66e0/To98IhWe84hlBvN9b3a6mev798D2H7pMZOWufbYOa5Mlaaw6psV/K+XpWxLmwcpTds+o9KfIZiVkt/mOH7utrNl12PU5yo8Nk1N5/5+6TiRc1j/5P+COTZWr68wm8O/2c3nKsvk+Xtv/XAlwv9S9QF8CsUfpOtZRuV7ndS7t9QXz59n5r7O0HxRUU6c3krLftMw+6XbLZl6UkK5/1tRftN39p0m4el85JedLQWus50+Hnv1/keo7Cnm53OVbhQXHSLHMuakvWvZx8Tbp4Lf+n8SbFns662f0p8fE+q5/B62eCeoWW/1pebUtvouc5SGXyxxNFfGj7D7D8A2y+LV2t5LcsYx/Lpm/bZY9NVe7+WypQcj49VZ97Of1mc2oO0cJHi8GzdmBdLHEvf1zjOEJiF7YJhk8L3wHlbL7uA62q+dPU9hbf7hWKTIhV+aXtfzn1d85wvy/isznMU7WLpn5ptvF9/GfqsovttF4Q+Q+KzJ96fb8z9G8UpigsVLsJSm7Xfdu5H6IVp7C42Uh6pP5+J9Bt2k+JUxWcVfiO3W7pk4stTfdqseUl9vU0LmxS+7OsPES93nSlz4eqi3h/OZyqOVbiIHaJFjuX2SvgNCl8q9fHzfcVHFfceYiAL2keJj8e3pvi6wsebz6K7QPSPp3bbyLlu5zLk4xJHnxH0dl2x1koWx+mzV/LZs4rv1+kqlzxbcjx6a39n+b3sz2Wf3PAfWfqPnBZ9y5f3XUMrcezzvq5hzIvIscRxywdjDc1vDufaLghryN1f3v7PhfRptcxLyZhWaSwl4+27DT59xbq3x7Hbpe9aHPuKdW+PY7dL37U49hXr3j78PzvTvRvWThPwfXv+i2n/50JoCCCAAAIIIIDA4AK+p442vMDdtcu1ZrcH6t83D58Ce0QAAQQQQAABBMoFajgd6/uk/AcTztVn2/zHEcvcfFbQ/5kZ39/2LoX/8KFvq2FeSse0SmMpHXOf7fDpozV5Wxwn2/R5Bsc+WpO3xXGyTZ9ncOyjNXnbIseijSbvg2cWJLBK87JKY1nEdOMTo4ojjjECMb1wPOIYIxDTC/cQxjjSCwIIIIAAAgggUK8A9xDWO3dkjgACCCCAAAIIhAhQEIYw0gkCCCCAAAIIIFCvAAVhvXNH5ggggAACCCCAQIgABWEII50ggAACCCCAAAL1ClAQ1jt3ZDSSKUsAAAJfSURBVI4AAggggAACCIQIUBCGMNIJAggggAACCCBQrwAFYb1zR+YIIIAAAggggECIAAVhCCOdIIAAAggggAAC9QpQENY7d2SOAAIIIIAAAgiECFAQhjDSCQIIIIAAAgggUK8ABWG9c0fmCCCAAAIIIIBAiAAFYQgjnSCAAAIIIIAAAvUKUBDWO3dkjgACCCCAAAIIhAhQEIYw0gkCCCCAAAIIIFCvAAVhvXNH5ggggAACCCCAQIgABWEII50ggAACCCCAAAL1ClAQ1jt3ZI4AAggggAACCIQIUBCGMNIJAggggAACCCBQrwAFYb1zR+YIIIAAAggggECIAAVhCCOdIIAAAggggAAC9QpQENY7d2SOAAIIIIAAAgiECFAQhjDSCQIIIIAAAgggUK8ABWG9c0fmCCCAAAIIIIBAiAAFYQgjnSCAAAIIIIAAAvUKUBDWO3dkjgACCCCAAAIIhAhQEIYw0gkCCCCAAAIIIFCvAAVhvXNH5ggggAACCCCAQIgABWEII50ggAACCCCAAAL1ClAQ1jt3ZI4AAggggAACCIQIUBCGMNIJAggggAACCCBQrwAFYb1zR+YIIIAAAggggECIAAVhCCOdIIAAAggggAAC9QpQENY7d2SOAAIIIIAAAgiECGxf0Mvmgm3YBAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEBgyQX+HzoXZtV4P1ktAAAAAElFTkSuQmCC)
Answer:Since, this is a grouped frequency distribution, this is solved by creating a table and using certain formulae. To find mean, we need to create a table showing class intervals, midpoints, frequencies and product of those midpoints and frequencies.
![](data:image/png;base64,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)
Now, we have
∑fi = 100 and ∑xifi = 14850
The formula of mean by direct method is given by,
![](data:image/png;base64,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)
⇒
[from the given information]
⇒ Mean = 148.5
Thus, mean is 148.5.
Question 2.Find the mean wage of 200 workers of a factory where wages are classified as follows :
![](data:image/png;base64,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)
Answer:This is grouped frequency distribution.
We shall represent them by creating a table having columns of class intervals, midpoints, frequencies, and product of these midpoints and frequencies.
![](data:image/png;base64,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)
So now, we have
∑fi = 200 and ∑xifi = 64300
For grouped frequency distribution, mean is taken out from the formula:
![](data:image/png;base64,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)
⇒
[from the table]
⇒ ![](data:image/png;base64,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)
⇒ Mean = 321.5
Thus, mean is 321.5.
Question 3.Marks obtained by 140 students of class X out of 50 in mathematics are given in the following distribution. Find the mean by method of assumed mean method:
![](data:image/png;base64,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)
Answer:We have grouped frequency distribution and we need to find mean by assumed-mean method.
Assumed-mean method is given such name because in this method, we actually assume a mean from xI (usually a centre value) and the formula of mean is also based on that particular assumed mean.
By using assumed-mean method, we can avoid the risk of miscalculation. Also, by using assumed mean method, we’ll be able to solve the question with ease and more accuracy.
So, let us assume mean from the midpoints. Let assumed mean, A = 25 (a value quite centrally placed).
![](data:image/png;base64,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)
So now, we have
∑fidi = 120 and ∑fi = 140.
And we have assumed mean as, A = 25
Mean is given by
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mean = 25 + 0.86
⇒ Mean = 25.86
Thus, mean is 25.86.
Question 4.Find the mean of the following frequency distribution by step-deviation method:
![](data:image/png;base64,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)
Answer:This is a grouped frequency distribution.
In step deviation, we need to mark the assumed mean in xi as similar to in assumed-mean method but the formula differs. In step deviation, we calculate the deviation of each value from the assumed mean value. This brings more accuracy when values are large.
Here, class interval is given by
h = 10 (∵ 50 – 40 = 60 – 50 = … = 100 – 90 = 10)
And let us assume mean as A = 65, which is the closest value to the centre-most value.
We need to represent it in tabular form:
![](data:image/png;base64,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)
So now, we have
∑fiui = 7 and ∑fi = 52
And assumed mean, A = 65
Mean by step-deviation is given by
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mean = 65 + 1.346
⇒ Mean = 66.346
Thus, mean is 66.346.
Question 5.Find the mean for the following frequency distribution:
![](data:image/png;base64,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)
Answer:This is a grouped frequency distribution.
We can find the mean of the data using any of the methods. Since here we have small values of classes, we can find the mean using direct method easily.
We need to create a table using the values, representing class, midpoints, frequency and product of midpoints and frequencies.
Also, this is an inclusive type of data, which needs to be converted into exclusive type of data.
For conversion, we need to subtract 0.5 from the lower class of each interval and add 0.5 to upper class of each interval.
![](data:image/png;base64,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)
So now, we have
∑xifi = 3735 and ∑fi = 200
Mean is given by
![](data:image/png;base64,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)
⇒
[Using values from the table]
⇒ Mean = 18.675
Thus, mean is 18.675.
Question 6.A survey conducted by a student of B.B.A. for daily income of 600 families is as follows, find the mean income of a family:
![](data:image/png;base64,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)
Answer:This is a grouped frequency distribution.
We can find the mean of this type of distribution by either direct method, assumed-mean method or step deviation method.
But let us try doing it by assumed-mean method since it assures accuracy of the answer when data given is large.
Also, notice given data is inclusive-type of data. We need to convert the inclusive type of data into exclusive type by subtracting 0.5 from lower limit of each class and adding 0.5 to upper limit of each class.
Let us assume mean by taking a value from xi’s closest from the central value.
Let assumed mean, A = 549.5
So, we have
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAqoAAATsCAYAAABIVKAhAAAACXBIWXMAAAsTAAALEwEAmpwYAAAgAElEQVR4Xuy9B7z0Rnm+DR8G03uH4JfeayA0E0wJLYQSINTASwkkhBY6gQTzp4VeErqJX1roJfRiwIDBhA6mmOoDGAzEQAKEavB3X68lGI+1u9qz2nNWe67n97vPkUaj0cw1I+nRzKx0spNpEpCABCQgAQlIQAISkIAEJCABCUhAAhKQgAQkIAEJSEACEpCABCQgAQlIQAISkIAEJCABCUhAAhKQgAQkIAEJSEACEpCABCQgAQlIQAISkIAEJCABCUhAAhKQgAQkIAEJSEACEpCABCQgAQlIQAISkIAEVpvAyZO941c7i+ZOAhKQgAQkIAEJSEACEhiagA8BQxMdX3q2gXHUmfU0jnpqc2l9jau+tiu3tpPtIj/ccY///4ZLy5QkIAEJSEACEpCABCQwHAEd1eFYmpIEJCABCUhAAhKQwIAEdFQHhGlSEpCABCQgAQlIQALDEdBRHY6lKUlAAhKQgAQkIAEJDEhAR3VAmCYlAQlIQAISkIAEJDAcAR3V4ViakgQkIAEJSEACEpDAgAR0VAeEaVISkIAEJCABCUhAAsMR0FEdjqUpSUACEpCABCQgAQkMSEBHdUCYJiUBCUhAAhKQgAQkMBwBHdXhWJqSBCQgAQlIQAISkMCABHRUB4RpUhKQgAQkIAEJSEACwxHQUR2OpSlJQAISkIAEJCABCQxIQEd1QJgmJQEJSEACEpCABCQwHAEd1eFYmpIEJCABCUhAAhKQwIAEdFQHhGlSEpCABCQgAQlIQALDEdBRHY6lKUlAAhKQgAQkIAEJDEhAR3VAmCYlAQlIQAISkIAEJDAcAR3V4ViakgQkIAEJSEACEpDAgAR0VAeEaVISkIAEJCABCUhAAsMR0FEdjqUpSUACEpCABCQgAQkMSEBHdUCYJiUBCUhAAhKQgAQkMBwBHdXhWJqSBCQgAQlIQAISkMCABHRUB4RpUhKQgAQkIAEJSEACwxHQUR2OpSlJQAISkIAEJCABCQxIQEd1QJgmJQEJSEACEpCABCQwHAEd1eFYmpIEJCABCUhAAhKQwIAEdFQHhGlSEpCABCQgAQlIQALDEdBRHY6lKUlAAhKQgAQkIAEJDEhAR3VAmCYlAQlIQAISkIAEJDAcAR3V4ViakgQkIAEJSEACEpDAgAR0VAeEaVISkIAEJCABCUhAAsMR0FEdjqUpSUACEpCABCQgAQkMSEBHdUCYJiUBCUhAAhKQgAQkMBwBHdXhWJqSBCQgAQlIQAISkMCABHRUB4RpUhKQgAQkIAEJSEACwxHQUR2OpSlJQAISkIAEJCABCQxIQEd1QJgmJQEJ7DgCt06JN6Ljo/vsuNJbYAmsD4FdKco7oi9EX41e2aNonv89IC0jyj5J9G+jw6PvREdHR0QHRmeMSjsoK8dEXKR/EJ222l6u3qaJ95P8J81zNGL5/5ptLNf6ecJuGo3R4DLL4FAzuFez05fz/0cR6dy7I6FHNPuynTQOrOKcLetPjDjxvhWR1qejp0dXreKyuk9k3XeAWSCoTxu4VNIv28BDphzv5NnG+djWOfWLHRq1bYVzcc8JwXvrvz1H/zfLHIf1b0SviK7VxCv/de3zvURAb40u17HPWRP2+OiLEcfg2vGh6K5R/UB8aMK68ron4W1eX5Pl2g5IAGn/Mvrv6F0RN4rfRccVgk1X2KkTPsn61NOkfTlv2L90VK+Tdcp4+Uk7Gb4QgT71RTttzyvazBU7jvjmhHG+/KqJe8P8v0qzzD6/aZZvUux74SaMe9OxEWlgXGfbdv22JmzSv+dkA2WgHR/aRLpZ/pNf2jLHbs+jn2b569G/ROU9tus8ZZ9WnK+fiFo7NAvleUc8zrcfR4dHf/H7mLMX5jnfZ+WTfPxs9iE3FaNPO2kTfk8W3tCsnDn/cVb7WNf532c/4/QjsLcOr1HEPU2W3xt9MrpyEX6RLPOk8ZVovyKcxfNHJITuX20rVz/VxOFkqw2HlxOzy16XwHV2VNsyT2KwOxFg+4to0k2vi13r/Lw0+52nOQgOw59GOBOkad03YJb4b54LJW2A+Nw8JjlVt2jiEK+Oc6dm29Wq8rTn6MOL8PNlGceSm+Kzqvisdu1z7oQfFnGDvnSxz0Wz/M0Ix5f9MBzqa0dc7HFuT3VC8O//TsrrrsRoryf3qvZpV9+ZhQOaFRzVl1fx/qcjDIei5lXuNk89VYfb+4DH/qWjirPDQ+HF6siuD0Jgnvra09QP96/Tdxyd8+XQjvBDEnZkR3gb9Kos1Pemtl2TvytM2JfziHOIODfqiPO1hNHGWztFFh4QEf/finAWu87TNsplslA6qoR3nXc4ZTjWx0XlPaFNp/6/mfN9Wj45f7bbUeV6xT0Wzq3hD/WxrvO/z37G6UfgeByXsreDk4Cn0BtEZQPnxLl59OvodRGVWhrbuSE9OKpvSMT78+i7J9qj/8ozEhUndyfbB5vCvzr/T9cDxL6J86aIHtm7RDg+GL1MpMXF9beRdX8Cl1X6+/ZkhhvZ3SZkil50HhoXNXo8HxnhDN4v4tydZfTQcHwu4G0P/ymzTI8S1wBugvSOYNxUPxDdMLpeRK9KX9tIRJyKZ0aXnbETIzR9ri1cn2j/W2Ufz4HowaMc2vYToPcdB+v5W5CVd+cYOH3/OOFYD0r4+yZs6wrmWs25wPlHr2tf+3YiTspDmQYPdk+KcIhvMSPxZZzvlI/71HYa90weZH9ZZALHVVsBAjgqDAVgF4p2Ry+JfnhC0In+4qTS80JPa/0USUP7l4inpq4Gx8nyhBOlNnuF4xwafTjqcyOaneJ4YzDUizNx8ei5PYpxx8Thovz0qKvngWFfHgCs+x4wtzjKK3O8o6KHRjypl8YDJI4gPeJD2YuT0OeiR0V9ehA2mgNzrmO0tUtEtKdJbe0N2fb30Tn27jHb/i9RbhORHg9n5XBnvTdOAaxm2dUTgWvYEPa3SWQjIp/0MDN6UVrrsJN/4i7buMnSLjgeN9oXNAfkQRWHiesn5d/JdlAKT48/7ZXpKMs0zl/O41tFXLNLY8gcZ/PgKrzPKvfrrnOsa9+3JpAHJc6PPoaTinEvn2ZDn+9PzcG4Nrx+2kGXvI3z9WvNMXig5lyi/ibZrPN/0n6Gb5IADb+96d0oy6zjGE6yjzQbbtwR4WUJ4wnuYVHb6InGXC0cX26G2uYJvCi7vjy6c6NpKVGX2OFTIj0k26z7KYC2aROOBb0b+0VcQEujB3TeB74qic5VenHPFPVxZi7SpMDNGGvn7s26buBMcS3oa1wv7htdMqqHO/umsYx4ONDPi/41Yg44Ts/jqgNxnrac+uSBoddZon4m2a+ygQcHHjra9kPcv4mYynXeaNq1gLg7we6VQjKUT3uiXS3TcHgYeWQEorT7Z4UHCeqsr/EA+aiIBz06hIY2RnDoTOI+zX1mmi3rfJ92zGVvK89X6otz6fYTDtrn/J+wq8GbJVAO/e5qEvn+lMS+12xr45ZRf5OVJ0cXjm5XbODm+vgy4oRlbmQ8LbZi6Ew7MQGe5L4U0at68SlwdmUb9dH2mE6JuncT8THrvgGxzf/25Pj0gj08as/R/bP884j540PbN5sEcY6nGec25zjD7Thq2K6ItvbjZr3r37TrRlf8NgzH66URziA9OatgByYTn4meFtF7+dXoOQtk7NTZF3az1DXKVR/2gQngnIfb6aNnR/esI+3gdXrAb92Un5562C/LuE4zkkC73dUc5Az5jwOEozrLrp0IGxHnJj+CpGOBTqBJUxdwjMv7J9Ptptkbs3EjYtj/mIgHQ5x3Rtum2a5sXOR8r/PJNIgx2YHJ7JDn/5jKvm15LR3VNhN9hhYmxTkoieDs8FTC0+RVm0T/q0cJecJkn1ZX6bHPTosyz4V2Uh1NY9Znn0lxrPtpZOfbxrnAkBgPI+2NlR6PPg988x3phNicc5OMm+NGxHDYO6KvRFeKvl7sMKlNFFH2LvaNV+73d1n5QsQNmuks22lnzMEZ5j+8ysQiDw9MR7hOD12vR8F5gKAX9YCIay7McHRKI5yh551qtCXmV1826voR4ZBcGP3YJ2qnpnBcHry4js+yDyTCrmi/6DQRjuf9ondG5YhlVvdae89t759vazdM+H/LhO+Kzhe9PuI8o2e1j/U9j7vi1fnkgW+VrTxf5jn/metbXydWuZwrnbfSUW0vaNMa67ma0hw1oVT0MDw9unR082iRmytPLX854Tg7OZjhei4ql49g3WXU5amis3Rt7Aiz7jugbHPQC3P8YyMu7DiGp40OW1KeuBlitVND2JOiXRHDYReL6CEqndQ+bW3WdYPjTDJ6kW8TcQN+dbTvpIhbEH6e5hh17zG9Ups1fuDFta6P+hzjXYlET94lokM6dvh/CftoR3gbdP0s/GyC6t8mTElmpTe9JLn794je5r+aklN6Dk85ZTvXWB40JtmnsoGHu7tGF4zuFm1mGgvzRjn3cXxvEE3LczbvtTtFH2lXpvzHaWaOKE7lY6fEazcNfb4/JglTF6tq5fkyz/mPk9qH56qWe6XyhaPazqXiAsdF8+pTcnjNZtu0p7XnJQ4Xcpyos0fvn5LetE3HZeOPpkXYwdtelrLTg4nDyoT92phziE2ryxtlu3Vfk1uddW4gz4yuEL024ia1LGPeGc5WnxtbnYc+bY3rBg+x8/zSuTzOl7Jyr4gfh9DTvF12THPgs1YZOPMCGRpy6J9scDPlgYIecKYA4OCXxrX7B1VYuUoboM11abPX8imH27ZN98mRGe5+UXShCbn474TDs+zQKaPy8EacacYoCHXMQwM9l5xnm7WvNTvSqz/LOM40J7rc//tZwXn/i4jpPdNs6PP9pzkYD6OrauX5Ms/5D9OW1aqWbTT54gTkqRDjJNgT7Y66euJ4srxvxIWM4YdJRsNjbhRPkEPcXOmV5QdE2okJUBefjXBYGV4q7RVZOTJiqKjLbphATiLrvovO6oTR+8L8NB7Y3r2kbN096TIMyg0VZ3Jea9vaP0zYkesAw4zPiBZ58OQ49DLjYFxlwrGWHczQ+hej+gEQB3qzNuTQP3l4fvTw6B7Rn0ZcJ1rjevzt6HFFWL2I08C9oEs8PK2L/SIFaXvquV91GcO+p4mu17ERJ5UHAh6iptmHs/EDESOVnAOL2AWanXGC+hijMPTq9rFnJRIPNZPuGW0aW3W+98nzsuPU50vf8/9yydh7Inqp63vzsvO8lunjqHLhbY2bwBERvasMLbe2KwtviE4RMWeua+7JH2Kf7GRPycrVomk9r2X8acv0XpxxWoQdug2nggstdUi9lMbN72YRT970GJyj2ciFiKdmLjb/FFn3DZgV/YeTetUIR29o48bJsNYLIm7Um+2pbNsaN+09Eem2Rk8qQ59cB2hvi9r9k8Cno7pHc9F059n/wETm2ohjzoMe0yYeOU8CVVxGsQ7tIZydWfbXicDDALy5UfIQ+8So7SXjob9POrOOsy7bv5KC/E3E2xu6jOvkd6ODo9tH1PX5ohtHb414KOA6PMvYl4erWb2v09LhWv6IiOlAr5kWsdjGvaF1bmft8uVEaKcpTLvfbuX5PivPy97edb4cmIPOOv/pqWe0U1siAZ4AmLPyseib0UaE8/rP0emj0h6fFZ7QfxNtRJzAXfawBJIWDi43341o3wgHimV6YdnGci3i40CP0WY59JSpiwEXT+wLERcmnuQ2ovaGs3djYzirk47DBfjJ0ZHRRiOGoHBiu8y676KyWNikuilTLdsANzMeFLuMc2Yj4pwgXc4pzi3svRH7En5MxLAv1p6jhDMlZyPinD0q4kZMr1ttXftcu45UrdPWnhTRw7QRfSs6LLpLxANSaZPySp4ZsuZmuBHd8cS77V3jHKD8B3RsY+RlI8L5Y54ly/t1xOsK6lNP7X73atLmGJ+MDojY/4fRmyPy3V7vCGPqxrIN1vQSUvfU1ZWb5bbeqVPs5dG0HtUm2sr/61NfjBRsRNQT0x0+PqFUz0n4oRO27Ur4noh2yX3u/yIelh4Q4QiW1rZr7mcb0Vmq7e3qG7NAryhl4D/rGJ0IGxHHoS5ZRrw1g/PppdFFota6ztONbGxFG+T+0Vp93tFmSrt+VsgTx2uvH1WU36/Oc7535ZOyboX1aSf1+bqRjNHRhnWdL7POf/ajnjj2Pick498FCPSpwwWSd1cB2wZsA+NoAzulnrpuvOOooRPncqfU1xjrZpXyvGg72ez5oqM6XCvY+wlVTQISkIAEJCABCUhAAitHQEd15arEDElAAhKQgAQkIAEJSGD5BBYddlh+Dj3CsgnYBpZNeJj0d0I9PTaomLfIPGJ+hzBm2wn1Neb6WZW8L9JONnu+MDeaH6Zx7NdH/AZB2zyBRepw80fdQXsKeAdV9oSi2gYmgFmxYOtpxSpkRnasrxmA3LyXgO1k/A3BOarjr0NLIAEJSEACEpCABNaTgHNU17NeLZUEJCABCUhAAhIYPQEd1dFXoQWQgAQkIIEOAswNPDri3acMAbNci3dUP7jaly/C/Tb6oyq8XeX91nxYgTTfNiFOG8w7WonHO44PbQKfmP/HNOG8E5iX7WO835r8HRfxIQGWL7d3y0ltnjTqMlO28p3ofH3r4dHnI+LynuXPRs+NrhtpEpDAGhNwfswaV27PotkGeoLa5mjW0zZXwJyHn6e++ELXpC9IPS7bSkeVr43xwnvSf+SUPN2piUO8K0yIx1fa+CQtcW5UxeETrITjINbG52vfWQd2rG82DT4CUDqqb8j6UdFlimP8cZa/3jMfHVlbmaB52snKZNqMnIiAc1RtEBKQgAQksGMJvDolf0tRer6YxJfE+LwqXzqbZu/ORno/+dRmlz0oge/r2rDNYXz5sHXc+cLULSJ6T+lRbe2TWZhUriKaixJYPgGH/pfP2CNIQAISeFUQ0LtT9lpJZfsI0KNIz+IRUTv0Tm7uEj0vemF0segaBE4weiFfGd0qungV56xZZyj/4An7bkcwPccHRnyyFQcb4/PG6JzNevnvTVnhc6GaBLaVgI7qtuL34BKQwMgItMOtOJ21zjyhLDg7t52wjWDmQr4iwvGhJ4/erJtPiV9uYli7zgfrz+y5v9H+QOBcWTxd9MVoT0Sv4+4/bO5cYq4ojt4jqq33z/oLol917rU6gTjrn4nuFz0qKh1W8s57dzUJbCuBfbb16B5cAhKQwPgIfC5ZfkpHtvnRTm04MU+P3hrdtN6YdXrePhLhnF4iwjm4ZcS8QZxV9ptlByYC8wlL46X+2h8I7JtFHPjSflit3zHrL27C2Pa66K8inLhJc1zhTF2x74HRRnSG6PbRFaPrRNtlN8yB6zI/piMzlPE/Il5wf2D00eg/o5dEP4g0CUhgjQnUF4k1LqpFm0DANjABzIoF960nelT7/NClLd4dssA8xXtEHKMe+ucHO4RftN2h+f/e/O/jbNKjerVq352w2re+YAGj2tFsh/5LVjDnx1StXTMLHAens7Y7JeD5TeCVmnjM88QeFtE7ifFwQhqr8GOqdui/ydpJ/lHeZ0XfaPL8i/yfNU/3JImsWMA87WTFsm52GgL+mMqmIAEJSGBJBE6ddB8f8aOaScavq+lF/WoVgV5beliZJ6kNT4De70sVyeJsXiVi6sVGI6Zj/CbaHU2zT2XjO6K7RheM7hbxiqtVMxzpp07J1IezjSkLF4p4LdV3I+bqnnvKPm6SwNIJOEd16Yg9gAQksGYEzpfy8COaj0dfjl4WlU5PW1wc1A9En24DOv7jMDE9AJX2u2YFZ3WW4Rh9KGJu5eERQ9Ve26dTo6etHNa+S9ZvHO2qxBSP60fU+TTjgYQHk0Mivu/+P9MiL7DtFAvs+/Ps+7OO/f+uI+z9CeNX/0yZuFzHdoMksGUEvJhtGWoPJAEJrAEBXpaO0TNFDxzC6flYdPm9W04weqHuG3Gzn2Y4sQw311MC2ndznnHaztn20+jYiPmIl46YSvDo6KUz9nPzHwicMovXi3Dya3tzArhP/nW9oVqnN5KHEur9GTPiLrKZDwQs+tsSylT21NPTep6OTLXHoX1pEtg2Ajqq24beA0tAAiMkcEzyfNmIHz9hP4n+NmL4/nFNGP/oYWMOI8On04w434yeHZ094prMvMA/aXZinuA0+4dsxBmmtwyHmfmw9ALeMWJagTabAPNI+QFR24td7sEDyPcielxnGXNZeXDhK1SrbOdN5sq5uOT14Ij5163xoMQDz0eiaSMCxS4uSkACYyTAjUPb2QRsA+Oo/0Xrid601kGhZ/Vb0WmLok/6MRVRLhDhKDBPlbmpOK+7I/LUOqxZ7G3Xafb9+957jC9in/o6R4q1EdHrTHyW+cFUaY/JCsP0P4raX/y32xlm34h4WGB/HiiuHJEGdU26G9FZoi57YwK/H7Ev/1nHeIj5dkT4j6MvnBB8sr/I/42IebEck+VaONP0dC6SBg9VZQ8+74GlB/7I6KiIKRG0RUYNzhSN2fq0kzGXbyfk3Tpcci0LeMmAR5C8bWAElZQs9q0nbtx1bxQlpCcTZwfj19Xc7DcKMXzKMb7ThN02/6cZ0wZwhJj3OMlwpM7asfFPE8axmKu6rta3vta1/JarHwHbST9OqxzLOlxy7Qh4yYBHkLxtYASVlCz2rac9iUvvaGn7ZgXHlB/STLJJPaqnyQ78WKe2dyfgeVUgTvI5i7BdWT663jHrTAegPPt3bFuXoL71tS7ltRybI2A72Ry3VdrLOlxybQh4yYBHkLxtYASVlCz2rac9icsrjPZrikWvJu+eZLiWnsxJNslRZV7gLyNeDo/x6396U78WMWe1NH7VT69tO6VgV5bJN+/tZD+M+bPHRO9q1tf1X9/6WtfyW65+BGwn/TitcizrcMm1I+AlAx5B8raBEVRSsti3nnAEeUfmERHzSZlriFM4qffymtm2EdVD/62zya/6Xxsx/5E0+Zwlc1TLntOs7jXe1UkcfqWOMQXhnhFzJpnnyBxD5hYyf5Ge2nW2vvW1zgws22wCtpPZjFY9hnW45BoS8JIBjyB528AIKilZtJ7GUU9tLq2vcdXXduXWdrJd5Ic7rl+mGo6lKUlAAhKQgAQkIAEJDEnA96gOSdO0JCABCUhAAhKQgAQGI6CjOhhKE5KABCQgAQlIQAISGJKAjuqQNE1LAhKQgAQkIAEJSGAwAjqqg6E0IQlIQAISkIAEJCCBIQnoqA5J07QkIAEJSEACEpCABAYjoKM6GEoTkoAEJCABCUhAAhIYkoCO6pA0TUsCEpCABCQgAQlIYDACOqqDoTQhCUhAAhKQgAQkIIEhCeioDknTtCQgAQlIQAISkIAEBiOgozoYShOSgAQkIAEJSEACEhiSgI7qkDRNSwISkIAEJCABCUhgMAI6qoOhNCEJSEACEpCABCQggSEJ6KgOSdO0JCABCUhAAhKQgAQGI6CjOhhKE5KABCQgAQlIQAISGJKAjuqQNE1LAhKQgAQkIAEJSGAwAjqqg6E0IQlIQAISkIAEJCCBIQnoqA5J07QkIAEJSEACEpCABAYjoKM6GEoTkoAEJCABCUhAAhIYkoCO6pA0TUsCEpCABCQgAQlIYDACOqqDoTQhCUhAAhKQgAQkIIEhCeioDknTtCQgAQlIQAISkIAEBiOgozoYShOSgAQkIAEJSEACEhiSgI7qkDRNSwISkIAEJCABCUhgMAI6qoOhNCEJSEACEpCABCQggSEJ6KgOSdO0JCABCUhAAhKQgAQGI6CjOhhKE5KABCQgAQlIQAISGJKAjuqQNE1LAhKQgAQkIAEJSGAwAjqqg6E0IQlIQAISkIAEJCCBIQnoqA5J07QkIAEJSEACEpCABAYjoKM6GEoTkoAEJCABCUhAAhIYkoCO6pA0TUsCEpCABCQgAQlIYDACOqqDoTQhCUhAAhKQgAQkIIEhCeioDklz8bSoj4dE51k8KVMYKYEh2sDdU/bLjLT8ZlsCEpCABCTwewLcFA+PvhUdG301ekl082ifJtbN8v/o6Ljol83y5Zpt5b9XZuUH0fHRD6NDqjjPyfr3ol9HpHdAsf1PsvymaCP6dnRU9I7owdGZI2xSPj6ebb+IOO53o1ueEP33f1n/TvTbiOPervlflofwUsQ9/e9T2JqFk+cwr4guHsHpHE2e/i//KVudR9Z/Ht20iAtb4n4/ekSE7R8Rl22EP+qE4N//vVSW9kTfiOD039EHokdGF4xaOzQLP4pIn3re8/stf1i4ShY5Fu3kN83yTYp4F27CyDft7c3FtvNn+XkRbZA28M3ow9HjI5i0dmgW6nzcPmGUjbz9LPrQ72P/YYGwn0Y/jg6MDo3KdGq+xHtqtJVWt4HNHvu/suNbIupek4AEJCABCYyawBWK3F80y/8ZccP/x6pUX8v6O2eUlBsj++IMdtklEviJasOVs44T9bho32bb6fIfB4W0rlbF78rHPzdxS6eo3O2GWaFcpXWl027HiRrCUSX/fe1+ifjl6BTVDgdlHcevy16XQBzV1h6YBY75tCryFbOO87JPFX6brOMIPyiCOXaq6K8jnDrqpbQ7ZaWrTqpoex9SjqwDi/VXZbnMN6x5WHpbdM4mHg9R5O9X0cObsPZfVz7IP3n+WBW3XOWhDBatdaXTbrtPFp5a7rzJ5SHawGYOfdvsdEx0xs3svAP3maeediCelSuy9bVyVbKSGbKdrGS1zJWpzjrEWfxS9KgqqWmOXRt1/yyQ6DyO6rMTHweD3qTayEcfR3VX4v0uek2dQLP+yvyve1qnlYe4tVM3IempwZ2AO/bAKaM3854d2w5K2CRH9ZrZdt5iH9L5aHRcRC81huP5ieiyzXr7j55UeqJx8rvszgkkndKmOXZlvEOyMo+j+peJDyt6ZGujl7WPo8p+B0ekQ9lqo1f2M1XgtPLw0FY+xNXp9V0fog30PVYZj7awEd1/MzvvwH361tMORLOSRba+VrJaVi5TtpOVq5K5M5VQK7gAACAASURBVHQ8N7Pa6MF6YsQQ7FYYecA5bof4y2PeICuf7ZGJjcRhuJrpAWep4p8p6zh0b+2RDlMNDozeGNVOWo/dNx2ldTjf1zMFeqEPjRgaZ7pDazjrzE9k6sKLI5xUHFGmVRzRRmr+4/zRe/uvVXi7itNf90JPiLpwcNsO297UMkGmIOCs97E9TaTdHZHvkjCmtfQxpg/Q/mvHts++m43T1QaYGsFDChfbzzUJ78l/esGZXkMP+iSjLbw/oldak4AEJCABCYySQJejSkFeGr16i0r0nhznlNHbo+tGZZ6Yq0ivXx/DCcHhvUMVmSFQHLXf9Elkm+JQbpzLbwxw/C8kDaZRXCaiHq8f/UtHujdKGL2ezMXsMhykW3VtWEIYDjfzVl8YMe3gNMUxmEd6bM9jfjDxjmrSKKdQ0KZuF72iZzrbEa2rDfDgdY8mM0yFwZim8bXoYtHTm7BJ/5hKco3o1JMiGC4BCUhAAhJYZQKlU7hd+aTXjvmwDLO+N6KH8OAIB6trOsCkfL4uG+hp2l1FYH3PhJ1umHB6q1o9ZUK8ZQfzK38cMnrBugwHvMwnPyCbZjim9MDhpD85qnuHT5uwc0T8aGsV7Jhk4tYR7RHnGseU3sTaaZ2VVxix/7kjHPHWaEufj35QhJWLh2el5NvO150QfSnBk9rAy3M0WPxbRJ09J3pMRI/qLOOHcZxD55oV0e0SkIAEJCCBVSSwCo4qXJhqwFzLe0efiugVpaeV4fyzRn2M4drXRwyLX7rZgV4nnA7S7LJ3JZAbeauHdEXagjCGvOnBnGRMxyjzeZVJEZtweo/pjaaXloeA+gda7e44Z6ti70hGLhDRi8vUi/0jnM6vRFeaI5PsQ7l2F/uwvGdKGlfPtpIvDzxbbdPawL2SGerw0IiyvaHK3C2yjrNdW9umdFRrMq5LQAISkMAoCAztqLbD6wzldxlzJn/dtSFhDEHzw5mbRDit/OL6WtGjJ8TvCn5JE7i7+X+X/G/DuuLXYc9NwBC/9K7TnbVOjyeOUl9j7uRfTolMuemhfVL0xxFzb0tjmJ1eS3oel2G0g0ltgONNagfshxPGj5zoYbx7dLboYHbqaUyfOCz6i4iHnDNGtKO39tyfaBeaI+5QUae1AXq+OQ/4kRgPcLXhpD62Dsx626ZWedpLR7YNkoAEJCABCZxAYJKjyi/GrzoHpLbHjqFG7PwT9iW8jdNGuVoWylcGEc6wJr2bzKGc1XvYpsP/90ffjHB0cIZuH80zLxEHjp7ZrTbeAcpwfF/DqcER7TKc/IdG/Nr7/0UwPDCid7m0t2flkhE/Nusyftx206j+cVpXXMJwitr2RB3jaE5qX3U7YB3HsjR6kf894kGDNxYw/aGv7Wni0zPfzlGe9IDUleakKQJdcYcKm9YG4MjUiI9FT47qHlL2pT5ra9sU2zUJSEACEpDA6Ah0ORJnTykOieYZbv3fxN8nOiriJo+D02U3SyA329KYS/i3XZETRpp9f0hDEgyLviyip/Ap0ReizdykmRNYO3akvyxjmB6HEOd6HmNY/87VDi/K+sMjeqhx9uiVJN2DorLX9glZx+G9d9RlD0sgPcx9h8H5kQ+OMfZf0Wmi6zXr5T+cUth+qQi8SJapry6jDfw0msfRfG3i89Cxu9GeroRnhF032yn/Vtm0NvCAZAKmnD/UISMPrV0uC/Sy0vZhVRrnAdzqh8MqmqsSkIAEJCCB1SVw6SJr3PQ+Hr0tqp2mryXsnROKQS9ke5OkN4+bJr1hOLv0/lwqekzU9rRl8fd2YJa4md4uah1nnBzC+XHRjaPSpuWDeDg9HB9N+9X6tHQ+kX0vc6Kjbm6FPPQxegyJy//acDB/WQc260xTuE+x7a5ZfmlH3GcmjPT/vtrG3MafRPeN2l+G8x+nkzq9fhX/TlknnatV4awyveBxTTi9sd+Jjo7o1d4vOl9EXTJtgR97lXZAVkj3SdHpmg04ZExv+EXEHObSpuWjjccDC2l+rtq3bzo8bL1uyr59Ny3aBnDqPxm19XPHLJMmXFtr23ztqL4qEeaZ8lAkueMW+9bTjgOzogW2vla0YlYsW7aTFauQTWRnbx3imDJcjrgh3i8qnVSGZDci5rnhNLBcC4eyvEneI+v0ANETxn7HRK+OcFhr25WAR0aHRRsRPUs4tPQS3TBqrSsfXY4d8Unrh1HtbLOtK52NhJeiJ3IrHVXy9cWIntDWzpGFjQiGVBTLtejJxlHdr9mGQ8t8RobLW6PX9bsRaVCujagczqdOXh4d1Wz7ev7/R3T5qDTeyEC9kA71uVGJqQiPK3bYleU90dERbYCe2U9H9A7WPflnSNi9IpwqHiA2omOjT0SUr4xf5+PF2d5l108gecXp7rI6nY1EKvX9rG+lo0oe6zbw1ITRM47o4cbgQ7k4FykDdpEmbJ9mnX84ttRX3eNeRHGxILD3YqiNhoD1NZqq2taM2k62Ff8gB7cOB8E4OZF5AN88yeBk4rRp60NgK9pAl6PKAwG9yaXzuj5Uhy/JPPU0/NFNcV4C1te8xHZmfNvJ+OvdOlxyHc4L+BHJz6HRvkvOl8lvHYGtaAO1o3rDFI85wBfcumKO/kjz1tPoCzzyAlhfI6/ALcq+7WSLQC/xMNbhEuGS9GYA8wMkXqukrQeBrWgDtaP6Z0HX920N60F58VJspp4WP6opbJaA9bVZcjtrP9vJ+OvbOlxyHQp4yYBHkPyy2wDztN8RcZzXR8xt1uYnsOx6mj9H7jGNgPU1jY7bWgK2k/G3BetwyXUo4CUDHkHytoERVFKyaD2No550QMZVT9udW8/r7a6BxY9/fP3r68WTNAUJSEACEpCABCQgAQkMQEBHdQCIJiEBCUhAAitNgHsdXzvki3naeAn8U7LubzjGW3+byvkkR/X8SY2v33w14r2mvGP1w9Hjo4tXR/qTrL8p2oiIe1TEnDleAM+L37X+BHin6Z6I79Xzwnzeg/mBiPfMtr/gZg4i7yblvaQMa7DMO0j7GJ/hZB9eGj/JrPtJZAyXgATGSICPh/Apbe5dvAKw6xrKdbQUH0LhHoYdGvGeaK6dfHmReMdEvN/48Ih3c5d2aFbq+GXa7Mc7kmu7RAIOjriHEp/7KffWa1cRr9Js573ZvKOauDcp4ly4CePrfLyP+s3NtifmP/mmHLyDuy4zbHh3dWtfzkJbjq4vGPKWGtJo70MHFvuyeLaIY34h+lZEWrxL++nRVSPsBRGsSYN3n7PeGvVF+sdFvAucT63znm98kXO2kfy/MwmcPsWmUb2taAw4tLeJeGF8+VL6K2edr0o9Lto3wviyEA4tDa/rC0ZNtB3xDwZ9Db44n7ygvv06Ex8s+Ouo6xOi075YNemYvFCfCxsfU+gy676LymJh87SBxY7k3osQsJ4Wobf1+85TX3zEBqfrFFU2p11Duae1jiq7dX0Nj44Y7pM4Uteo0u6K30bhIya1o8p7tH8W8WGP9l3a3FPv0oTTWVHbIQk4sg4s1vky3U2r7XREwK68j7dRLpOF0lElfHcTnw+MXL6NWP3HYa6NTheczJdGbS82fsSfRnzYhDy0zHC8fxvxY9DarpmA91WBdKK9vY44YX2edjIhCYO3mUBnHfLZSjbQeGqjgZQN/NlZx4niibW2LyVAR7Wm0r3OSc2F4J+7N+/9uhAXw9KmXWS7kjlXAj8ZvSjiosAFqzbrviay+HrnSbZ4sqYwMAHraWCgS06ub33hHDE6dc+O/Ey7hvI2DXr0WpvkeOJ4kZcnV+lPik+0i0ZXKOJfLMv0fk66/t8h2zjGzYp9WBzaUT1T0rxBdYzdWWdUj/sTTnHbiVJGqx1VHOyvRHw5r8s3uFDCuZ/tXySCb0EZb1SE8WDBlzO5P5ZGjzFxJznOZdy+7aQ6hKsrRKDzx1TtdICurnWe6ji5WyMujbJriJ8G/9kirouTCeD8c1L+64Qor0n4f07Y1jeYC+eLo+dH1FvXpzWt+740jScBCYyBAD1y543qXrlJeWdU6djoiIhe2FnW9tLy8N/H6DX9avSZIjKfud4nmnT9f2W20Tt5YLHP0IuMtjG0/u6OhGFBrzSO+3M7ttdBd0wAzjhD/F2O4jcS/oyIqQCtwYCpbjBoR2fpeabe6IEtjeH/jYhRSG2HEqCbniFonkIZdj7NFA4MV9AQD4+uG7WOzpRddtSmrpO0CwDznj7XtWFK2LTegK7dPpLAMzYbeErtughb913kFgvr2wYWO4p7L0rAelqU4Nbu37e+Hp1s0XvXdW/quoa2jmpdGh70OWY5SnjurDONCseWXsLSuuKzHUe1Nq7/szp1Xps4HJ+RsdYOyQK9nJNsnqF/HNUDOhLanbB/a8Jflv/koe7kqHtU6Vgh3rw/erprsx89y5QTB7mrBzfBJ3tnxD1tlvVtJ7PScfv2Edhbh1fvOP6NE3ZMRAScViZjT3JaH5FtDAsQl8nYB0fXj7q6/BO8o6zPSXLaECFe15PsNFhdF9lJ8a+UDS8sNt69OaZ1P4nYcOF92sBwRzOlzRKwnjZLbnv261tfjCDhCHYZ11DSqYXjWVvreHJf3Ij+p9nvafl/jjpy1tv4ddp1vvte/+lpZN8/KY61iKPala8DOsqxO2Gto4rTSO8mzja9q63VjurHsuHXxfa+i/gM/FAKfwJHlKlokwyn+ahJG4vwmnePXYyyYgT2Dv3v7sjUOxJ2gehW0Ruj/aOXRsw7wekp7YlZYWjl3tGnojtEPGUyr2XeJ6oy3Z22vMwT6i6ByQW7tVdmgV997i7C2kXrvgOKQRKQwCgJMIWtdqTKgvwqKzhIrdofMk0q7C2zYVd0vogf//xddO5JkRNOZ0CZPh0/Xdb3+j9UBxAdTGW++FHYLCPvt24ivTr/Tz1lh77lKZNgH/yIfSN+SPyGKelTp2Xv8pSobloHAjwZTmtwlJGGc7eICd+zhijOljhPiWh0z2LnHWx9T1bm5sziWmPs26N6yuzINI6NSj/NunVfUx1+vW8bGP7IpjgPAetpHlrbH7dvfTEM/e0J2e26huK8df0+o+0hvVqRFo4SzhuvkKqtKz5xutKmB3fW9b8dTi/3p1OB+ZqTDEev/nHU+RMGu4dXO/E7E5zD2nYnoO1Rbbcxukoaz20C6geBdprCWerEeq6THnUzzdhOZ8ss69tOZqXj9u0jsLdHlV/63aLIAw35L6o88dT579FLIn4NieOKcdJesVlu//0wCw+JjoyuUm1ztZvA2xN8yYi66DIuIjeN+p741Gv75M1+XFB2VWJYxboPBE0CElhbAt9PyRhe72s4NpOmCtRpkDb3RO6XF643TljvSvudicv1n+t8l3Etp2f2k1G5Px0c54m65t+SDvdy4vQxOi36Dtcz7I6jSG8yo661cT/DuqaWtXH5df9F6h3nWKdO4a/tAAI08J9Eu4uy0njoEe0yfplIT1zboGlsf9sVMWHE7ZrrMyH6jg5+Qkp/XMSwR5c9LIE4m5OGjep9mFN8vSZwd/7/Zx0h64dG1n0HGIMkIIG1IUBvKg/4Xb2FQxTyWUkER5Jfxfe16yZi2xvJPv8S/S7iV+5d9lcJxOk8sNr4X1k/TdRe68vNxL9Y9KVqn2mrOH9M3+tj900keoFxWLnXl/aKrNBRNYnJDbMNZ3aROjl39j/6xId1bZ0JvDqF49UazLnBDoh4qnxS1P7ijhORHjgmOTMntbUDs4DTeruofarjxCGcE+/G0U62eYYd6NXGceQC0E7F4P+DIiavX78CyQWiHnJpo/ALTuIzyX/ahcq6r6AuYXWeNrCEw5tkTwLWU09QKxKtb30xAkhc/tc27Rpax71Tkw6jiLUxv5Nrd/tWFbZPi88o1+uqRLiH0hHxwKjtAWbaFq96Im06K2qjB5ZpXThst4/2i7iPc9/9TIQDXBsOLDweXm/I+umjunNpd8Lqof92V15BxfB7V12w7VvRiyLuQxh+BL3PHOORTVjXP+5r1M00+142PnhahGZbV9567GaUFSKwtw5/HLHw/YgnujNE94pwdr4WbUQ0rE9EbC+HGXZlnQZ3WLQR8fTKUAM/puKpaafbvCfJpQLs5dFR0UbE/KP/iMoXG3PSs42ebdJnudbPE/aPESczy1+IamMekXVfUxl+fd42MHwOTLEPAeupD6XViTNPfX0x2S4ds65r6HunFI1t3Nc45jER97vS6BRgG9fbF0d1/I2EleJeWzuqCdo7/M/+/GiZewAOKp0J04bQd2X7nghn9TcRzu6nowdE9ZSAxyeMezR55dq/UembWS8dVe4brJMP4nZNb7hNwifVBb9XeXJ0ZLM/aRwS3Szqsr9p4pEe97eN6NwdEa+cMDrXdnVsq4Mm5a2O5/rqErAOl1w3Al4y4BEkbxsYQSUli9bTOOqpzeU89XXz7IQTSSfMWIzRzI2IaWHMQ6U3UjuBwJvyr5w6MY3LPO1kWjpu2z4C1uGS2Qt4yYBHkLxtYASVlCxaT+OopzaX89YXr2M6NNp3RMVkJI2hfcr6zBHle5lZfUwSf+cc9ThvO1lm3k17cwSsw81x672XgHujWtuItoFxVK31NI56anO5mfriR0dnHVcx9/5Y6rYRP8DSTnjLwCnmALGZdjJH8kbdAgLW4ZIhC3jJgEeQvG1gBJWULFpP46inNpfW17jqa7tyazvZLvLDHXfve1Q1CUhAAhKQgAQkIAEJrBwBHdWVqxIzJAEJSEACEpCABCQAAR3VE7eDa2eV95lqO4+Adb/z6twSS0ACEpDACAjwTjPewXZcxIt2Wa7FO8tO35TlifnPu+SY+8HLftu4LPNyeV7CiwO8q9nGi/95vxvx6nei8Y413tPGuz7fFZXGS4Y57h9V4azyHjzS451x5IPle3XEK4Nul5UPR7xHDvGuuldGdy0i8cLmj0b/UIQtsthnfsy0snw5B/9RRDpdX63il6yUvWVwYJZbbtRnK7bDsgyjnNZ9IDQ2dN236fZpA3/IhUvbRcB62i7ymzuu9bU5bjttL9vJ+Gv8RHXIy/157UOX4Uy2jirbzx+xc/kS5X2yzqsjCC+/ovG+rOMA8xm7LsPxrR1DPq3Ge+9Ia9oXLA7KdtKeZXzK7VfRLYuIfMHjbVG9P44xX+C62qxEe2yf5ySZVJbdOQ7pkKfyxf/l4csy4Kjeo9h4hWb/MuwyCcNRbc26P4HEkHXfsp2nDRRV4uIWE7Cethj4goezvhYEuEN2t52Mv6J7/5iKL0bUDl1dfHrrHhvRe3qrYuNLssy76/jEW230vN4uekW1gc+s8eUkej3vXO+0iXWctEOiNxb78n66u0f0+JZGbyvH7vpkXRV1y1Y/2ByJr5S0n7WddHAc/P+ZtLEJx2nfmBGn3Wzd9wRlNAlIQAISkIAEhiUwa44qw/gHRjh4OKKzjK9nIIaZW+NTcT+Ldhdh7eL1s/C56AfVtrtk/XnRC6OLRdeots+7SjnP2bETTt0VO8Lfm7AbRWUvcke0LQs6IkeiV/ji0awvcjwucWA+zb6ajTwgTDPrfhodt0lAAhKQgAQksHQCsxzVeTLAi4lxkrCnFTsyj/T10VWiSxfhLO6O6HEt7VxZodeQ7zPviejJ3V1G2MTye7IP3wd+aXSpan/mgdZG2KmjRR3kOt1F1l+UnV8e0cM8RC/zInmp97XuayKuS0ACEpCABCQwKAHmKTKfo9aBHUdp56j+ONs2ou9HDKG/M7pkR/wDEka6Tym2nSnL34qYj1raA7NyhyLgZVlmKBvHsbZJ8zrrePSMMr2APJIPfvRFXmrHud3vwk08enYXsXnmx0wqy+5kgHmnWOvA00NN72pr06ZldM1RLXbdu2jd/4HIUHXfpjhPG6jrxfWtI2A9bR3rIY5kfQ1Bcf3TsJ2Mv45PMkeVX963w/f8f8iMMj4p23dF54mY03nD6Jod+3wgYd+M7hSdotl+2/x/U/TrKv6fZ70cun5+1nFqyx9CVbvMXMWxu2N00eifo59GDG1/PnpOx96t40fv7ioZvdO3bjLEfNUu532z+bXuTyC3qnW/2Xp1PwlIQAISkMBaEKBXjR7R0k6bla55mm2P6sOr+J/IOr2r/Hiqtv+XAJ5ucEQxXhV1pWa5/cf6T6KNSjizOFK1TeqFrON1reO0kiZ5qp3gtnz12wi60pkWNs/T3KSy7M4B2h7V9lh/3eS7na86RI+qdX8C3aHqvq2redrAtLbktuUSsJ6Wy3fo1K2voYmuZ3q2k/HX60l6VOsi8X5TeiP7Gu9F5UdL5dB9u287F/WuCcBJPEP0qSrhu2T9xtGuSgzT88MrXinV15h/S68wRi8k7ystjR8UtXM9mT9bGg46htO9isZ0CBzbv4vKNywMmVfrfkiapiUBCUhAAhKQwNwE+v6Y6s1JmV/fz7I3JMK3o/t3RPx6wg6LePUU81Bbx7WNesosXC86vGNfjk9e6Unsa+xDeth9Ihzd2vZpAo6tNpy7WT+63mGF1u+bvHw2wmFty7GM7Fn3y6BqmhKQgAQkIAEJzCTQ11E9b1Kqf/TUlfhxCfzXiBfTX6cjwp4mnXvkP79gL+2mWeEl9PV7TYnzsYhXSdHjull7QnYse06ZV8vQOV9+emWVKG8G4IdiXU7zZo8/9H4M998mog7beb9DH4P0rPtlUDVNCUhAAhKQgAR6EaCHcyPiRf18/YjlWr9K2GUi7PERvabM/Wh/9c+8vtbOnAWmC/BL/S8U4SzymUp+EPSWKvwxTXycxhdX23DCNiLyxjH5UdafNWH8KIowttdi6LrtRb1qlp8RfaaJ9938/070H9HFo9remoB/rwM3sd5nfgxTEjaisix/0xwLfvT2tvN2L9yRB5zVScfBEaesbCedw6v9rfuTAh2q7tuUJ9XNSY9syHYSsJ62k/78x7a+5me2E/ewnYy/1q3DjjrkAwA4jRfq2DZvkIDnJba98Yes+7YktoHtrdO+R7ee+pJajXjW12rUw6rnwnay6jU0O3/WYcXoAlk/MrrJbHa9Ygi4F6aViDR03beFsg2sRPXOzIT1NBPRSkWwvlaqOlY2M7aTla2a3hmzDitUl8v6JXrjmx1RwLMZrUqMoeu+LZdtYFVqeHo+rKfpfFZtq/W1ajWymvmxnaxmvcyTK+twHlqbiCvgTUBbs11sA+OoUOtpHPXU5tL6Gld9bVdubSfbRX644858j+pwhzIlCUhAAhKQgAQkIAEJzEGg7+up5kjSqBKQgAQkIAEJSEACElicgI7q4gxNQQISkIAEJCABCUhgCQR0VJcA1SQlIAEJSEACEpCABBYnoKO6OENTkIAEJCABCUhAAhJYAgEd1SVANUkJSEACEpCABCQggcUJ6KguztAUJCABCUhAAhKQgASWQEBHdQlQTVICEpCABCQgAQlIYHECOqqLMzQFCUhAAhKQgAQkIIElENBRXQJUk5SABCQgAQlIQAISWJyAjuriDE1BAhKQgAQkIAEJSGAJBHRUlwDVJCUgAQlIQAISkIAEFiego7o4Q1OQgAQkIAEJSEACElgCAR3VJUA1SQlIQAISkIAEJCCBxQnoqC7O0BQkIAEJSEACEpCABJZAQEd1CVBNUgISkIAEJCABCUhgcQI6qoszNAUJSEACEpCABCQggSUQ0FFdAlSTlIAEJCABCUhAAhJYnICO6uIMTUECEpCABCQgAQlIYAkEdFSXANUkJSABCUhAAhKQgAQWJ6CjujhDU5CABCQgAQlIQAISWAIBHdUlQDVJCUhAAhKQgAQkIIHFCeioLs7QFCQgAQlIQAISkIAElkBAR3UJUE1SAhKQgAQkIAEJSGBxAjqqizM0BQlIQAISkIAEJCCBJRDQUV0CVJOUgAQkIAEJSEACElicgI7q4gxNQQISkIAEJCABCUhgCQR0VJcA1SQlIAEJSEACEpCABBYnoKO6OENTkIAEJCABCUhAAhJYAgEd1SVANUkJSEACEpCABCQggcUJ6KguztAUJCABCUhAAhKQgASWQEBHdQlQTVICEpCABCQgAQlIYHECOqqLMzQFCUhAAhKQgAQkIIElENBRXQJUk5SABCQgAQlIQAISWJyAjuriDE1BAhKQgARWmwD3uodE5ymyuSvL74i+EH01emWxrV28exYu0xFukAQkIIG1IHD8WpTCQixCwDawCL2t29d62jrWQxxpnvo6eQ6IE3pQxHJr78nCG5qVM+c/zmptOKlHRfvXG1wfBYF52skoCrQDM2kdLrnSBbxkwCNI3jYwgkpKFq2ncdRTm8t56ut+2enL0SmKIuKw/iJ6QBF2mgkIbpvwY6IzTthu8OoSmKedrG4pdnbOrMMl17+Alwx4BMnbBkZQScmi9TSOempz2be+GPL/TnTPqninbur8b3sUmzQ2ovv3iGuU1SLQt52sVq7NTUnAOlxyexDwkgGPIHnbwAgqKVm0nsZRT20u+9bXtZq6vUhRvDtl+egm/MfNctf81JLIwVk5rAxweRQE+raTURRmh2bSOlxyxQt4yYBHkLxtYASVlCxaT+OopzaXfevr0dnhuKj+4fA8Paoc8+HR7yL208ZDoG87GU+Jdl5Oj69P3p2HwBJLQAISkMC6EuBX/j+KcDIXsf/OzsxrPdciibivBCQwPwEd1fmZuYcEJCABCYyDwDmTzV/OkdWnJe5TOuK3aeiodsAxSALLJLDPMhM3bQlIQAISkMA2EmDYv3wl1aysvDwRuoaL2zR+MysBt0tAAsMS0FEdlqepSUACEpDA6hD4frJy2jmy8+kJcds0SE+TgAS2kIBD/1sI20NJQAISkMCWEvh2jnaW6FQ9jnqHxMFR7fp1/7kT/uuIuaqaBCSwhQR0VLcQtoeSgAQkIIEtJcAnUhm2v3iPo/5H4jxnQrxLJZwvWTn0PwGQwRJYFgEd1WWRNV0JSEACEthuAkckA1+K/rzIyB2zzJeqsMdHG9HVmvWuf7yS6nrRa7o2GiYBgWkEJwAAIABJREFUCUhgzAS6JuWPuTzmfX4CtoH5mW3HHtbTdlDf/DHnqa+b5zDfi87Q43D3SJx66J/PrH4u8jcdPQCuWJR52smKZd3sNASswyU3BQEvGfAIkrcNjKCSkkXraRz11OZy3vp6RHY8NNp3RjFrR/WGiU+P7AVn7Ofm1SQwbztZzVLs7Fwd7xPizm4All4CEpDATiDwxBTyY9Hpol/NUWA+FHCNiE+tahKQgATWjoBPc2tXpXMXyDYwN7Jt2cF62hbsmz7oMurrdsnNJ6Jjo+duOmfuuEoEltFOVql8OyEv1uGSa1nASwY8guRtAyOopGTRehpHPbW5tL7GVV/blVvbyXaRH+64x/ur/+FgmpIEJCABCUhAAhKQwIAEdFQHhGlSEpCABCQgAQlIQALDEdBRHY6lKUlAAhKQgAQkIAEJDEhAR3VAmCYlAQlIQAISkIAEJDAcAR3V4ViakgQkIAEJSEACEpDAgAR0VAeEaVISkIAEJCABCUhAAsMR0FEdjqUpSUACEpCABCQgAQkMSEBHdUCYJiUBCUhAAhKQgAQkMBwBHdXhWJqSBCQgAQlIQAISkMCABHRUB4RpUhKQgAQkIAEJSEACwxHQUR2OpSlJQAISkIAEJCABCQxIQEd1QJgmJQEJSEACEpCABCQwHAEd1eFYmpIEJCABCUhAAhKQwIAEdFQHhGlSEpCABCQgAQlIQALDEdBRHY6lKUlAAhKQgAQkIAEJDEhAR3VAmCYlAQlIQAISkIAEJDAcAR3V4ViakgQkIAEJSEACEpDAgAR0VAeEaVISkIAEJCABCUhAAsMR0FEdjqUpSUACEpCABCQgAQkMSEBHdUCYJiUBCUhAAhKQgAQkMBwBHdXhWJqSBCQgAQlIQAISkMCABHRUB4RpUhKQgAQkIAEJSEACwxHQUR2OpSlJQAISkIAEJCABCQxIQEd1QJgmJQEJSEACEpCABCQwHAEd1eFYmpIEJCABCUhAAhKQwIAEdFQHhGlSEpCABCQgAQlIQALDEdBRHY6lKUlAAhKQgAQkIAEJDEhAR3VAmCYlAQlIQAISkIAEJDAcAR3V4ViakgQkIAEJSEACEpDAgAR0VAeEaVISkIAEJCABCUhAAsMR0FEdjqUpSUACEpCABCQgAQkMSEBHdUCYJiUBCUhAAhKQgAQkMBwBHdXhWJqSBCQgAQlIQAISkMCABHRUB4RpUhKQgAQkIAEJSEACwxHQUR2OpSlJQAISkIAEJCABCQxIQEd1QJgmJQEJSEACEpCABCQwHAEd1eFYmpIEJCABCUhAAhKQwIAEdFQHhGlSEpCABCQgAQlIQALDETh5kjp+uORMSQISkIAEJCABCUhAAhIYAwEfAsZQS8vNo21guXyHSt16Gork1qRjfW0N57EfxXYy9hpMZ6pD/+OvREsgAQlIQAISkIAE1pKAjupaVquFkoAEJCABCUhAAuMnoKM6/jq0BBKQgAQkIAEJSGAtCeiormW1WigJSEACEpCABCQwfgI6quOvQ0sgAQlIQAISkIAE1pKAjupaVquFkoAEJCABCUhAAuMnoKM6/jq0BBKQgAQkIAEJSGAtCeiormW1WigJSEACEpCABCQwfgI6quOvQ0sgAQlIQAISkIAE1pKAjupaVquFkoAEJCABCUhAAuMnoKM6/jq0BBKQgAQkIAEJSGAtCeiormW1WigJSEACEpCABCQwfgI6quOvQ0sgAQlIQAISkIAE1pKAjupaVquFkoAEJCABCUhAAuMnoKM6/jq0BBKQgAQkIAEJSGAtCeiormW1WigJSEACEpCABCQwfgI6quOvQ0sgAQlIQAISkIAE1pKAjupaVquFkoAEJCABCUhAAuMnoKM6/jq0BBKQgAQkIAEJSGAtCeiormW1WigJSEACEpCABCQwfgI6quOvQ0sgAQlIQAISkIAE1pKAjupaVquFkoAEJCABCUhAAuMnoKM6/jq0BBKQgAQkIAEJSGAtCeiormW1WigJSEACEpCABCQwfgI6quOvQ0sgAQlIQAISkIAE1pKAjupaVquFkoAEJCABCUhAAuMnoKM6/jq0BBKQgAQkIAEJSGAtCeiormW1WigJSEACEpCABCQwfgI6quOvQ0sgAQlIQAISkIAE1pKAjupaVquFkoAEJCABCUhAAuMnoKM6/jq0BBKQgAQkIAEJSGAtCeiormW1WigJSEACEpCABCQwfgI6quOvQ0sgAQlIQAISkIAE1pKAjupaVquFkoAEJCABCUhAAuMnoKM6/jq0BBKQgAQkIAEJSGAtCeiormW1WigJSEACEpCABCQwfgI6qqtVh/slOx+Kjl6tbJmbFSbwquTt+OgyK5xHs3ayk1lPtgIJSEAC20zg1Dn+3SIcrS9FX4g+Et1qQr6I+9noyOib0Qujs3TE3T9h742+Hm1E74gu1RFvFYNwIPra7RJxI6Kc0xzVvjz+KOm8Ijoq+kr0yejmUR87KJHIe61n9tl5E3FumH3eGH05OiL6XPTQaN+OtMZW/r5tAEfzeRHnDgy+GD03OncHgzboGllo66jLUR1TG5hSzC3ZZD1tCebBDtK3vi6cIz4t+lQjroXvi64zWE5MaJUJ9G0nXWU4fQIfER0Wcf/Ep/lMdK+uyAm7WROP+xfX7wdGJ++Ie8mEvauJQ3vkOn+GjnjLCpq3XMvKR990F6nDkxzjFgn5TXSjYsvds8xB/r6KjRPyq+haTTiVhIN7eHSKIu41s/zr6GFNGJX+jOjYiJvwqltfwDhkh0YXiF4XTXJU+/I4a9L4dvSmqHX2bpnl30Y3jWYZjuqjoztV+uNZO25i+5mzD5weE7U9/FfM8k+i11bpjbH8fdsAF8C3R2dsynyO/OfieFTEhaU2zoWPRm+JOEbtqI6pDdRl245162k7qG/+mH3r6z45xHejizSH4v7CPeSX0WU3f3j3HAmBvu2kqzhcU4+L/qLYSMcbad6z2uEGWcdXaR+AdmX5+9Ejq3jnyfoPon9qwk+T/4dG767iLXN1nnItMx99016kDk9yDBxVHKPa6B36ahGI4/TTiN6+0nBayRA9i629JwvfisopCqfLOk7M84t4q7rYFzBOR1vGaY5qXx6cHBz7ohWY92adHrtZhqN6tVmRBtqOo/qjqJ6G8q8JowznL44zxvL3bQM4qleomLYXxTt2sL5DwugZukfDqXZUx9QGOoq35UHW05YjX+iAfeuLB/S/q47ENYX96TDR1ptA33bSReGCCXxBx4avJYxOhdIYHebeXRq9sT+P6DRo7VlZ+F60TxF29SyTzxsXYZMWd2fDi6OunlrS4R552kk7N+HzlGtGUluy+fjaOVjkqG/OzrfuSICn2XJI/+JZp4cIB7Y0ussxus9bowePLvTfFWH/l+WvR2W8YvMoF2mkZRknFaIvD+LRY10+IJAmjC8RXWzSAbYh/H9yTIa36/LTbjAc2dbWsfxt2f4kCzirpbUM6ikxTLN5fPSgKn65OqY2MKUYK7fJelq5KpmaIaYUMaWmtHbU4tipe7pxpxM4KgDqYX4cREaAy7ZDb/3lIjoOSmOdHtObFIF0Pnwwoqe2tf/KAn4N22bZNxLh9tEzq4iMQuI801vLaME061uuaWls6bYhHVUcjRJ+WxB69Q4tSkWFYOUQP+uto4Ij1Rpx63htXLrQ2wtOsctaL/blQTxOqPqpq4vxJGB3ywamY/CgwJSM+0VDtpfyuAyZ1IYzzZPnl4sN61p+ijiJAds+UMHBQSXs01V4uTq2NjClKCu1yXpaqeqYOzP0Jj07wlmoR/XmTswddhSBM6W0zHfmGvDYouQ4qRgOYGnterudntXzdcTjvvytqI1XJXOiVdotDi2jBHRWYO2cV+4Jd4nqTp8m2sR/k8o1aQc6GulAmqUu321Smtsa/mc5Ot59OSxJ5n8cvb7KWTv0T7d6a/TSHhOdsghrh/7phSyHhYsoK7NIHue1aUP/fXk8MAfl2PUcLIb+Cb/TjEwxh+sJEUMIOLvXjX4YvXzGfkNtPnsS+t+IYe3Sxlj+zbQBygx3JvHXzOl9xoE/bwNm0tD/2NtAWe9bsWw9bQXl4Y4xb33RYXJ0xH5viM41XFZMaYUJzNtOJhXl49nAbzwY4r9yFemeWec416zCGfkinKF6jM4X1pmWVRu/N2CkuK/dJhHJz1Oi70QM+be/R+mbBvGmlWtSOuSVcszS/pMSmDN8qDrsPOzZEgr42tkgMj+uovcV2NyQufnSa/ez6IioNebs8fTy1OhUERXP3NSfRmSeY6yybQbwNEe1Lw8czI3o/RFOHz2hd45abn2GGGquD08A5fnjesPA6+SV4bqXdaQ7xvJvpg1Q9H+IPh/xtFsaF70Di4BJjuqY20BV5C1ZtZ62BPNgB9lsfdGrxVQAhkhrh2OwzJnQyhDo0072SW7L3kE6w7oM/+Nvol9Edy8ibIejyuEfHFG+I6NJeS6yOXFxUrkm7XClbDigh+p716T0ZoVPrEPmVuA01vrIrBSb7XQN43j+45T4d23iAJkh5r+M8O7rScp45YQx35JfQTNBmR4/8rasoegkPYhNBDwl9WmOKrv15XGBxD04gtvnIhz83RF5Yp7dvHadZl8eMibZY7KhbjPtet9G+69J461R2YteHm+Vy9/FZTNt4K+SEPVWjxhcPmEMEZWT5Sc5quRlO9pAF4MxhO20ehriXN3Oet1MfbX5ZVTva1Hf+9l2ltNjL0agTzu5UQ5BvFbvnHFI7qs/j3BuMXwX9iWd0s7ZhD+5CeQhiXj/UsVjlSl2H+sInxR09mz4QvTNiJ7VO06KOEd4Xa5Ju2710P/EOuQGeZEO/dGknBfhFALH81E94tZRju25H9MGDql3XsH1iYCn5HWWo9q1a18e983O9KryBDXJuIhzQtX2pwmgPMxVnWT0cHe1G8L6PFTwAIKTOu8QxqqUv4vLvG2A3m7m5eJk1vbgBNATtFGIc4ZjMPxD+G2jabbsNjDt2Ku8bafV06Ln6nbXZd/64scsjNrVxqjNL+tA19eOQJ92gsNJB0irSzcUGMWlt7W2+yeAdPmVPcb9jfV7N+vtv6s24Xcqwo/O8muqeNwb6dA5qAqftMpvcz4RfT7iPOb1nb+JbjFphyq8b7kmJTf6oX+6nz8Y1U7qwQnjx0+tMXzczrFrw66RBS4c+xXxuFnTi1Qax/hRNOuGXO22Lat9TpI6Y9Mc1b48uDhfv0446++O6l/A0tPJk19ru7LAyVQbQ9GUh5N5Gfb0JFo7qfdJ2E2Lgy2j/OdP+mUP5a6sD1n+edoAT+a1k8rF8NEFg3rxHgngGJepNoyxDdRl28p162kraS9+rL71dVgO1XXN4kb/3cWzYQorTqBvO+kqxuMSWPsyxHtqRLrMOW2NUcvXFussMl2OnlecydaenQV+d0OHUGtXywLp9Xk9FfcqOgK/FpU+FXn9VXSDNtEp/+cpV1cyV0rgAT3UdxS16xhl2CJ1eJK0cSA/EOFt8wRRCqi7ij0OyvIron2aMHpqmaT8gCIOi6Txpajt4aOSXh7xNDwG2wzgaY5qXx7nDxycfl5ZgdGjQE8a9cCQQWkMOeD4t87ariyTb57S2p6Iy2aZk+td0TLsaUmUnkLm/ZTt5i1Z310ccOjyw4mTuxzq2ZX1Icvftw3gpDL3iekyJYMnZ31PNMkmOapjawOTyrdV4dbTVpEe5jh96wtHlc6T8mGcayH7P3SYrJjKChPo2066ioBD9/2o7CzjB1OMSr692gEHkXvJtZvw/fL/e1H9wymcS+51bTgdCu+P3tPsN+vfExPh2xHp1/bMBPwwOn29oVqfp1wzktqSzYvU4UkyeLeEkOAk7Sr2YD4FT7RHRZ+MuJjcutjeLuK5HxIxD+MzTdxH5P+k+YsdSWxr0DyA+ZHMRsRrhY5rlj9V5b4vD4YGeLqD2xER7JijWl6s26Tf0cRpmTIscM/ovRFzYI6MmC/5+IiTami7UBKc1GYI310ccOjy86TLSf+C4hhDl79vG2Du6SQOe4r8tYtcMDeiY5v92qH/9oFjTG2go3hbHmQ9bTnyhQ7Yt772z1H2RFzL6AzhwRzHlR/yautPoG876SJx4QTSUUC7oce0vZc+JMtd98KbJZx7NnHpYHtQ1DXt5FIJZ3STtviViFHOM0R9DCeUfHUZx7pc14YqbN5y9UhyqVEWqcOlZmxdEhfwutTk5sthG9g8u63c03raStqLH8v6WpzhTkjBdjL+Wh70y1Tjx2EJJCABCUhAAhKQgARWhgC/NtMkIAEJSEACEpCABCSwcgR0VFeuSsyQBCQgAQlIQAISkAAEdFRtBxKQgAQkIAEJSEACK0lAR3Ulq8VMSUACEpCABCQgAQnoqNoGJCABCSyfwKtyCH6BXH+YYflH9ggSkIAEJCCBCQR8NcYEMDso2DYwjsruW098SIG4XWq//V2XmK/utfG7HFU+eMIHUI6KeK8i75a+eZ3IhPWDirTLPPHy73W2vvW1zgws22wCi7aTec5N3qPKuct7VHlH6gOjrveoXjLhfDynfY/qc7Pc9z2qibrjbNE63HHA5i2wgOcltn7xbQPjqNO+9YSjygvAy6+HtctdHyLhRsXX+vjKGseoHdWzJoyPTrwp2jfCbhn9Nrppsz7tH47qo6M6P388bac12Na3vtagqBZhAQKLtJN5zk2+TPXr6DpNXnflP1+1mvRlqn9q4vHhgEMjPgCgdRNYpA67UzT0RAQEbIOwDYyjDfStJxzV8pO7s0p3h0R4XzTpU7fcyDj2RauE+DIcX7eZZTiqfCt8p1nf+tppXCzviQks0k7mOTd5eH1dBZ+vaP48wuFt7VlZ4NOq7efjCb96RD5v/PtYLpQEfOG/7UECEpDAkgicOuny6WE+pTjJ6PnkG+F8prg0hg8vEV2sCndVAhLYGgJ9z82LJDt8upQH0tJYp8f0JkXgrbLMJ3yPK8L+K8t8Op1tWgcBf0zVAcUgCUhAAlMInC/bXhl9PPpy9LKI73fXhoP6gejT9YZinRsU0wPquWy/a+LgrM6yuyXChyLmvB0e3S/qc23HkWZe7Sy1UxJm5cPtElgnAn3PTZxU7Kiq8O16u52eVa4ddTzO9W9FbbwqGVf7XMykJAEJSEACJxBg7ij21OgqjRi2+1h0+RM27f177ui+0T8WYV2LOLGniuq5q1doIp+xa6ci7KdZPja6YXTpiOHKR0cvnbEfmw+MftxDD+mRllEksG4E+p6bZ28K/pMKQLt+tiZ8Ujw2E7eNt24cLc+KE1hkfsyKF83s9SRgG+gJapujLVJPp03efxi9pSjDi7N8YLE+aY4q+25E74+4kdF5cOcIB5Q8bWY48OHNvn+c/9PsQtl4QA/tNy2Rbdq2SH1tU5Y97DYQ6NNOmC9ajiqcrsln33PznonPca5ZlY8RC8K5FmBM42G9/oEV2/jB5df3xtJqAseXE3rrja5LQAISkMBsAvxg4vNR+6Mmelb/LOozbM++fxo9JmLY/hfRRyJ6Yw+OeCPAvMacN4z88LqcSfbdbPjRpI1FOHnSJLCuBK6fgr2jKByvjrpR1PfcZEQDq18x1Y6G8BCLTYrHNuK28Zro/pPA1hDo8zS3NTnxKNtFwDawXeTnO27fejpTkmWovjZ+ONE6fQ/O8g+ijULcpDjGd5qw2+b/NMNRpVeVXplJdopsKH9R3MbD8eVY95u0YxP+L0084k7To2aksx2b+9bXduTNY64OgT7thN7U/QsxhWaa1ecmP6biOPeudrpqE86r41o7OguvqeIxivKziDd4aCcl0KcOT7qXIb0JCLg3qrWNaBsYR9X2rac9KQ7D+KXxYyMc00Oq8HJ10tA/vwqmR6c23qv4vCoQJ/mcRdiuLHPjq+0fEkB5uPlOM4f+p9Fx2zoQ6Hted5V1nnOTt3S8tkqEKTj0ypZzT5+d9WMiHjJbY+SDfPp6qgJKsbhIHXanaOiJCAjYBmEbGEcb6FtPe1Icvh61X1Msbji8G/E3ET2Zk2ySo3r+7PDL6IrNjvz6nx6br0Xtjy/aNPlVP722zJ3DdkXk+2FR+9aAy2aZGyHDl+tsfetrnRlYttkEFmkn85ybN0hWeM3ctZsscX34XlTPRz1PwniobcNxht8fvafZz38nJbBIHZ40NUNOQkDAJ0Gy4wJsA+Oo8r71hCP4b9EREb0ozCHFKZzUe8kPLDaieui/dTaZm0ZPzDcj0vxM9Pyo7DnN6l5jHh1x2i9gMQWBH3LwcYAvREdGX414dys3wHW2vvW1zgws22wCi7STec5NcnKz6FMR14UvRQ+K6tfOEe9SESMmPHjy0MvIST2/lXjaCQQWqUMZ9iAg4B6Q1jyKbWAcFWw9jaOe2lxaX+Oqr+3Kre1ku8gPd1y/TDUcS1OSgAQkIAEJSEACEhiSgC/8H5KmaUlAAhKQgAQkIAEJDEZAR3UwlCYkAQlIQAISkIAEJDAkAR3VIWmalgQkIAEJSEACEpDAYAR0VAdDaUISkIAEJCABCUhAAkMS0FEdkqZpSUACEpCABCQgAQkMRkBHdTCUJiQBCexQAqdPuR8RHRZ9MuKdprwP9V4TePC+ReLxvkXepfjAqOt9i5dMOO9obd+3+Nws+77FQNAkIAEJSGAYAr7DbRiOY07FNjCO2lukni6TIh4X/UVR1FtlmTR5IX9pfMHm19F1msBd+f/9aNIXbP6piccL/A+NeFG4dgJbOUhgFoFFzutZabt9awhYh0vmLOAlAx5B8raBEVRSsrhIPV0w+7+go5h8BvXtVfhns/66KozeWL4JftYinM+y8gnGfYqwq2eZfPpN8MXqq0Dq4poTWOS8XnM0oymedbjkqhLwkgGPIHnbwAgqKVkcup4Yyqen9KVF8S/SHOfeFZKrNuF3KsKPzvJrqnhM1fpZdFAVvhNXh66vnchwJ5TZdjL+WvbLVOOvQ0sgAQmsGIEzJT9Pixjif2yRt8s1y0dV+W3X2+30rJ4vquP9LmHfitp4VTKuSkACElg/Av6Yav3q1BJJQALbR+DjOfSPoutFt4y+WmTl7M3yT6rstetna8InxWMzcdt4VTKuSkACElg/Ajqq61enlkgCElgOAeaLnrnQ6ToOc5WEEf5v0Yeiu3fEMUgCEpCABHoS0FHtCcpoEpDAjidw/RD4caHXTyDyy4S/KHpV9K8Rzi12bPO/fsXUGZvwH86Ix2bitvGa6P6TgAQksL4Eyl+Urm8pLZkEJCCBxQl8NElcq0gGpxU7VcT8UV5RVRrvUt0d8T7UwyPem4pdqPnf/uOtAVi7nakD34nqeHQsXCDCAdYkIAEJSEACCxPwF4cLIxx9AraBcVThIvX0uBTxUR3FfGrCSPdixTac0ddWcR+edV5PVc49fXbWj4lOUcS9WpZJz9dTDf+WhqpKXF0TAouc12uCYPTFsA6XXIUCXjLgESRvGxhBJSWLi9QTjiqvorp8UdRrZvmnUf0eVV74/6vo2k3c/fKf96VOeuF/G84L/98fvafZb6f/W6S+djq7nVR+28n4a9s6XHIdCnjJgEeQvG1gBJWULC5STxfO/k+OeJk/PaZHRAz7PyTCwayNT6h+KiLul6IHRV2fUL1UwvkSVfsJ1edluZ7fmqAdaYvU144EtkMLbTsZf8Vbh0uuQwEvGfAIkrcNjKCSkkXraRz11ObS+hpXfW1Xbm0n20V+uOP6wv/hWJqSBCQgAQlIQAISkMCQBHw91ZA0TUsCEpCABCQgAQlIYDACOqqDoTQhCUhAAhKQgAQkIIEhCeioDknTtCQgAQlIQAISkIAEBiOgozoYShOSgAQkIAEJSEACEhiSgI7qkDRNSwISkIAEJCABCUhgMAI6qoOhNCEJSEACEpCABCQggSEJ6KgOSdO0JCABCUhAAhKQgAQGI6CjOhhKE5KABCQgAQlIQAISGJKAjuqQNE1LAhKQgAQkIAEJSGAwAjqqg6E0IQlIQAISkIAEJCCBIQnoqA5J07QkIAEJSEACEpCABAYjoKM6GEoTkoAEJCABCUhAAhIYkoCO6pA0TUsCEpCABCQgAQlIYDACOqqDoTQhCUhAAhKQgAQkIIEhCeioDknTtCQgAQlIQAISkIAEBiOgozoYShOSgAQkIAEJSEACEhiSgI7qkDRNSwISkIAEJCABCUhgMAI6qoOhNCEJSEACEpCABCQggSEJ6KgOSdO0JCABCUhAAhKQgAQGI6CjOhhKE5KABCQgAQlIQAISGJKAjuqQNE1LAhKQgAQkIAEJSGAwAjqqg6E0IQlIQAISkIAEJCCBIQnoqA5J07QkIAEJSEACEpCABAYjoKM6GEoTkoAEJCABCUhAAhIYkoCO6pA0TUsCEpCABCQgAQlIYDACOqqDoTQhCUhAAhKQgAQkIIEhCeioDknTtCQgAQlIQAISkIAEBiOgozoYShOSgAQkIAEJSEACEhiSgI7qkDRNSwISkIAEJCABCUhgMAI6qoOhNCEJSEACEpCABCQggSEJ6KgOSdO0JCABCUhAAhKQgAQGI6CjOhhKE5KABCQgAQlIQAISGJKAjuqQNE1LAhKQgAQkIAEJSGAwAjqqg6E0IQlIQAISkIAEJCCBIQnoqA5J07QkIAEJSEACEpCABAYjoKM6GEoTkoAEJCABCUhAAhIYkoCO6pA0TUsCEpCABCQgAQlIYDACJ09Kxw+WmglJQAISkIAEJCABCUhAAqMg4EPAKKppqZm0DSwV72CJW0+DodyShKyvLcE8+oPYTkZfhSc73qH/8VeiJZCABCQgAQlIQAJrSUBHdS2r1UJJQAISkIAEJCCB8RPQUR1/HVoCCUhAAhKQgAQksJYEdFTXslotlAQkIAEJSEACEhg/AR3V8dehJZCABCQgAQlIQAJrSUBHdS2r1UJJQAISkIAEJCCB8RPQUR1/HVoCCUhAAhKQgAQksJYEdFTXslotlAQkIAEJSEACEhg4SddPAAAgAElEQVQ/AR3V8dehJZCABCQgAQlIQAJrSUBHdS2r1UJJQAISkIAEJCCB8RPQUR1/HVoCCUhAAhKQgAQksJYEdFTXslotlAQkIAEJSEACEhg/AR3V8dehJZCABCQgAQlIQAJrSUBHdS2r1UJJQAISkIAEJCCB8RPQUR1/HVoCCUhAAhKQgAQksJYEdFTXslotlAQkIAEJSEACEhg/AR3V8dehJZCABCQgAQlIQAJrSUBHdS2r1UJJQAISkIAEJCCB8RPQUR1/HVoCCUhAAhKQgAQksJYEdFTXslotlAQkIAEJSEACEhg/AR3V8dehJZCABCQgAQlIQAJrSUBHdS2r1UJJQAISkIAEJCCB8RPQUR1/HVoCCUhAAhKQgAQksJYEdFTXslotlAQkIAEJSEACEhg/AR3V8dehJZCABCQgAQlIQAJrSUBHdS2r1UJJQAISkIAEJCCB8RPQUR1/HVoCCUhAAhKQgAQksJYEdFTXslotlAQkIAEJSEACEhg/AR3V8dehJZCABCQgAQlIQAJrSUBHdS2r1UJJQAISkIAEJCCB8RPQUR1/HVoCCUhAAhKQgAQksJYEdFTXslotlAQkIAEJSEACEhg/AR3V8dehJZCABCQgAQlIQAJrSUBHdS2r1UJJQAISkIAEJCCB8RPQUR1/HVoCCUhAAhKQgAQksJYEdFTXslotlAQkIAEJSEACEhg/AR3V8dehJdjZBF6V4h8fXWZnY1j50ltPK19FezO4X/Sh6OhxZNdcSmBLCPx9jvLz6B5bcrQlH2R30n9r9Jnoc9GXoydFp+s47t0S9tnoyOib0Qujs3TE2z9h742+Hm1E74gu1RFvFYNwIPoYTsbzoi9FR0RfjJ4bnbtj5748/ij7viI6KvpK9Mno5h3pdQUdlEDyXuuZXZEHCLt20nhJRJuh7ZDf/4gu1JH22Mrftw1cOGV9WvSpRjB4X3SdDgZt0DWy0NZRl6M6pjYwpZhbssl62hLMgx2kb321B7x9Fg6LuA5+I/qv6DZVbm6X9Y2Ie42OagVnpKvztpOymOfKyj9F3JM+H3F/fnN0xQksbpZw2hf3Me7hD4xO3hH3kgl7VxOH6zz3+jN0xFt20B/nAPhr3HPw1SjfY6qDnqOJQ7lguR2O6iJ1WBXnhNVj8+8J0SmarRfLf8JwOkp7aFZ+FV2rCaSSeIo9PGr3ZdM1o19HD2viUenPiEiTm/CqW1/AnAhvj87YFIjGQcM4Kjp9Uci+PM6afb4dvSnat9n/lvn/2+imRXqTFnFUHx3dqRINexn2uiT6nqgt/5myTHvghnLq4oBjLH/fNnCflPO70UWa8nIe0NZ/GV22YNAuci58NHpLxDFqR3VsbaCjiFsaZD1tKe6FD9a3vjjQI6JPROdrjnqq/H999G9FLrhOHhpdIOJ6pKNawBnx4jztpC4mHTN0orUdJqfM8r9HXJPre+ENEoav0nYs7Mry96NHRqWdJys/iHCAsdNEh0bvbta36t8BOdAx0dWKAz4oyzjkpZHPv4u4v8ByLRzVN6Ygpz1xOU+G0/N/UftkwQXhpxG9faXhtAKCp9rWcF6+FZVTFOid/Un0/CLeqi72PUlwVK9QFeJWWWf/OxbhfXlwcrDvRas035t1nppmGXVWNuBZ8RfdzlPc1atEcJIpw58U4WMsf982wIMEF4TSzt8w4MGutjskgB5XLhwco3ZUx9YG6vJt9br1tNXEFzte3/qis+Q3UX19paOjDOP+1N5ndFQXq5tV2rtvO+nKM47qA6oNZ8s6ab6oCmd0mHZTGg9IP4/oNGjtWVn4XrRPEca9jzRvXIRNWtydDS+OWn+qjEc63CNrH6xOi06Qr0d12egU+rMqcttxuK2O6tBzVLnZUjGl0Uv2w6htMBfP8umjI6p4dJdjdJ+3xlMLXei/K8JweoFcxis2j3IRZwxntTR617ByOkRfHsSjx/qrZYJZhvElIi7eq2SPTmboTS+t7V2l7bS2ruWnfDzkMf2jtJbBsVU4F5THRw+qwsvVsbWBKUVZqU3W00pVx8zM3CUxcAzq6ysjTmUY96fyPjMzYSOsPYEHp4TPrkrJ/Yh7a3lfZhTschEdB6WxTo/pTYrAW2X5g9FxRRjTUPBr2DbLGGW8fYQTXRrTERiVpbeWHt9pdt1spJf4zVUk9sPRLe231fq2rA7tqJaFoJv8r6MbRfcvNlAhWDnEz3p7kcCRao24dbw2Ll3o7Y282GWUiwwZ1NY6kx8oNvTl0fZg109dXYzr47brd8sCw+88KOBE3i9aZntpj0ueeTJ8ePSkiIeS1nZC+duyXjALXCS5qNWjDziotItP/57MSRfG3AZOWprVDbGeVrduyBnzuL8W3TH6cHRkdFjEzV6TwDQCOJP1w8t+CWunibT74qRiR7UB1Xq7nZ7V83XE4xjfitp4VTInWuV+gEPL6BudFdglo3dF3BN4MKvzfEKsP/zlnCDOOSKcW+7xPLT9c4TftmOMG+wvIrx7LhCl4Xj+OGKOUGnXygpPtVxUWsPjZx5FCa8d+icuQ6OrbORxM4azxsX05dXOfXk8MPtx7Hpu43ubcIbVpxlzI58QMYRAXngC40myzs+0NDazjbbCcXDcHxedqkpkjOWftw1cNGU+OmK/N0RM6C/t3Fmhh+i8TeA98p+49dD/WNvAiUu7dWvW09axHuJIfeuL+8nPIm7w54x42GbaDDdqfsncZQ79d1EZZ1jfdtK3dDiHX4nK4fV7Zp3jXLNKhJEvwhmqx+h8Yv2RzXr576NZKTtlOqKcKOg2WaO38ynRdyJ6QnGg+9hBicS+34joicUYgeO+8tpmvf63rUP/dWaGXMchvU4ExH+vEuYCwdMKsHGEuPnSa8cF5Ygi7hWyjNPy1AinhYpnbupPIyr8bNEq22ZPkn9IoZjUfKaqcH15cBJtRO+Pzh5xcb5z1HLrM8RQHXpvDyfloUEv2zih6c39VHTm4mBjLP9m2wBP30wF4GHvygUDLnoHFuuTHNWxt4GiiFuyaD1tCebBDtK3vtqHvvIcIhNvi5hS0zVip6M6WDVte0J92sk+ySX3mVZdbymiIFeN6Ehpnbu2cNvhqHJspiZQPkYJJuW5zWP5nw4n9mP/0h7ShF++Cmd1Wx3VSUO570vGcBprfaSjAJOC8NhxlP4xumt0gyLic7L8NxG9Pvy4By+eJwOWmTvUGt3R9OZdKvpC9OHomxFPBAxt0jO7bvZXKdC9I6ZM/G9VuL48fp79/jTaiHgAYD+6++/bpFcyboJm/mMeDXa1KTEfk211m2nXa6d7SjJ7n1jp9eWC8NAi4qqXf1qZ5t32o+xwn+gn0bObnbmA/Fn05B6JbVcb6JG1tYoy1noa6lxd9cpsH84/V2WUaTN0dFxw1Qtg/pZO4Po5Ar5Eq3q0lwwwJRE/hfszbac0HniwM5w4+PdTE3FusUnx2HbGqI3XRJ/67+zZil/FlAFG4W4xNfaJN3JOYNxPS2vLdZUqfNtXeZLoMnrf6L2sjUnEk4wnU9Kr47Qw6Il7d7HzwVlGpb0wK/9ZhR2W9ZtUYTQkusoZvlkno6fzsdH1InoCuqwvDxowDbk0HFUcx/qiXcahHnEquQGXxoMH1tUD0cbDoXpZuVOx3J4cXZvp/cOxKo0Hkv+J6h7cVS5/V9n6hjHp/pdR2QMA8yOi9tegOKmcl8wpau30zQJzlH4TPSx6dRO2HW3gDzlbz6V1qafNnqtjq1V6m3AyTl5lvL2eTeqsGVs5ze/mCeBLXKvYHYe1tItn5e3R3aP3VttYbe+nF6q2tQ9B7XbuqYww1/FogxeIXtWRdlcQTu07I+4VV4ruEe2J6Lx7UzTLOCewuu3viHOCp5JDOgjdNGEApXu8NZyP81Zx6fHjRr1fEU7l0YtUGl3cVPhtq/BVXC2djln5+8tE+HJEmVvjR0WPLtb78uBmSn3UxoMCw8ml4ZSeswjYleUuJ5npCJRn/xPtvfjKPkkCJ5WpHaVxMnLi/EcRuIzynz/p4yi3tisLQ5a/bxvAAe9i+4mEf7fIX73IRYpjMDRT2pjaQF2m7Vi3nraD+uaP2be+7pZDEPfK1aHo7KAHq+vB+3UJ77oGbD637rldBPq2k0n5w0n9ekQnQWvcq95c7YAzWs/vZLoc9zZ67lvjAZHf3ZTtjlFK8tl2SBTRT7LIvepD0dei8xRbH5dlOgnLkeuT7NwEXDj/6eSrh/7pyCIf9dQGduP+wjbuN1tti9bhifJ7/azhWNyhCP2jLH824iniLEU4Q/eviHBSsDbeA4o4LDL8y3SAszbhVNLLozdW8VZ1tS9gnNRfRP8YUeZWDPHuKQrXlwfOF05/2+DoTaAR0rgZMiiN3jkc/9ZZ25Vl8k3PXNsLcdksc3LRaze00QY43rOifZvE23r+ddb3Lw44dPnhxMnN02lru7IwZPn7toHDctwPRuVDQ3vheGiRv3qRCwfHqB3VMbWBukzbsW49bQf1zR+zb32dModgVI8fm7TXuOtlmdEHfivRZTqqXVTGGda3nXSV7mIJpJPg4Ki9J/OfkcqNagccRO4l127C98v/70X1D6dwLn9QhNOh8P6I9tnHnphI345Iv7ZnJoCHr3aUrd5erj83K6TT9vqS3lFR7Wy3+6yNo0rP3IOij0TMJ+UJAyfo36LztaVt/t8x/+kpAswnI27St67isEq39iERw8BcbIj7iIiLzxjs+J6ZZIiWuF3aU6TRlwe9kTQ4uDF0DLvnR6UT1Cb7jiZOy5SnxXtGDHFQjwwTfDV6fMRJtQzj5H9bRHvhwYaHkzdE9VyZocvPky4n6wui1oYuf982gEO+J4I5DGCB43qbNmPV/2tmfSM6NuIYPAyy3t6Mx9YGkvVtNetpW/HPffC+9UXC54j2RFxnvxwxF49rTm0vTsBGxBDqcc3yp+pIro+KwDztpC7YSxPQdU8mbKOOnPWbRbQXfB/uYfhD9ZQTdrtUxOgm1/ivRIxynoENPQwnlB7RLuNYl+va0BFGB9GjI3qLySv3+MdG3P9Ko5NqI+L+Qrm537DO9NCtskXqcKvyOOrjCHjU1TdI5m0Dg2BceiLW09IRD3oA62tQnGubmO1k/FV7fD2ZdvxFsgQSkIAEJCABCUhAAmtBQEd1LarRQkhAAhKQgAQkIIH1I6Cjun51aokkIAEJSEACEpDAWhDQUV2LarQQEpCABCQgAQlIYP0I6KiuX51aIglIQAISkIAEJLAWBHRU16IaLYQEJLDiBPjqDL9Art93u+LZNnsSkMCABA5IWrwSkffBaxJYCQK+GmMlqmFbM2Eb2Fb8vQ/et574kAJxu3TmCUfjq3tt/C5HlQ+evCI6KuK9irwv+uYT0qqDDyrSLvPEy7/X2frW1zozsGyzCaxKO+E95U+IPh/xnt5JjirXB96ryrtNeQc671rl5fznjkrrG4996JDkAz6kxTtePx7dqEysWOZdsFx/2vfgPzDLXe+CnbD7UoJXpQ6XUrhVSFTAq1AL25sH28D28u979L71hKPKBxl4YXyt9qMZ5TG5yPMt8bdEHKN2VM+aMHpY+Eb3vs2Ot8x/vvJ302Z92j8c1UdHdV74TPU6W9/6WmcGlm02gVVpJzdMVnE4+WgOL82f5KjycZ63R3ywBeNjFTiOR0Wnb8L41zcecR8XfStqP7z051nmq4/XZmNhfF2L8Os0Ybvy//tR/XWtcp+tWF6VOtyKsm7LMQS8LdhX6qC2gZWqjomZ6VtPOKrlJ3cnJthsuEP+vy+a9KlbbgIc+6JVQnwZjl6VWYajyrfCd5r1ra+dxsXynpjAqrSTUxTZmuWoXqGqxFtlnXLwRc/WcFT7xKMnlk+73uf/Z+9c4LarxvzPX+TQgQoRva8mSTogmlKUkSEahibHxoyGxow0yCFhqpkaxxnEkGS8k8Io54jOB5NQSYWivE/p4NCBGhWl/r/f215Z72rv+17386z7sPbzvT6f3/Psvfbaa6/1vda997XXPkXretKfQ/92kuYT8KOTNH8J9EbJJ9TTMl74Py3ybBcCEOg9gXurhQdJ/pRil3nk0wcSf8IwNl9621jaKElnFgIQqI+Ar5Dk2FbK5CA0tiubmQdEibn5fFXGn0X1yXJsnncZPvG2bSj586tt+TwK/Kwm31T++XuvGAQgAAEI5BPwJbRPS965+xLdd6R3SL4HLDYHqKdK/rZ816V436/m2wOsePTntqYgB6u+b3WQ7a6F75HWln4juW4fkkIZXes6kLaG2U3K4GAag0BfCTgWii+td7XzFi3wb3Zc5kvvqYWTVe9LguXmc/BpW/7HVVea9/LLpZx8SRGTm+Wp/8mxZksQgED9BMLIyHvVlCc2coDpYHWLqHm+5PYaad8hTXYQ6xGPTZN84bJeuFetq5gbtMCXEn0P3GMk30qwn3R41wpR+v6avi5Db8woiywQqJnAjhm/A/9WvjThRvoE9pWSH7Y8f8C2u/Kto3VulXyyGdv1zYxPbm3OZwvpzeyd8yFfSJ/of0ZUJ4qbjUEAApUTuEr13yxqg3fsr5L8gMKB0l80y3zJ/xApXLaLVllp0nn2kg6WdpWulfxglC/L2dIDTJN857/XJQm+dOfRVY/wvk/ygxhddqgW5Nxvm47GdJVHOgRqJeATzfAQ0aA2OFgdZPePFvoE1lc4FmKv1cou89VDCsnNN6SY2VxMoDqbfqFWEIBAPQT8sIFfOxMeavLI6tMlX7YfZl73KdIB0rckB6ZnSB6N/YTkNwKMauEhCddnUKDqINqB8TAbFiwPW5/lEJh1Aj7hTO8NbauzL/13mW+jiQNZ3y6Tc2tNV3kv0IJ/lBxADwp4B+Xz1RbHea7HzdGGwpWaa5o057OtHuXxZJovWcxsHwjE95z1oT20YXQC9IHRmU1jjVw/ranK+VJ9ah7JDEHfGzT9S2kukg8E3sYVTdoL9X+QOVD1Zf1BBzo/Sdz2NK4DX2/LI7WD7J1NPucdpLcNKmRKy3L9NaXqsdkZIZDbT5455DcQfh8nDGiXL79vF+lJHXm9LziiY1lI3kUTF0nrLzDfK7S+675JUo7fq+r0+GEqzzswju1Pm3y+yjMty/XhtOpX/XYBXL0LF9wA+sCCEU6kgFw/LVNtvPOPbVXNODAddBALB4z0XlQ/UbtjUp5nj5M+kqQ7SH5QlLZU05cneTzr2wHcHh80B9kGWrhDhpYMKmRKy3L9NaXqsdkZIZDbT3zCl/Nb8NWShdqwQPX52kAapG6jtP2SDefkC6+nSm8d8C0/6eupzlPaUck29tG8r/pM8x7VXB8mVWc2lwCAc0n1Nx99oA7f5vppmZrjp/BD8OZRzQ9IviTokcwu6wpUPaLhS3KPa1b0qIxHUy+WwgMOoUy/VcCjtvdtEpbqv+vt0RGvZ9tM8n20fk9iny3XX31mQNuGE5jFfjIoUHXw6Vtt/BCmRzGD3q3pZVFzc/N5lQOlS6WHNuvvpP9+a8D2UXme/HPJtyuEdO/jfi75Ac1p2iz6cJo8im8bwMWRVlcgfaAOl+X6yYGgX/3kJ3A9AuF7SB0Udo1ebqtlc1J66T8Em74HzKMYPpC4TN8nd4gUj5xqdoUdKznPPZt534Kwh+SPA/xAulDy+1j9IJdHavtsuf7qMwPaNpzALPUT/0bnJL855P+a6Q8nTfAXpFznNi2L8ubm8yp+u5NHRn8keZ91luRgtc2eo8RzmnzOv7cUToLb8k8ibZZ8OIn2TnwbAJ448pnbIH1g5lzSWiH81IplZhPx18y6ZqYqRj+ZKXfMqzJ8mWpe2FgJAhCAAAQgAAEIQGDsBHjh/9gRswEIQAACEIAABCAAgfkQIFCdDzXWgQAEIAABCEAAAhAYOwEC1bEjZgMQgAAEIAABCEAAAvMhQKA6H2qsAwEIQAACEIAABCAwdgIEqmNHzAYgAAEIQAACEIAABOZDgEB1PtRYBwIQgMAfCTxYk2+X/A7UCyS/f/DLUniJf8rK7yo8W/I7Df0S/9dLbe8qfLTS/Y5W5/FHBvzOxfRb3ErCIAABCEAAAvMjwDvc5setT2vRB+rw5kL89H410S/s36Bpql/I/1+Svzi1ZdJ8f/3FX4V5apO+VP9/IaVff3mI0vxZVgfANr/A/xTJn1bF7nghOhwgMIzAQn7Xw8pm+WQI4MMxcwbwmAFXUDx9oAInqYoL8ZMD1dcmzfS3sV3mx5L072v+6CTtLZr397TXitL9WVZ/vnCVKM3f+3aZXV+VibL2fnIh/uo9HBp4JwH6Sf2dAR+O2YcAHjPgCoqnD1TgJFVxIX5yMNl2G5VHVOOgdMNmO/+YIPnTJt3f9Q52uSY+m+TzNvzpxcOS9MU4uxB/LUZei7XN9JP6PX97fLZef3NoAQQgAIHJE7i1ZZNLlLaqdEq0bPNmenmSP8yH5R5ZXU9K892mtMukkC8phlkIQAAC/SPQNgrQv1bSIghAAAKTJbCHNvcTyfeqBlunmbg+qUqY9+0Ctq58Xua8IV+TnX8QgAAE+kuAEdX++paWQQACZQl4f7laVOQtmv5tyyZ8Kf9V0o6S7z3FIAABCEBgngQYUZ0nOFaDAAQWHQEHntdF+lwLgY2VdpT0Aul7yfKrm/n0FVNrNOnXNP+78nmx84Z8SfHMQgACEOgfAUZU++dTWgQBCIyHwJkq9slR0Q5aY3uUZr4m/Z10YrLMs35vqi28xipkeUQzEZZfq/krWvJ5YGF96TNhRf5DAAIQgAAEFkKAJw4XQq8f69IH6vDjQv3kIPUS6elRc++l6S8nzXcw6hHX2PbRjG8RiO89PVjzV0n3iDJurWnXk9dTLewtDTF7pvtNYKG/637TqaN1+HDMfgLwmAFXUDx9oAInqYoL8dNGWv9K6ROSXzEV9HJNzyXN9wv/fydt36Qv0X+/L7Xrhf8h3S/8P1k6Pilvsc4uxF+LldlibDf9pH6v48Mx+xDAYwZcQfH0gQqcpCouxE+HN+u7jFRzLc33J1TPkTy66s+t7i21fUJ1E6X7S1ThE6of0XR6f6uSFqUtxF+LEtgibTT9pH7H48Mx+xDAYwZcQfH0gQqcpCripzr8FGqJv+ry17RqSz+ZFvly272dp/7LwaQkCEAAAhCAAAQgAIGCBAhUC8KkKAhAAAIQgAAEIACBcgQIVMuxpCQIQAACEIAABCAAgYIECFQLwqQoCEAAAhCAAAQgAIFyBAhUy7GkJAhAAAIQgAAEIACBggQIVAvCpCgIQAACEIAABCAAgXIECFTLsaQkCEAAAhCAAAQgAIGCBAhUC8KkKAhAAAIQgAAEIACBcgQIVMuxpCQIQAACEIAABCAAgYIECFQLwqQoCEAAAhCAAAQgAIFyBAhUy7GkJAhAAAIQgAAEIACBggQIVAvCpCgIQAACEIAABCAAgXIECFTLsaQkCEAAAhCAAAQgAIGCBAhUC8KkKAhAAAIQgAAEIACBcgQIVMuxpCQIQAACEIAABCAAgYIECFQLwqQoCEAAAhCAAAQgAIFyBAhUy7GkJAhAAAIQgAAEIACBggQIVAvCpCgIQAACEIAABCAAgXIECFTLsaQkCEAAAhCAAAQgAIGCBAhUC8KkKAhAAAIQgAAEIACBcgQIVMuxpCQIQAACEIAABCAAgYIECFQLwqQoCEAAAhCAAAQgAIFyBAhUy7GkJAhAAAIQgAAEIACBggQIVAvCpCgIQAACEIAABCAAgXIECFTLsaQkCEAAAhCAAAQgAIGCBAhUC8KkKAhAAAIQgAAEIACBcgQIVMuxpCQIQAACEIAABCAAgYIECFQLwqQoCEAAAhCAAAQgAIFyBAhUy7GkJAhAAAIQgAAEIACBggQIVAvCpCgIQAACEIAABCAAgXIECFTLsaQkCEAAAhCAAAQgAIGCBAhUC8KkKAhAAAIQgAAEIACBcgQIVMuxpCQIQAACEIAABCAAgYIECFQLwqQoCEAAAhCAAAQgAIFyBAhUy7GkJAhAAAIQgAAEIACBggQIVAvCpCgIQAACEIAABCAAgXIECFTLsaQkCEAAAhCAAAQgAIGCBAhUC8KkKAhAAAIQgAAEIACBcgTurqJuL1ccJUEAAhCAAAQgAAEIQAACNRDgJKAGL423jvSB8fItVTp+KkVyMuXgr8lwrn0r9JPaPajBVC791+9EWgABCEAAAhCAAAR6SYBAtZdupVEQgAAEIAABCECgfgIEqvX7kBZAAAIQgAAEIACBXhIgUO2lW2kUBCAAAQhAAAIQqJ8AgWr9PqQFEIAABCAAAQhAoJcECFR76VYaBQEIQAACEIAABOonQKBavw9pAQQgAAEIQAACEOglAQLVXrqVRkEAAhCAAAQgAIH6CRCo1u9DWgABCEAAAhCAAAR6SYBAtZdupVEQgAAEIAABCECgfgIEqvX7kBZAAAIQgAAEIACBXhIgUO2lW2kUBCAAAQhAAAIQqJ8AgWr9PqQFEIAABCAAAQhAoJcECFR76VYaBQEIQAACEIAABOonQKBavw9pAQQgAAEIQAACEOglAQLVXrqVRkEAAhCAAAQgAIH6CRCo1u9DWgABCEAAAhCAAAR6SYBAtZdupVEQgAAEIAABCECgfgIEqvX7kBZAAAIQgAAEIACBXhIgUO2lW2kUBCAAAQhAAAIQqJ8AgWr9PqQFEIAABCAAAQhAoJcECFR76VYaBQEIQAACEIAABOonQKBavw9pAQQgAAEIQAACEOglAQLVXrqVRkEAAhCAAAQgAIH6CRCo1u9DWgABCEAAAhCAAAR6SYBAtZdupVEQgAAEIAABCECgfgIEqvX7kBZAAAIQgAAEIACBXhIgUO2lW2kUBCAAAQhAAAIQqJ8AgWr9PqQFEIAABCAAAQhAoJcECFR76VYaBQEIQAACEIAABOonQKBavw9pAQQgAAEIQAACEOglAQLVXrqVRkEAAhCAAAQgAIH6CRCo1u9DWgABCEAAAhCAAAR6SYBAtZdupfGbjr4AACAASURBVFEQgAAEIAABCECgfgIEqvX7kBZAAAIQgAAEIACBXhIgUO2lW2kUBCAAAQhAAAIQqJ/AOAPVxwjPrdLR9WOiBRMkcG9ta066eoLbnMVNfUaVul3adEjlcvMNKYbF8ySQyz833zyrwWpDCCzR8tOlywvlG1IMi3tE4L5qy0cl7483XKTterXafaP0ih61f0VTviHZsV2B6u5a9n3pQulS6VDpAVJq2ynhROkSaU46VtokzTSj825/jv2JMv27dE6jH+v/SdJTW1bO5fFwrXuktFxyeWdLz20pry3pMCW67qne35a5cNpbmu12Baq1tT+3D8QYnxSxHxSoDstXax8o3KWyisNPWZhmJtMo/nqRaj0n+RgyKFDNzfcwlbNM8rHrPOkH0lule0rYbBEYpZ+01fxxSrR/vye5rEGB6nO03MdZ94kfSq+X7i6l9mglOD5yHh+bPyytnmYa83xuux6oehwjuV1u/6BAdTctP0s6X/qR9FXp8dJCbaE+7Nz+s7TEDbtCagtU36T030lPbkqwk3y2+y3pHk2a/20r/V56c5Nmp79PchDjg/CsWy7gPdWQK6XwIzADt/NmabOokbk81tI6P5O+KK3arP88/f+DtHNUXtekA9X9JHe8WFt2rVAo/cEq5yrJQXpboFpj+3P7QEDoPn6m9BXJ63YFqsPy1doHAodJ/8dPkya+sO3l+sv7v1Ok9SUfi7oC1dx8DkYvkL4trSnZtpD+T/JgAzZbBHL7SVetfSXkKZKP0S6rK1D9cy1zrBIGl5Zq+heST2Bie4hmfim9vUm8j/6fIh23Uq7xz+S2y/X8B8nHIbe/K1B9cbPc/22rSJ+QrpMWGqst1IdNlVb+5wr6DGR7yTsF7xxi8w7hBsmjfbE5aHWFfFYb7HhNXCbFtyjcT/PXS4dE+WZ1Mhewg0h3hth81u71HdQHy+XhH4fXfWS0ridPlHymM8wcqG49LNMYlh+qMveTjpDaAtUa25/bBwLOl2jCgbp3CF63K1Adlq/WPhA4TPo/fpo08YVtL9dfPqELx49BgWpuPo8QedsvT6r/Wc17YAabLQK5/aSr1mHgbFig6qvDaazjq4O+XO5Bg2Af0MTPJcdJwbbRhOu5U5TWNfm3WvBxqW2k1uX4GOlbFYZZbrtCvmGB6pe1wUuTjfrKt9v1ymGVGbL89nHco/r32qiHs0/t2PijlL6a5OHh2M5rZjx8HswjeB4evy1K+62mL5HifNHiKie/oFp/JKn5Gs18HLDl8nA+j1j/JCnTjDeWNkrSZ2HWI8fPlN4zoDJ9br+bfW/pIGnvAQxy89XYB4Y0e2YW46eZccXQivhAGR8/ulbIzXdrU0AcaDjJ875ihfWLQI5PN1STN5c8wBCb5z1i6ivMwXbRxGlS6EdO9+i84xovG2Y/VQaPWqa34flS/tckj9b6Suwwy2mXy8jN5/a0/SZGKaOzzqUDVV8K8UhOPAqYbtwOscWX+D0fdiYOpII5b5ov5PUQegjmolV6MfkIteJgyR06HnnO5eF8PuNKz7raGHcB8z3Ep0s+UfAtGXtJpftLvO3/0Mw/Sz4D7bI+t99tdoDqEzzfDzXIcvLV2AcGtXmWluXwd31z8uGnWfLs8Lr4ZP/zkveHvupl20HySfa/NPP8W1wEHKTalifNDvNhuUdW12vJ5+PyZVLIlxSz0qxjAge0vgLrQQ3bo6VvSD52/I2Uc2J2x5rl/r5XRTkee43kuMNXvveXHD/4asOCrHTg8famUulIXlzJOc38WvIllNge28y4scF8wPaQs+8LCmYA4ZJ2nDfKUu2k23W55LOm66UXSB4ZDZbLw/nuJZldbG2MkywrZm+QPJL7DMlvb/DJx37S4V44BttZZa6dUX5f22+k60r+ke87hG9uvtr6wJBmz8ziXP65+fDTzLg2uyIe0TpDmpP8bMGXJAeuvmUKW3wE1mma7GN2bGHexzZbVz4vc96Qr8ne+c8PlL9U2kfyFcgTJN968EIpHqntLGAMC/x78HH8ddKvpGskP3u0o+T7t2fG/kQ1uUryWUMwB11Ht9TQrzow0F0lR9/eqXvUzg06P8rvwMo3KDtad+DlS26HSA6kfKkm17HKOhVzHedjZuhbATyM/4SogFwevkdlTjpZ8o/DJyQvkwK3XaIycyf9o3B7tsxdITOfLxf4vtkdovxHaNqBcmo1tj+3D/i+o/2jBr9C0143PdnIzVdTH0j9PI15/DQN6vPfZq6/4i34WORj0jAblM+/K1+qPUnyw5+2raRfSO9s5vk3OwRy+omPQfeP5MGw1PZUgsvaMF2g+T2aZdsmyxyveB3vs22+5c7zHvhJ7UwlXJImDpl/g5a7vAultjoPWX3F4kHtitf3ccjb8nGpzfzMhK+GenDN8YZveXAM44e625i1ldGV1nmPqn+EDhpTOWrusndrwbuka7syROn/qWnfYPt6yUHKUZLPDDzthgU7VxN/Jm0i/UD6X+lSyWeuvmR2ndRHM0N3IJ9lHRw1MJeHO8xTpDnJJwBe70mSR+xsMeMmaeg/75xtWw/IeYCWpX0mzK/ZsZ4vYVwkndKxPE6e9fZnNKE1yxZKfbrk39Agy83nMqbVBwbVv/Zlufxz803TT/P5rdbuvxL1f5UKcWDq/bODU9t3pP+Q3iT5WIXVRWBHVdexRNDnRqz+1U1+jyDGFq74enTR1pXPy5w35GuyD/znAaiXS75lwFdi/3Jg7vEu9O2ZjumOkT4r+daDm6TXSmYSblHQ5PzMZxJt5tE3nw2kFl+GTpdtr4QnSq5cMI+U7iTNSR5t3eaPi1a8usCKzU99+zJKbN/UzLOSNHckn4FM416MpCpFZn32cbPkM5ZgvonZo8vmF1suD3dgd+TYHKg6cDwvSY9n3ekcVKYnHOGm6rZ7hsP6Dqo/2VG2R3Pb7GlK9I5/LlroH6GZhDT3LZ+g2Ga5/U0VR/7nINW/tx9Ga67WTPveo1ukN0sPz8z3P8260+gDURN6N9knP83nt9o7h86jQZs166S3t/kBYl8d9PL4dzyPTbDKhAk4lnhytE0HrKNYOJ5ukKz0iGY+LPcx9QopzecRyPWlz2Ru1EHt1yXHC4+XPMq5TPLg3RelSZvv1b6/5N9AbI4XfdzePEmfudnLVaOjW2rly8cPTdI94udgbUmUbud5dCI2D3Hb4S9M0mdxNg48B9XPwdd2LRnOUprvgQqWy8NBns8SUztOCR6Oj81B6YOihKWatt9S870nbk9bPdO8C50/QgWEs8+4rHG03z8yX84LtlQTJduf2wfidnraOx+vu2m6IJnvyld7HxjS7OKL8VNxpGMtcD7+8rGo7bedVnRQvncps7f9J8lKHqBx+g5pYcxPlcB8+klbhfds/Lth20KlORj1leHYfLucr2zFtyj6BNGDdvGAj69Sup7poNRKhTUzPladLl0sPSTKcKCmHRj+edtKA9KGtSus6uOQ6+jjTWoeNfWtnOkgldvo4/gp6QojzpfyYedmvVPwjz41X7o/UlqlWeCRIt8MHI/GetFukm8HWKvJZycdIX2hmZ/1f7mAv6mGnCbFAaNHP72+LycFy+Xh4MtBv19ZYfOZvstz5/ZoZWw++3fgH4K1pZr2dj2C5/VsHiXwj8uje5Mw+9gdPLXS7Tcn/7h9dhpsqSZKtj+3D0RVWDHpHYLX9Q5ikHXlq70PDGrzOJbhp3FQHV+Z8/HXoAA0rumgfI9SRo9cfV7yyaDNI2QeOfqeNOiKU5OdfxMkMJ9+0la9YQGdA0QfS7ZvVl6i/z+X0vtRHVz+Mkp3HzpZOr5Zb9i/dyjDzySXn9r7lXCNtFq6YMD8sHaFVX0cMsu2QNV5fB9u3H7HDv/SrDOfZ2LCdv2/lA/jMldM+8xiTrpV8o/a0/tKwfzE2lnSculsyYHaX/1x8Z1THtY+QfJO4Nwm71v0/54teWcxKRfwdqr8Msn34Tpgd/DowHXXpFG5PHxpwD4wN98+YHaHSHEgHIo+tskTmN5L83tIJ0quz4WSL3MdJIUdsybHYnur1DnJtyf4VgNPfznaUun2+0zXP/qPRtso3f7cPhCq4Bvy3e6rJa/rS0Wej0d9Nbviq21O78pXax9w26Zh+Gka1Oe/zVH85YPonORjkY9Jnj6nZdO5+Xzi/jnJ+0aPpHl//V7pAS1lkjRdAqP0k7aavlKJc5IDQJd1eTO/UUvm5yjN/cp9wgNsPp6FwZ44+yaa8dVN9xtfLvdVztXjDAOmHYSmo/khu7e1+YB140W57XJfn5N8HHL7fbzxvG8Pjc3xgwcaHWtcILn9J0vPWCnX/GYW6sP5bXURrQXgReTsjqbSBzrAzFgyfpoxhwypDv4aAojFKwjQT+rvCJ1P/dffNFoAAQhAAAIQgAAEIFA1AT9thkEAAhCAAAQgAAEIQGDmCBCozpxLqBAEIAABCEAAAhCAgAkQqNIPIAABCEAAAhCAAARmkgCB6ky6hUpBAAIQgAAEIAABCBCo0gcgAAEIjJ+AvzrjJ5D9PkIMAhBYnAR2ULP9SkS/K3yQLdFCv9jfr8PCIDBWArwaY6x4qyicPlCFm7JfY+MPKdinbfJnBNvMX90L+dsCVX/w5EhpueT3Kvrd0s9tK6gl7bCo7LhOfvl3n43fVZ+9W65ts9JP/J7Rf5P8jlG/z3dQoPoiLZ+TLpEGBar+opU/wuP3sfp96d+R0nevK2nFLZ7+gI/z+R2v35We6QUt5nfBev8T3g/8ek23vQu2ZdWxJc2KD8fWwGkXDOBpe2D626cPTN8HOTXI9ZMDVX+UY7cW+WCUmnfy/pb4VyRvIw1U11KaR1i+KK3arPw8/fcHL3Zu5gf9c6C6n5TWZ8tBK/VgWa6/etBUmrAAArPST/zi+w9L/miOX5rfFah6H3CK5M+FHy11BaqP1DJ/GMdlhivjf6dpt9fBZmwHauYyab0m8dn6/3tp+5Wzrfj8qtOf2qQv1f9fSOnXtZLVxj47Kz4ce0OntQEAT4v87GyXPjA7vhhUk1w/OVCNP7k7qEwve4l0kvQKydtIA1UfBJzuA09s/jKcv+4yzByoemRlsVmuvxYbF9q7MoFZ6Sfxp3UHBao+sQ2B56BA1SOdbtsjEof786y+OhNsXU3406Z7Jvk8EvvtJM0n4N5mbP4S6I2ST6inZbzwf1rk2S4EINB7AvdWCw+S/CnFLvPIpw8k/kxxbL70trHU9qnGJCuzEIDAjBPwFZIcc/B5W0bGW5s8qyR5HRDH2/JVGX8W3CfLsXl+K8kn3rYNJX9+tS2fR4Gf1eSbyj8eppoKdjYKAQhUTMCX0D4t+V6vi6RPSv5+d2oOUE+VvpcuiOZ9v5pHUdL7wMLBysHqMNtdGfzghe9B+5a0l5Szb3cg7ftqhynckjCsHiyHQK0EHPAN+x14+f1mpIG+deBiaX/JgWS4D9WB6vuiOjr4tC2P0uL5sDw3X1LMZGZzdmaTqQlbgQAEIDD7BMJoxXtV1Sc28iiIH2TYIqq+L7m9Rtp3SJMcxHrEI70l4LHNemsMWf8GLfelRN8D9xjJtxLsJx0+ZD0v3l+6LkNvzCiLLBComcCOGb8D/1a+NCONvFb1eJrkk2ZP/0ry7UUe+YxPjNfRvEdfb5Jiu76ZWbv573y2kB7ypvlC+kT/p8PGE904G4MABCBQGYGrVN/Nojp7R/4qyQ8oHCj9RbPMl/wPka6M8rZNOo9HQA+W/MSuDzp+MMqX5WzpAaZJvvPf65IEX7p7j/QOySMrfoK3yw7Vgpz7bdPRmK7ySIdArQR8ohkeIhrUBgergyx+84dPYH8zKPMClvnE9njpU5JPUm+RvN84QfJ98X44szdGoNobV9IQCEBgSgT8sIFfOxMeavLI6tOlnMv2Xvcp0gGSL9s7MD1D8mjsJyS/EWBUCw9JuD6DAlUH0Q6Mh9mwYHnY+iyHwKwT8AnnuRmVdEDYZb6VJg5kfe+508Zh/9YU+ib9D1d5fBXlxZJPfkOg6qstjvNcj5ubdfwvXKm5pklzPtvqzf/wL82XLJ7MLIHqZDizFQhAoB8E1lQzHLj5NS6x+WARnux1kOoDg+8ZDbZaM+GnbX2w83sN/6dJu0z/X35nzjsmHKj69TN+qKrLvD3XJw02w4Er1Kdr/f21wPUYZm9XBo8WYxDoKwFf+j82o3F+G4fztpkD0ydHC3IeimorJyfNV3UukcJvPazj9zA/U3qw5FdLhf3HBpqO90fhbQFheZwvlOX/ab542cSmCVQnhpoNQQACPSDwAbXhm5JfCxXMDxv5Utw5TYLvX7Vie4VmPib5Mp1HX4P5QYhtJV+yi823EBwhxaMgDkq9Lb+CxvZwyXUJT+42yXcL71AN9Qnp6X8u/adEmF+sBEpc+velfv8eJ2HeB6wv+SFMbzfYEk04YP51k3CM/od3o8aBqm9zcJsvb/L5wazzJad/uEnzP8/7xDwniI9WY7ImAnEHqqne1LUcAfpAOZbjLCnXT8tUCY9a+IBg86ilg1ePkvoSfpc5UPU2HNDG5iDTwejjmkQfeDya6gNHeMAh5PeBxqOn920Sluq/y/SoqNezeaTF99F65LbPluuvPjOgbcMJzGI/8WV2n4QOs6OVIQSSad6/VkL47YdlPgm+VfL97rEdqJlLpYc2iTvpv4PX7VfOtuKF/w5yQ7r3cT+X3prkm/TsLPpw0gzGuj0AjxVvFYXTB6pw00qjEoNq7EDwQ5JHH3y5zPeQOijcrmMlj5bOST44uS9c0cyHYNP3gB0l+UDiMn2fnO8xe5CUmkc1nOeezQK/LWAPyZcjfyBdKP1E8oNcHqnts/G76rN3y7VtlvqJf6Nzki/X+7YeT8ejl6HVH2+W+dV1Djydr+3qiK+6nCb9SPJVGj/t/2ppFSk2v91pH8n5vM86S3Kw2mbPUaK35XzO71fshZPgtvyTSJslH06ivRPfBoAnjnzmNkgfmDmXtFYIP7VimdlE/DWzrpmpitFPZsod86oMX6aaFzZWggAEIAABCEAAAhAYOwFe+D92xGwAAhCAAAQgAAEIQGA+BAhU50ONdSAAAQhAAAIQgAAExk6AQHXsiNkABCAAAQhAAAIQgMB8CBCozoca60AAAhCAAAQgAAEIjJ0AgerYEbMBCEBgkRDwK6c+KvlJ4w0XSZtpJgQgAIGxEiBQHSteCocABBYJAb+w/7vSVhnt9bsKz5b8rkK/xP/1Utu7Ch+tdL+j1Xn8kQG/c3F1CYMABCAAAQgUIcA73IpgrLoQ+kAd7luonz6jZvrLVHtKg0ZU/fWX8ElDk1kq+Zvc6ddfHqI0fybx7c4k8wv8T5GOa+YX+7+F+mux81ss7aef1O9pfDhmHwJ4zIArKJ4+UIGTVMWF+smfUrUNC1S/rzz+NGJsb9HMjdJaUaI/y+rPF8ZfmdlG865n11dl4jL7Pr1Qf/WdD+27gwD9pP6ewAv/6/chLYAABGaAgD+LOMx83+rm0klJRs97xPRZUfoumvbnEf0JxWDf1oQ/q+hlGAQgAIFFQYB7VBeFm2kkBCAwAwQcpNqWJ3UJ82G5R1bXa8l3m9Iuk0K+pBhmIQABCPSPAIFq/3xKiyAAgdkksE5TreuT6oX5tZv0rnxe7Lwh32y2klpBAAIQKEggvv+pYLEUBQEIQKB3BLy/XC1q1S2a9qV4DAIQgAAExkSAEdUxgaVYCECgdwR2VIuui/S5EVt4dZM/fcXUGk36Nc3/rnxe7Lwh34ibJzsEIACB+ggwolqfz6gxBCAwHQJnarNPjjbtoHUU83tTbRskKz2imQ/Lr9X8FS35PLCwvuRXYWEQgAAEIACBBRPg1RgLRlh9AfSBOlxYyk/DXk/lYPSoBMk+mvfrqeJ7Tw/W/FVSeO2VV9la4vVUd8Ar5a87SuNvXwnQT+r3LD4csw8BPGbAFRRPH6jASapiKT8NC1T9wv/fSds3WJbov9+X2vXC/5Du11edLB3frLfY/5Xy12Ln2Pf200/q9zA+HLMPATxmwBUUTx+owEmq4kL99EqVMSf5/lGXdXkzv1FL8/0J1XMkj67+SNpbavuE6iZK95eowidUP6Lp9P5WJS1KW6i/FiW0Rdho+kn9TseHY/YhgMcMuILi6QMVOElVxE91+CnUEn/V5a9p1ZZ+Mi3y5bbLl6nKsaQkCEAAAhCAAAQgAIGSBHg9VUmalAUBCEAAAhCAAAQgUIwAgWoxlBQEAQhAAAIQgAAEIFCSAIFqSZqUBQEIQAACEIAABCBQjACBajGUFAQBCEAAAhCAAAQgUJIAgWpJmpQFAQhAAAIQgAAEIFCMAIFqMZQUBAEIQAACEIAABCBQkgCBakmalAUBCEAAAhCAAAQgUIwAgWoxlBQEAQhAAAIQgAAEIFCSAIFqSZqUBQEIQAACEIAABCBQjACBajGUFAQBCEAAAhCAAAQgUJIAgWpJmpQFAQhAAAIQgAAEIFCMAIFqMZQUBAEIQAACEIAABCBQkgCBakmalAUBCEAAAhCAAAQgUIwAgWoxlBQEAQhAAAIQgAAEIFCSAIFqSZqUBQEIQAACEIAABCBQjACBajGUFAQBCEAAAhCAAAQgUJIAgWpJmpQFAQhAAAIQgAAEIFCMAIFqMZQUBAEIQAACEIAABCBQkgCBakmalAUBCEAAAhCAAAQgUIwAgWoxlBQEAQhAAAIQgAAEIFCSAIFqSZqUBQEIQAACEIAABCBQjACBajGUFAQBCEAAAhCAAAQgUJIAgWpJmpQFAQhAAAIQgAAEIFCMAIFqMZQUBAEIQAACEIAABCBQkgCBakmalAUBCEAAAhCAAAQgUIwAgWoxlBQEAQhAAAIQgAAEIFCSAIFqSZqUBQEIQAACEIAABCBQjACBajGUFAQBCEAAAhCAAAQgUJIAgWpJmpQFAQhAAAIQgAAEIFCMAIFqMZQUBAEIQAACEIAABCBQkgCBakmalAUBCEAAAhCAAAQgUIwAgWoxlBQEAQhAAAIQgAAEIFCSAIFqSZqUBQEIQAACEIAABCBQjACBajGUFAQBCEAAAhCAAAQgUJIAgWpJmpQFAQhAAAIQgAAEIFCMAIFqMZQUBAEIQAACEIAABCBQkgCBakmalAUBCEAAAhCAAAQgUIzA3VXS7cVKoyAIQAACEIAABCAAAQhAoAoCnARU4aaxVpI+MFa8xQrHT8VQTqQg/DURzNVvhH5SvQvvdjuX/ut3Ii2AAAQgAAEIQAACvSRAoNpLt9IoCEAAAhCAAAQgUD8BAtX6fUgLIAABCEAAAhCAQC8JEKj20q00CgIQgAAEIAABCNRPgEC1fh/SAghAAAIQgAAEINBLAgSqvXQrjYIABCAAAQhAAAL1EyBQrd+HtAACEIAABCAAAQj0kgCBai/dSqMgAAEIQAACEIBA/QQIVOv3IS2AAAQgAAEIQAACvSRAoNpLt9IoCEAAAhCAAAQgUD8BAtX6fUgLIAABCEAAAhCAQC8JEKj20q00CgIQgAAEIAABCNRPgEC1fh/SAghAAAIQgAAEINBLAgSqvXQrjYIABCAAAQhAAAL1EyBQrd+HtAACEIAABCAAAQj0kgCBai/dSqMgAAEIQAACEIBA/QQIVOv3IS2AAAQgAAEIQAACvSRAoNpLt9IoCEAAAhCAAAQgUD8BAtX6fUgLIAABCEAAAhCAQC8JEKj20q00CgIQgAAEIAABCNRPgEC1fh/SAghAAAIQgAAEINBLAgSqvXQrjYIABCAAAQhAAAL1EyBQrd+HtAACEIAABCAAAQj0kgCBai/dSqMgAAEIQAACEIBA/QQIVOv3IS2AAAQgAAEIQAACvSRAoNpLt9IoCEAAAhCAAAQgUD8BAtX6fUgLIAABCEAAAhCAQC8JEKj20q00CgIQgAAEIAABCNRPgEC1fh/SAghAAAIQgAAEINBLAgSqvXQrjYIABCAAAQhAAAL1EyBQrd+HtAACEIAABCAAAQj0kgCBai/dSqMgAAEIQAACEIBA/QQIVOv3IS2AAAQgAAEIQAACvSRAoNpLt9IoCEAAAhCAAAQgUD8BAtX6fUgLIAABCEAAAhCAQC8JEKj20q00CgIQgAAEIAABCNRPgEB1Nn34GVXrdmnT2awetZohAvSVGXLGgKrgpwFwJrBoibZxunT5BLbFJiCwUAKvVgE3Sq9YaEGsf1cChynJAVaq99816912V9r3pQulS6VDpQe05NtOaSdKl0hz0rHSJi35ZjHJHEa1J2mFwK8tUM3l8XCVc6S0XPqxdLb03MzKjOLHzCIHZttNS9M+4/lzW9aqrf25feBhHQy8/v1bODhpWF+pqQ90NHGl5PM15748DsNP46A6vjJz/eUavEiak3wM6QpU/0TL/l06p5H72UnSU6XUFvK7SstifrwERukn3s9+TLpI+pH0VemR463eXUp/oFKOkXy8dt27AtXttey/pfMkHyfdXz8lbSCllnvMTNcrPf9oFfgN6YeS6/thafWMjYziw4zi7nY3Bzj7SQ48Ym2ZrP0mzf9OenKT7sr6bPdb0j2ivNtq+vfSm5u0u+v/+6SrJe8sZt1GBez2nSl9RfK6aaCay2Mtrfsz6YvSqg2k5+n/H6Sdm/lB/3L9OKiMUZa5r3jEKe03z0oKqbH9uX3AgapP3FIGnr9nC8xhfaW2PtDSxJWSnqC5WyTzdD8obfipNNHxlpfrL+//TpHWl46WugLVPbXsSmnDpto+DvlYc7O0WZPmfwv9XUVFMTkBArn9xPvT06SvSe4znn+XdIXk4HFS9nZt6B8kH/td965A1X35eGmNpmJr6r9jqJ9K927S/C/3mBmtMpbJh6jUX0pun+0+0inScc38oH+5PhxUxkrLHOBsPSS3O8ENkkf7YnPQ6gr57DeYHXGZFN+icD/NXy8dEuWb1clRAb9EDfFZvDun100D1Vweb23WT88GT1S6zxSHWY4fh5UxynIHY/tkrFBj+3P7gAPVwrVhPwAAIABJREFUr2cwCFmG9ZXa+sCwpn9QGV4r+WTr0GGZ57EcP80D2hRXyfWXA45w/BgUqPpE3gFCbP5NejseWAm20N/VShtgZuwEcvuJ/Z8ecx3w/UZywDrMtlCGk6W2q18OdB0EP2pYIVoeBuqGBaoHKO82SXk+jroNW0XpucfMjKotKMsHtPbPpVWiUlx/13enISXfPo17VO2s1SRfxovNQ9i250SJHon1MPFtUdpvNX1Jki9aXO2kfxQHSXsPaEEuD+fziPVPkrLMeGNpowHbmOVFi739wTe5fWVW+8DSETvZvZR/e+lDkkc8XiD5jHzWrXY/zTrfnPr5QBgfP7rW+YIWfCRZGEarro7S+7pv7eKyWNJ3UUN/JV0QNdij6WdIXjbMPFroq7zeP3kwLZgDV48aeiQ+7kdRlpUmfSKeY/spk69Axxb66zVRYu4xM2ebC8ljhg7Wb40K+bamHc8N5TuOQHV3bdhD0A4wDXIvKd6OK2aLL/F7PuxMHEgFc940X8jroeTgmGiVaif3Vs1Plb43oAW5PJzPIwlWbG2MuzY3zI9d6803/Ula0SOKvt/GAfV7pfSe5T6339zWkz4tfVe6SPqk1HY/dm5fmdU+4ABuDzc40/5C+Xwbi3dyvpLiy1weAZmWLRY/TYvvLGz3EarEwZIPrvHVvxL71lloH3VYmcDmml3eAsVpG0hx8NmS7W5XKXFHycHqlyRfOfaAnJ+p8a2NT5fiAFKzxcz7eY9O+qqkR389kBcs95gZrbLSpAPtYfL+eJA5SPc+M+XreOQyyewHWulA9QZtzWcNz5AeI/kyiSP/w6NazGn619LjozRPPraZj4NPB20eAo/v0XOHCZe0+xKorqs2vUbat2HQ9S+Xh/N5FMrsYmtj3LatHD+2rTffNJ+52l4uuY4OQp4q+Ww2vtm6r+1328OZtAP0JzbyaNB3pC2cobFR+sqs9oEL1RYH4O7zOeZLWh9rMnrHf6n0NzkrjiHPYvLTGPDNfJE+tvg+Vt/r51vMPHrvKxPBFrpvjYpicoYIrKO62N+pOc2BoIOtYTanDA5IHXgdJX1Z8u0jT5McyI7DXqpCHXOdKjnO+udkI7nHzLa6eUDhugwNC8DN1tbFd+22jU86zVG+D7gegg72ak14dGRXyZ3AB1+Pvv6fdH7IpP8OWvwwlQ/ePuganEdUHEi5zJlooOrRZa5jjn1cmfaPMnbdo5rL474qa046WXIn8QnJy6TAbZdoW7mTbX7MXXc++bbWSua3d7Ryje3P7QNtjOxH7wS+Ei3M7SvT6gM7q67+HQ/TTcpjNt4HDLIHaeHnkgw+AXbA6LP0UrbY/FSK27TKmY+/jlZlHYTmmAMT3wrgS7pPiFYYx+8qpz7kmR+B3H5ypYo/vmUT71Say/BIaa55oMGjhY5dHp27UpLPg0zebtfDVGmxGynBV7LPkTwCGiz3mJmW53nHDTtkaPu2laM0181t8X47tTOVEI8Ap8s933mP6kla2Hag8QjXqOb7EGwOPIL9pyZeKb1e8sM9Pvt4TzP9sztz3XEZ+M8079GXH0j/K3k05TDJQ9qO9ms3j5b5LOzdGQ05V3lyeNyofE+R5iSfAHg9X1oPI1gxYyVnWZsf0xUPUEJbv3HammnmIfNnabmDkbjfzHr7hzRp5MX24wURg1H6yrT6wNmqr0dAh+kzynOK9NUhVFzOk6W5SP+gaZ/g+uRrFqxGP5X8rc6CD0rX4VoVuKfkUaCDo8LH8bsqXXfKG52ARyXjq3ehBF+1dZDl/pBjDu4c1zg28Uj8P+WsVCDPj1WG95WPk94UlZd7zGyrgoNtr5+jtvVDmtnauvgOG5HtLNvD1Ru2aNBZhe8lbRsed8BkR+/VubU/LnCD3paRzyMsJ2Tkm3aWnLO5N6iSPmufi2QOXveKJu2FQxqSy8OBqkdVPTLdZQvxo0e42/qN0/wD7rIHtixwPW6RPt+yLE2alfan9fJ8Th9wPgfyvmqQmk8aw06yRF8Zdx9I698271Ep33/r/8PMJ6ertmRyum8hKGWLzU/z/a2W4r3QcnL9FW9n0IiqH87zyU9qX1DCzWliy3zO76plNZLGTCC3nxyhevg4nJpvNbo4TRww7zeS+OTGo6o7SL5y9N4B+bsWbaoFrnvXiGrXvtMB8je6Co3Sc46ZjhNch2G6NWN7vpLx2SSfYwIPYh02ZP1cHw4p5o7FS/Wv7bLK65TuDW0XlbKlph+alOoRP+8QlkTp62vao0ix+R5VH7iHBW/JalOZnS9gd06v684aWy4P73R3bGnxcUrz5azYHCD58mqwpZrI9WNczkKm57Syg9nYfGZoBvGJyzja75Oy+Ee/VPMl25/bB5Zpu+lOyQGad56DTsq6+sos9wGfvHbtaLXoTnMfcHDRZm9WotnGI+5t+XLT8FMuqdnIl+uvuLaDAtVvKmN8jArrnaUJXxYONsrvKt4209MhkNtPnq/qOa+frQnm/e+vpXdFaYMm/0MLw4h7yPcsTfgWgP0HrdiybFCgukqznXRgw6O/vgr5qai83GNmSxWKXfp32b4qcZXkAahg4fa+naK0tslcH7ate5e0pUpxgT6AhDPTzTTtyqURviPoIyUDt3mk9vvSa5v58G83TfjWgDBS64PbEZLPcmuw+QLuCj5yeTj4ctDvA73N/vAZ/8XSOk1a+PdDTTjwD4HDUk3n+jEpat6zc1rTZ3g+CbHZ36dJHlGO61u6/ebkyzNfX7HVO2yp/pVsf24fWKbt+vLNkqYe/kF/QPKosgO7LuvqK7X1gbb2uf32eZs9Wolme0jbwnmk4ad5QJviKrn+iqs4LFD1Pic+afc+09uJL6WO8ruaIh423RDI7Sc+Rtr/vhUpBIDv0LRPUtqu+KWAn6EEH0vagq6/Uvqtkgfjcm1YoOp2ef8YrjaF2MhB8XbRRnKPmbn1mm++h2hFD7qE+1R9wney1HZfcLqNXB+m67XO27l7SCdKvp/Ul+V+Ih0kuVKxvVQzPlNdLp0t+WzWzkzt8Uo4QfJ9qb5PwnnfIt0zzTij86MC3lbtmJOulrxuuPQfgshcHj6z8n2/5na+ZHY+oMc7Yc2uMF/acJ7AdBQ/hjIW+t8/7s9KDpp9T+Zl0uGSzwZjK91+X/70/bofjTZSuv25fcAndR+S7Ivzmnr5BC/e6UTVXPHFkTmpq6/U1gfitnnabffJlg8Ur0wWhrabrQ8OFyfL5zOLn+ZDbXrr5PrLNfy4NCf5uQYHDJ4+R4rNv7Nlko9dHjTxvsiBy65xJk2P8rtKVmV2CgRG6Sf3V/0Okzxg4AGyr0kbjVDnzQfkTa8Md2X1cWBO8rHfdff+3fMvk2JzAOqg2v3U/dX1/bzkWw5iyz1mJquNZXYTleqruq6zGfvq7uoZWxrFhxnFkSUlAOCUyOKbpw/U4XP8VIefQi3xV13+mlZt6SfTIl9uu51P/ZfbBCVBAAIQgAAEIAABCEBgHgT81BUGAQhAAAIQgAAEIACBmSNAoDpzLqFCEIAABCAAAQhAAAImQKBKP4AABCAAAQhAAAIQmEkCBKoz6RYqBQEIQAACEIAABCBAoEofgAAEIDB+Av5krJ9A9vsRMQhAAAIQgMBMEODVGDPhhqlWgj4wVfzZG8/108NUovO2ye9hbDO/6DvkbwtU/cGTI6Xlkt8v6PdFP7etoJY0v/exrS7vb8k7ziQPevhjL35Hot8D/F3pmWPcYK6/xlgFiq6AAP2kAicNqeLt4ctQQ/KxGAIQgAAEGgIOxN7TQsMvlE/NX7z5D+kYaed0oeb9FbYzJAenG0v+gMHzJL+828Gq1xtm+yvDJUkmvwB8kvYv2phfSr6N5JeVP1v6svR06dRJVoRtQQACEIBAPgHO5vJZ9TUnfaAOz+b6ySOq8Sd3h7XuJcpwktT1qVt/UtDbfmRSkL/wlxNsekTV38yepq2rjTvA3jOphL8u9u0xVSzXX2PaPMVWQoB+UomjBlSTF/4PgMMiCEAAAgshcG+tfJC094BCttQyB3n+3HRsHrX1COson3BMipjYrEeK/elhB+SxeX4rycE9BgEIQGBeBHiYal7YWAkCEFjEBNZT2z8t+T7Mi6RPSv6OdWoOUH3Z+3vpgmjetwv49gArttuaGQerw2x3ZThd8v2h35L2knL27Q6kfV/tMK06pALhG+fLk3xhftA30IcUzWIIQGCxE8jZmS12RrQfAhCAQCDwh2bivfr/xEa+vPgdaYsIky+Hv0baN0prm3QQ69HI9CGrxzaZ12hbKUq7QdNXS8+QHiP5VoL9pMOHrOfF+0vXZeiNQ8paR8tvlW5K8l3fzK89ZH0WQwACEIDAlAhwf8yUwM/QZukDM+SMAVVZiJ/uq3Kvkb4Slf9xTe8fzXfdo+p156STJQd8HjzwQ0kOQF2nXaRRbZ9mXd9WMMg20MIdMrRkUCFa9inplpY8furfbfjrlmULTVqIvxa6bdavhwD9pB5fddWUp/67yJAOAQhAIJPAjcp3gRQeavLIqp92z7ls73WfIh0g+bK9RyX9FgCPxn5C+pk0qoUHmFwfv02gy67Ugmu7Fkbp6UhpuopHdP0GGd9KcHO0MIwGO4jHIAABCEBgBglwNjeDTplwlegDEwY+z83l+mlNle9L9an5waEQ9L1B07+U5iI5mPM2/Oomp79QGmQOVD2q6uCvy+6hBX69VWoOfL0t36s6yN7Z5HPeQXrboEK0LIwWp/fp+r2qLnccD1Pl+mtI1VnccwL0k/odjA/H7EMAjxlwBcXTBypwkqqY66dlyuvALDY/bOTA9IQkPZ7tuvR/H2XasWW945T2kSTdQfKDorSlmr68Zd3XKc3t2a5lWZxU6tJ/eD3Vq5PtfV3zvJ5qiBNYPFYCub/rsVaCwhdEAB8uCN/wlQE8nFHfc9AH6vBwrp+WqTn+etSSplke1fyA5Hs0PZLZZV2Bqkcbfbn8cc2Kfvrfo6kXS75nNTY/1e9RW9/Xalsqud4euQxvDdhM01dJfofpJO1AbexS6aHNRnfS/99L24+pErn+GtPmKbYSAvSTShw1oJr4cACcEosAXIJi3WXQB+rwX66fHAh+SDpf8rtOfQ+pg8Ku0ctttWxOSi/9h2DT93EeJTnIc5nnSodI8cipZlfYsZLz3LOZ9y0Ie0j+OMAPpAslv4/V7271SO0kzQ+B7SP9SDKXsyQHq+OyXH+Na/uUWwcB+kkdfhpUS3w4iE6BZQAuALHyIugDdTgQP9Xhp1BL/FWXv6ZVW/rJtMiX2y5fpirHkpIgAAEIQAACEIAABEoS4IX/JWlSFgQgAAEIQAACEIBAMQIEqsVQUhAEIAABCEAAAhCAQEkCBKolaVIWBCAAAQhAAAIQgEAxAgSqxVBSEAQgAAEIQAACEIBASQIEqiVpUhYEIAABCEAAAhCAQDECBKrFUFIQBCAAAQhAAAIQgEBJAgSqJWlSFgQgAAEIQAACEIBAMQIEqsVQUhAEIAABCEAAAhCAQEkCBKolaVIWBCAAAQhAAAIQgEAxAgSqxVBSEAQgAAEIQAACEIBASQIEqiVpUhYEIAABCEAAAhCAQDECBKrFUFIQBCAAAQhAAAIQgEBJAgSqJWlSFgQgAAEIQAACEIBAMQIEqsVQUhAEIAABCEAAAhCAQEkCBKolaVIWBCAAAQhAAAIQgEAxAgSqxVBSEAQgAAEIQAACEIBASQIEqiVpUhYEIAABCEAAAhCAQDECBKrFUFIQBCAAAQhAAAIQgEBJAgSqJWlSFgQgAAEIQAACEIBAMQIEqsVQUhAEIAABCEAAAhCAQEkCBKolaVIWBCAAAQhAAAIQgEAxAgSqxVBSEAQgAAEIQAACEIBASQIEqiVpUhYEIAABCEAAAhCAQDECBKrFUFIQBCAAAQhAAAIQgEBJAgSqJWlSFgQgAAEIQAACEIBAMQIEqsVQUhAEIAABCEAAAhCAQEkCBKolaVIWBCAAAQhAAAIQgEAxAgSqxVBSEAQgAAEIQAACEIBASQIEqiVpUhYEIAABCEAAAhCAQDECBKrFUFIQBCAAAQhAAAIQgEBJAgSqJWlSFgQgAAEIQAACEIBAMQIEqsVQUhAEIAABCEAAAhCAQEkCBKolaVIWBCAAAQhAAAIQgEAxAgSqxVBSEAQgAAEIQAACEIBASQIEqiVpUhYEIAABCEAAAhCAQDECBKrFUFIQBCAAAQhAAAIQgEBJAgSqJWlSFgQgAAEIQAACEIBAMQJ3V0m3FyuNgiAAAQhAAAIQgAAEIACBKghwElCFm8ZaSfrAWPEWKxw/FUM5kYLw10QwV78R+kn1Lrzb7Vz6r9+JtAACEIAABCAAAQj0kgCBai/dSqMgAAEIQAACEIBA/QQIVOv3IS2AAAQgAAEIQAACvSRAoNpLt9IoCEAAAhCAAAQgUD8BAtX6fUgLIAABCEAAAhCAQC8JEKj20q00CgIQgAAEIAABCNRPgEC1fh/SAghAAAIQgAAEINBLAgSqvXQrjYIABCAAAQhAAAL1EyBQrd+HtAACEIAABCAAAQj0kgCBai/dSqMgAAEIQAACEIBA/QQIVOv3IS2AAAQgAAEIQAACvSRAoNpLt9IoCEAAAhCAAAQgUD8BAtX6fUgLIAABCEAAAhCAQC8JEKj20q00CgIQgAAEIAABCNRPgEC1fh/SAghAAAIQgAAEINBLAgSqvXQrjYIABCAAAQhAAAL1EyBQrd+HtAACEIAABCAAAQj0kgCBai/dSqMgAAEIQAACEIBA/QQIVOv3IS2AAAQgAAEIQAACvSRAoNpLt9IoCEAAAhCAAAQgUD8BAtX6fUgLIAABCEAAAhCAQC8JEKj20q00CgIQgAAEIAABCNRPgEC1fh/SAghAAAIQgAAEINBLAgSqvXQrjYIABCAAAQhAAAL1EyBQrd+HtAACEIAABCAAAQj0kgCBai/dSqMgAAEIQAACEIBA/QQIVOv3IS2AAAQgAAEIQAACvSRAoNpLt9IoCEAAAhCAAAQgUD8BAtX6fUgLIAABCEAAAhCAQC8JEKj20q00CgIQgAAEIAABCNRPgEC1fh/SAghAAAIQgAAEINBLAgSqvXQrjYIABCAAAQhAAAL1EyBQrd+HtAACEIAABCAAAQj0kgCBai/dSqMgAAEIQAACEIBA/QQIVOv3IS2AAAQgAAEIQAACvSRAoNpLt9IoCEAAAhCAAAQgUD8BAtX6fUgLFjeBz6j5t0ubLm4MM996/DRdFy3R5k+XLp9uNdj6jBPoaz/pa7vm3Z3W1ZqHSudK50vLpU9L901K3F3z35culC6VvM4Dkjye3U46UbpEmpOOlTbxggrMAUSOPUyZnLdN908KyOXxcK13pGT+P5bOlp6blNU1e5gWtNXl/V0rFEhfVWW8ramn+477xNelzZKya2t/bh8IzXyxJr7ZcPip/n9b2jVhEGafpIngp7ZAtbY+0NHMiSTjp4lgLraRUfz1Im11TvIxpCtQ9e/nI9KPJB+3fih9WPLxrM22VOIx0jnSRZLXO6AtI2lTJVC6n7gxPiZ/TAp+/6qmH9nSSg8EvllyXzpP+q70zJZ8407K6f8PViXeLvnYe4Hk/vxl6XEdlZtk/x/Fhx3VXTnZP2oHRn8v3b1Z9Kf6f4u0TpT1TZr+nfTkJm11/ffZ7reke0T5ttX07yU72+Yy3yddLfkgPOuWC9iBqoP23Vp0z6iRuTzW0jo/k74oOQC0PU/6g7RzMz/onwPV/aS0Pu6c4zD/oI+V/ku6d7OBB+m/Dyx/FW2wxvbn9gE38y3SWdJ6TZvvpf+fkz4UMQiT/i2cKX1F8jbSQLW2PtDSxIkm4aeJ4l7wxnL95f3fKdL60tFSV6DqA/TXpDWamj1Q/31y7+PZak1a+LeDJq6Sto7S99a0D/DYbBEo3U+83z1Ncl9x3/L8u6QrJPeZ2A7UzGVS2J8/W9OOZ7ZP8o1zNrf/exDKg0MbNJVx3OHj8c1SetzfQWmT7P+5PmyqPvzffyuLg6PUnqEEH3RtBneD5NG+2By0ukKO/oMdrwk7Or5F4X6av146JMo3q5O5gB2ofj2jEbk83qqyvO30LO9EpflMaZg5UI13wsPyL3T5y1XAL6QQVIfyHq+J8CN3Wo3tz+0DG6l9t0iPDY1v/vuELE3zopdIJ0mvkLyNNFCtrQ80zZ3aP/w0NfTz2nCuvxxIhOPHsEA1/Z3t0vy2XhrV0AMpPoF+bVJrn2A/fV4tYaVxEijdTzzgk+5v7fvfSA5Yg3nQzoNxe0ZpnvyG5Ktkw8wnTCdLaZ/0eu6Dn5a6rrTFZef2fweqaZ9eW2lu68eiAqfR/2+PA8C4cfOZ9qjoCyUPF6dm5/hMwvYoyWeo5zfz4Z+Hxm3PidIdyXvY/LYo7bea9o4izhct7vVkLg/n84/kJwkNM95YclA0S+Zgy33EdY7Nl9V8phqsr+13+/5G+rl0btReT3pkPE3zjvEgae8kbzxbWx8Y0JSZWoSfZsodQyvjA218/OhaYSstSH9nVzaZ41vS/kxpHnVKj3MeefKJNFYngdx+soua9yspHj2378+QvCzYzprw4JwHE2LzvPuaB6cG2Y1a6AG54yQfs4M58PRAkkdn56L0rsncdr1BBRycFHKN5n1Mnnr/LxmoevTLI2I3SR+Xzpcuknzv6UOkYA40bfElfs+HnUnsFOdN84W8LjNcpllRYOXmkUOfJfk+FnP7pJTei5vLw/ncoa3Y2hgnWe6c3V1Tp0s+UfiWtJdUsr+EDfkSwxMkX5LbX3Jw6gD7S9ITpdj62P7QPt9verHk0Zv/lS6UfK/qi2MAzbQD1FOl77UsC0k19YEBzZi5Rfhp5lxSpEJhICUuLJzQ+7cWzP73fvSBki//ev/oAPefJe/LsH4T2FzNW97SRKf5BMZXfG3OZ0vzhvmwvMl2l3+3KuUFkgeXTpCWNjkcTHpA0IGwY4VS5u2lJ3RLlOaY7pRoI9X3/93UGEfvPgvw5XsHNQ+SfLD1CGgIKh14Xif53rvYwqV/H6yD+az1KineAYRL/97WsLOSuPxpTLuOOeag24G9R8FsZnW49H/SFk2a/+XyeL3yetvpg0i+9O90+2qQ+T7gf5P8AJyDXY8i+OzqiEErzXOZfeg6ua0fkPzD8IjhByWfqQYmmqyy/bl9wP3eDE6T/Lvx7+clkncer5aC+ZKSR14f2iR0XfqvqQ9EzZvaJH6aGvp5bTjXX3Hhgy79p5Xwfs/HrnSfd5jS/iD9VHpcs5L3Uf5NHtXM8292CJTuJx5lbxs5f6fSvS3fqmX7lHRLMx3/e6ZmnO+vW5a1JTne8WitYyg/q+ARzp3aMmakjdL/XZyv2v1Yih+En0b/n48PO3GEA+YxSQ6PinlD/xSl+8B7q7Sr5B2CD74etfOB2gFbMN+f4TPd90oeRncAc4h0g+Qy15Zm2RYC2J3DweFXogbm8vC6c9LJ0jqSg56XSYHbLlGZuZP7KKPbEweOuesOyrdhU+7V+u8gNZh97fZ/IUqrsf25feBytdN5Pboc21c1YzbhyoKvVuwfZegKVGvqAyu3eDpz+Gk63Oe71Vx/xeWPcqB+nVa8QFozqaADV2/7DUn6G5v0eGAhycLsFAiU7ieTDlSN7P6SbwFzW7y/n6+N0v/9ELyPv+FkLGxzGv2/8x7Vk1QrB42pHNl3mYMgW3qfj+cNOL6M+5+af6XkUR8/3OMz0fc003ZIMK/r0TxfAv+B5Euil0qO6n8reWS2r+Z7VLyj3DpqYC4Pr/sUaU7yCYDX85D9a5qyYsZN0tB/4QbwuD7pSgcoIe0zYT7d4Yd1Q7+5UAk+Wwzm0VT3jbjfzHr7o+qPPBlOInypJ7bvacYnZI+QfBB8uvTulbO0zk2rD7RWpkeJffHTfH6rPXLjwKb4kus/Sh798kMysXUd5/w7tcX7q5XXZK4PBDxosHpLQ3wV1HHOtc0y51tF8oBLbOHKsoPAXPOVNV9B83H776VQRu76o+bbWCs4JvPvIPTrUMZU+r9BtplH31LAzhcHEul6DjRsHr2Lzc6z0vRPKM2K7VDN+N7E2L6pmWclaZ/T/JlSek9Fkq2aWQdxvrfXo8ex+RJTGEkL6bk8LtMKL0/Kc6DqwDENhuJs3p7rE35wYZnrYkvrE5b7/8HSJ+OEaDp08HSxn/b3CUfaP5zP20zTZ7n9adtGmffvxzsIX2GILXA3Bwep/l3+MMqwWjP9Df33paY3S//TpE2jD0RV6+VkX/w0n99qLx2aNGoXzf+r9DTp8pYGdx3n4t9py2ok9YSAj51/3tIWDyT4dhAPoNnCMXYDTcf7a+eLlzeznf98i8AHJZ84fUU6XTpG8kmUByNK26NU4Nekv5NObCm8+v7vA+ycZIixbaYZB6q+lBJsS02Ee+xCmkf8PIq2JMq3vqY9ihSb79lwEOUbimfd3O4cW6ZM6ZC+L4P/UjohKiCXx320zo4tGz5OaR9J0h2UPihKW6rpth20/ef2bJesX2L2cBXiM0zf3hHMJ1EOYuMTl3G03/fI+jJ5sKWaKNn+3D6wu7brvE+I6uJJn5SZTdcJgvuN19s0Wa+2PpBUf+Kz+GniyBe0wVx/xRsZdunz+crsB1m9nwm2jSb2i+b/RNMeIHlDlOZJDwK4Tuml0iQbsxMmULqfuI+4zMdE7fCx+tfSu6K0dTXtgT3f5hjb1zUTrk4mi+4y6235FknfVhJsqSZ+JnlgIj5eRlk6J4f1fwepl0geEAnmbXw5mp9G/5+PD6Mq33XSQ8UG62jf5oOlo3M3Ph6u9qX7IyUHI7aHS9+XXtvMh3+7acKXf9dqEhxQHCF9Ick3q7O5gJepAT+WljQNcVDyAckjZE+JGpfLw8GXg/6w0/RJhHekF0vrROV50md7DvxDsLZU0663R+bC6J5PNq6S/OMYh22oQn8jHRgV7oOD2+CTmmCl229O3pl45xFsqSZKtj+3D/iBQd/RVTdwAAAgAElEQVTa4Bv1gy88quM+kO7sQl39vytQra0PxG2axjR+mgb1+W8z11/xFgYdqB0U+KrWvpL3M0Hv1vSypJof1ryDhTA65v32csmXS7HZIlC6n/iYeJr0VSkEiu/QtO9dfWDSdB/PLpXCoNxOmvZV0+2TfG2zjnl89fNfWxY6oPQgjvvqKDao/2+kgtyGT0hx/3+55ueSjUy6/8/Hh0O5OFj1Addnpm6gR8sekqzlV/CcJfnHfbb0Temvkjyefbx0gmRnu0znfYvkg3oNlgvYgeCHpPOl86RwxrRd0shcHj4p8E7T3Fym2R0ixSOnoehjmzyBqX98e0ge9vd9wR7q/4l0kOQTj3GZg2r7ek7yJRQHbFslGyvd/rVVvll/NNpO6fbn9gFXwTu6ZZIv2fv34/uDvNNos22VOCf5Xihv44pmPgS5NfaBtnZOKg0/TYp0me2M4q+PN78NX5a9tZk+J6mGf3Mus03LkrweYNlP8gCMB1K8f3RAEQKXJDuzUyRQup+4KfeXDpM8uGT/ezDOgV5q/08J+zR5fFx3zONgNdc2H5DR22u7PbNtlZz+7zitre87bS4pdNL9fxQftrWftCEEADwE0CJYTB+ow8n4qQ4/hVrir7r8Na3a0k+mRb7cdjuf+i+3CUqCAAQgAAEIQAACEIDAPAh4aBqDAAQgAAEIQAACEIDAzBEgUJ05l1AhCEAAAhCAAAQgAAETIFClH0AAAhCAAAQgAAEIzCQBAtWZdAuVggAEIAABCEAAAhAgUKUPQAACEBg/gc9oE34COf0ww/i3zBYgAIFJE/BrAv3aQ//m/Z5wDAIzS4BXY8ysayZWMfrAxFAvaEO5fnqYtuK8bfL7FdvMX90L+dsCVX/wxB9AWS753Yx+X/Rz2wpqSfP7HNvq8v6WvH1KyvVXn9pMW0YnMI1+4neC+x3kfg+2t98WqPodqLtLp0t+F6vznyH5E75ttqoS3yZ53+D3ovsd6f5Qjd/BHpv3QR+T/B5ul+sPEzxy5Swr5nLztaw68aRp+HDijZzmBgE8TfqzsW36wGz4YVgtcv3kQNVf0fOHGFK1fYjEX7I5U/J3ur2NNFD1F2j80YkvSj4Y2Z4n/UHauZkf9M+B6n5SWpf4i26D1q91Wa6/am0f9S5DYBr9xFdP/EXJPSVvvy1Q/Uul+6uD4Suebu3fNfnTLxH6yrc/zPNfUnjJvz/e4w9OxB9KCl/N8gcIvC/xvD/r6o/BxF/Nys2n1WbCpuHDmWj4pCoB4EmRnt3t0Adm1zdxzXL95EA1/uTusNa9RBlOkro+dftWLfO201EPfxnOIyLDzIHq1sMy9XB5rr962HSaNAKBafSTezT1Gxao+uQ0NX9J0l86i82fMfUnU8OJbFjmLzWuF2X0Ca7bG58MO7D158kdsAbLzRetMtVJXvg/VfxsHAIQ6DMBHyT86eG9BzTSI5+/k9KDkz+5uLHU9mnGAcWxCAIQmDIBXw0ZZl9WhrbPxl+p9AckK/sk9xuS9xOx+TPAHi0N5tsGfiVdEKXdrOn0loLcfFEx053kYarp8mfrEIBAfQQ8ivFp6buS7wX7pLRJSzMcoJ4q+V61LvP3530pzorttmbGweowC/e6/VAZvyXtJeXs2x1I+161YUpHcobVh+UQqI2Av18/7Hfg5fcr1DD/vm9tKctXVk6J0n070ROky6X9JQenPqn9kvREKbbNNbM8SfOs0zaQQt1z87UUNZ2knJ3ZdGrGViEAAQjMHoEwWvJeVc0HCsuX274jbRFVd11Nv0baN0prm3QQey8pvXf1sU3mNdpWitJu0PTV0jOkx0i+lWA/6fAh63nx/tJ1GXpjRllkgUDNBHbM+B34t+IAcVz2dBX8UGn/aAMP1rT3Dz759EjrNpIfoLpM8oNY8b3o62j+eik1p/lE2PfD23LzpeVMbd5nERgEIAABCOQRuErZ4idtfRB4lfRs6UDpL5pifMn/EMmX8gaZ8/ggdLC0q3St5AejtmpWumnQylr2umS574d9j/QO6X2SnxLuskO1IOd+27ZRmq4ySYdAjQR8ovnUjIo7WB2Hra1CvS/wfa3xpfvw8JQv4b9JCpf/ffLo+9/fJvme014bgWqv3UvjIACBCRC4UdvwwSU81OSRVY+O5Fy297p+QvgAyZftHZj6njKPxn5C8hsBRrVvNyu4PoMCVQfRDoyH2bBgedj6LIfArBPwCee5GZX0k/qlbTUVeIz0cckPR8bmKya2C6X4HlUHrn7YMr787ysrq9+RfaW/virjqz7ht56br6UokvpIwJ0DW9wE6AN1+D/XT2uqOb4Ul5pHMsOB4A2a/qU0F8kHB2/DDz84/YXSIHOg6oNUGFFpy+uni8PlvHi5A19vyyO1g+ydTT7nHSSP2sya5fpr1upNfSZLILefPHPIbyD8Pk4YofoeHfV6Gw5Yx0GqL+EP+o15v+KT19R8/3t8xeYIzXu/k5pfbXVxlJibLy1nWvO5PpxW/arfLoCrd+GCG0AfWDDCiRSQ66dlqs0rkhr5YSMfIAYdxLyOt7Fpsu59NL9jkubZ46SPJOkOkv3+xGBLNXF5ksezvh3A29quZVmc5AcsdsjQkiHlTGNxrr+mUTe2OTsEcvuJT/hyfgu+WpJrwwJVP9x0mpQGqZ9Q2kOijfh+82uk+ATZV8P9yqr4ntnna97t9b3qwbxv+rUUv54qN19UzFQnc3041UrWvHEA1+y9MnWnD5ThOO5Scv20TBXx16OWNBXyqOYHJF8S9Ehml3UFqg/TCr6M97hmRT/04NFUj4D4oYfY/FS/R1f8eUbbUsn1frMU3hqwmaZ9H61fZ9Nny/VXnxnQtuEEptlPBgWqDlI9InqmtFsi//aXRk3bUNO/kQ6M0vbTtPcb8cNU3gc48P2qFIJa36vuUdcHRuvm5otWmerkNH041YZPauMAnhTp2d0OfWB2fRPXLNdPDgQ/JJ0vnSf5HlIHhV2jl9tq2ZyUXvoPwabvHztKulRymb5Pzg9VxCOnml1hvoTnPH5ljc0Hoz0kfxzgB5LvY/Ora/wgl0dq+2y5/uozA9o2nMA0+skrVa05yaOg3r6venh+IynY7prwsi4tjfJ60ieyvmIzJ/1UOl4KD1x6eTC/QuswySfTvof1a1K83VHz3VnwFCem4cMpNnfymwbw5JnP2hbpA7Pmkfb64Kd2LrOair9m1TOzVS/6yWz5Yz614ctU86HGOhCAAAQgAAEIQAAC4yfw/8a/CbYAAQhAAAIQgAAEIACB0QkQqI7OjDUgAAEIQAACEIAABCZAgEB1ApDZBAQgAAEIQAACEIDA6AQIVEdnxhoQgAAEIAABCEAAAhMgQKA6AchsAgIQ6B2BJWqRvyjT9sL93jWWBkEAAhCYFgEC1WmRZ7sQgECtBF6kivtl3Q8d0gC/0/Bj0kWS32noF3E/smUd74f90n6/0N/vZv2u5E86YhCAAAQgAIGxEuAdbmPFW0Xh9IEq3LTixds55k8SniKtLx0tdY2ohq+/+IXbXsfz/ozhFVL8lRjNrvjizGXSep6RPVv6vbR9M8+/uxLI9ddd1yRlMRGgn9TvbXw4Zh8CeMyAKyiePlCBk1TFXD854AxXogYFqs9rytw0av69Ne1PIcbf3V5X87+T/LnF2Py1q28nacz+kUCuv2C2uAnQT+r3Py/8r9+HtAACEJggAR/4bsvY3i7K8yvpgiivv819huRlwXbWhD+FelKU5knP+xOJD0vSmYUABCCwqAhwj+qicjeNhQAEJkRgc21necu2nLaBdL9mmfPZ0rxhPixvsvEPAhCAwOIiQKC6uPxNayEAgckQWEebub5lU07z7QNrNcuc71bppiRvWHftljJIggAEILBoCBCoLhpX01AIQAACEIAABCBQFwEC1br8RW0hAIE6CFytaq7eUtU1lOb7XK9tljnfKpIftIrN+WzXrJzMHAQgAIHFRYBAdXH5m9ZCAAKTIeD3ofpe1NQeoYSfSr9tFjifLc3rfLawvJnlHwQgAIHFRYBAdXH5m9ZCAAKTIfB5bcbvS31MtDm/T3Ub6XNR2jGa9jtTnxqledLz35G63tOaZGcWAhCAAAQgMDoB3uE2OrO+rUEfqMOj8/HToPeohhf++2tUfv2U7R3SlVLbC/8vVXr40tVOmuaF/3cw6/o7H391lUV6fwnQT+r3LT4csw8BPGbAFRRPH6jASariKH76uPLPSb587yf2PX2OlJo/oXqY9GPJn1D1V6o2SjNp3le29mny+FL/WZKDVaybwCj+6i6FJX0nQD+p38P4cMw+BPCYAVdQPH2gAiepivipDj+FWuKvuvw1rdrST6ZFvtx2+TJVOZaUBAEIQAACEIAABCBQkgAPU5WkSVkQgAAEIAABCEAAAsUIEKgWQ0lBEIAABCAAAQhAAAIlCRColqRJWRCAAAQgAAEIQAACxQgQqBZDSUEQgAAEIAABCEAAAiUJEKiWpElZEIAABCAAAQhAAALFCBCoFkNJQRCAAAQgAAEIQAACJQkQqJakSVkQgAAEIAABCEAAAsUIEKgWQ0lBEIAABCAAAQhAAAIlCRColqRJWRCAAAQgAAEIQAACxQgQqBZDSUEQgAAEIAABCEAAAiUJEKiWpElZEIAABCAAAQhAAALFCBCoFkNJQRCAAAQgAAEIQAACJQkQqJakSVkQgAAEIAABCEAAAsUIEKgWQ0lBEIAABCAAAQhAAAIlCRColqRJWRCAAAQgAAEIQAACxQgQqBZDSUEQgAAEIAABCEAAAiUJEKiWpElZEIAABCAAAQhAAALFCBCoFkNJQRCAAAQgAAEIQAACJQkQqJakSVkQgAAEIAABCEAAAsUIEKgWQ0lBEIAABCAAAQhAAAIlCRColqRJWRCAAAQgAAEIQAACxQgQqBZDSUEQgAAEIAABCEAAAiUJEKiWpElZEIAABCAAAQhAAALFCBCoFkNJQRCAAAQgAAEIQAACJQkQqJakSVkQgAAEIAABCEAAAsUIEKgWQ0lBEIAABCAAAQhAAAIlCRColqRJWRCAAAQgAAEIQAACxQgQqBZDSUEQgAAEIAABCEAAAiUJEKiWpElZEIAABCAAAQhAAALFCBCoFkNJQRCAAAQgAAEIQAACJQkQqJakSVkQgAAEIAABCEAAAsUIEKgWQ0lBEIAABCAAAQhAAAIlCRColqRJWRCAAAQgAAEIQAACxQgQqBZDSUEQgAAEIAABCEAAAiUJEKiWpElZEIAABCAAAQhAAALFCBCoFkNJQRCAAAQgAAEIQAACJQkQqJakSVkQgAAEIAABCEAAAsUI3F0l3V6sNAqCAAQgAAEIQAACEIAABKogwElAFW4aayXpA2PFW6xw/FQM5UQKwl8TwVz9Rugn1bvwbrdz6b9+J9ICCEAAAhCAAAQg0EsCBKq9dCuNggAEIAABCEAAAvUTIFCt34e0AAIQgAAEIAABCPSSAIFqL91KoyAAAQhAAAIQgED9BAhU6/chLYAABCAAAQhAAAK9JECg2ku30igIQAACEIAABCBQPwEC1fp9SAsgAAEIQAACEIBALwkQqPbSrTQKAhCAAAQgAAEI1E+AQLV+H9ICCEAAAhCAAAQg0EsCBKq9dCuNggAEIAABCEAAAvUTIFCt34e0AAIQgAAEIAABCPSSAIFqL91KoyAAAQhAAAIQgED9BAhU6/chLYAABCAAAQhAAAK9JECg2ku30igIQAACEIAABCBQPwEC1fp9SAsgAAEIQAACEIBALwkQqPbSrTQKAhCAAAQgAAEI1E+AQLV+H9ICCEAAAhCAAAQg0EsCBKq9dCuNggAEIAABCEAAAvUTIFCt34e0AAIQgAAEIAABCPSSAIFqL91KoyAAAQhAAAIQgED9BAhU6/chLYAABCAAAQhAAAK9JECg2ku30igIQAACEIAABCBQPwEC1fp9SAsgAAEIQAACEIBALwkQqPbSrTQKAhCAAAQgAAEI1E+AQLV+H9ICCEAAAhCAAAQg0EsCBKq9dCuNggAEIAABCEAAAvUTIFCt34e0AAIQgAAEIAABCPSSAIFqL91KoyAAAQhAAAIQgED9BAhU6/chLYAABCAAAQhAAAK9JECg2ku30igIQAACEIAABCBQPwEC1fp9SAsgAAEIQAACEIBALwkQqPbSrTQKAhCAAAQgAAEI1E+AQLV+H9ICCEAAAhCAAAQg0EsCBKq9dCuNggAEIAABCEAAAvUTIFCt34e0AAIQgAAEIAABCPSSAIFqL91KoyAAAQhAAAIQgED9BAhU6/chLVjcBD6j5t8ubbq4Mcx86/HTdF20RJs/Xbq8UDXuq3I+Kvm3t2GhMikGAuMiQP9vyPrH6h9tl96deGB3zX9fulC6VDpUekCSx7PbSSdKl0hz0rHSJl5QgZnFKPZiZf6mdLb0U+nb0q5JAbk8Hq71jpSWSz9uynxuUlbX7GFa0ObH93etsMB0Hzzatue07yRl19b+3D5wxAAGLsMHxtSeFK3TFqjW1AfStk16Hj9NmvjCtpfrL2/lRdKc5GNIV6D6MC3r2gfdP6nq4zT/A+l7zToEqgmgGZrN7Sfef35E+pF0vvRD6cPSui1tcX/4mHRRk/+r+v/IlnweCHyz5LLOk74rPbMl37iTcvq/63Cx1PYb+MukgpPu/7evUpiQdwT7J2XaWYdIJ0Tpb9L0v0o7Sj7LXV36WiMHIn9o8m6r/ydJb5feJd1d+g/pNMmwfib1xd6ihuwiOZi8QrqX9Glpe+moppG5PNZS/jMkB7wbS7+Tnid9XnL5x0jDbH9lsD9j8494XOYTl1uSwt+g+bjf9Ln9bvp7JO/QYnu2ZpZINybp4bdgX+6cLPNsjX2gpRkzmYSfZtItrZVaVamvkp4i+dixdWuuOxL927NvU/ttkuDg4x+kzaUPppmZr5KABwqulP5Uul56oPR16VvSZtL/STbvd7/czNv/v5feKZ0iPVb6lRTsXzTxMmkbycd078u97tOlU0OmMf8fpf+7LX/dUp+zkrSq+38YvUnb6YOoI3U72GZwN0ge7YvtyZpxNO/oP9jxmrhMim9RuJ/m3ZEc/M665Z7NbaSGOEhzR4/NTOO0XB5v1XrednqWd6LScoJNj6gO2qGvXMuFzzkYdWAe2zqacXC2NEqssf25feAdaqcD8dS8k/DOLrWXKMEnca+QvI10RLW2PpC2b9Lz+GnSxBe2vVx/+bgTjh9Ha3rQiKoDkxy7R5NpT/13PRhRzaE2nTy5/eRcVS89/nrgyOu/NKq6B3zS/e29lfYbyYNpwdbVhAeI3Edi+4ZmfKV0mK2hDCdLaZ28nvufB7HSq61tZeb2f697QVsBLWmT7v+3xwFgS31GSvLoZuzQsLLPPMO9PE57lLSa5OH12MJI0nOixC017WHz26I0n916pC/Ot1JBFc78jer8c8k/ltjMNE7L5eF8/pH8JCnPjD3C6sB4lswj6z6bi+3lmvEPdS5K7Gv73USPqP9vDEDTT5QeIX02SfeO8SBp7yQ9nq2tDwxoykwtwk8z5Y6hlXFQER8/hq6QkeEPGXnIUheBrVTd9PjrEVZbfEuig1ePmsZB3c2a9xVMLwvmAToPvngwITbPe1u+1WSQeZDGA3LHST5mB3Pg6YEkj87OReldk73o/yUD1TZQS5S4g/SJaGG4jBKi8rAo7Exipzhvms/5nfchks86+mC+19Cjzg70HaxcKH1TenHSuFwezucOHUaxQzFtjJNN3DnrS/GnSz5R8OWPvaRx95ewcdd7D8n3DMW2WNof2uxLlv7teEcYmwPUUyXfI9dltfeBrnbNYjp+mkWvjF6n9bSKR6q+K10kfVKq5XmI0VvLGjGBdKDEy8KAjve1wXy5f3m8YjPttA0kX/G1OZ8tzRvmw/Im213+3aqUF0geXPIVx6VNjoP1/4WSA2H305Lm4/u/Sz7e/1jyFYZnldzAfMsad+Dx96rYF6SrowrOafrX0uOTSoch7jj49IHYlzTvGeV1RwiXtPsSqPoSv0fPzMuXFrxz/LDk2yNeLQXL5eF8Ppszu9jaGCdZVszeINlnz5AeI/ky8n7S4V44AXu6tuH6fy3Z1mJpv5t9f8k7JF+NiM2XlF4j7Zukp7O194G0PbM6j59m1TOj1SuMkr5Xq3lfbN0u+WHOLUYritw9IODBkldKPgafH7XHt6R5pDM1p3mdtZoFzudg86YkY1h37bSAlnlfFX2udJnk2/Y+JHkAxyO3p7XkX2iS4zIHv74Fzcf9r0h+BsIcemsONH4hudGpOfiyE3eV7FwffB3F+4bluFM4sPKZjnceLs+XPA+RHEh5J5LjbGWbmrmOOeb7ppz3CUnmr2reAWMYVc7l4SfE56STJf9gfELyMilwc0cf1fbRCq7jlqOuOI/8PrlxcJxaje3P7QNpW/9JCceniZr/uLR/lN51j2rtfaCl6WNNwk9jxVu88Pn462jVouse1bYK+jd0jeQDdpvtqUTXg3tU2+jMRtp8+olr/jrJl/fXTJpxpebb9svvVLq35UEn26ekW5rp+N8zNeN8f92yrCvJJ8O+DdDreX8/Xxu1/3s7HlW9VooHC8P2J9X/O+9R9X0UDhpTnTECoecrrwPV/21Z5z+V5ij99ZIf7jlKek8zbYcEO1cTfyZ5hPEHksu6VPI9Gr60eZ3UBwsB5HlJYzwq5mD8EU16Lg/f3/IUaU7yCYDX8+0FHomzxYybpKH/wg3gWw/IeYCWpX0mzKc/+K5ifO+OR3IdkKU26+1P67uQeV9OTm998MiOR5vfnVHwtPpARtV6laVWP5X4rfbKkS2N8W/IwcqgfV7LaiRVTsCX3P9RclDph6Ri88CR31KUmq/uOpB0UGdzvlUkD67FFq4C+wQo116ijA+VfNz2VddJXkn2cd/36G6UW9lJ5nOw4LPEVOFsIacupyqTnT2K2blvy1jhc8rj+zZm3XLP5jyC6LyrJg3ywcTpwzpJLg8Hqg6K0x9PvFmP3obLF3G6A1/XZa84MZl2UJ32mTCfe5uJ2/zZAdtoWzQr7W+rW24fiNd9qmaukLyji+0NmvmlNBfJvxlvw/md7tsFBtm4+8Cgbc/yssXmpxK/1Wn6cz7+GjSi5BNpX7VLzYM2IfhIl01qRCndLvP5BEbtJ77a6PuT1+/YxBFK9z44tWOVcHGU6JFPb9uDbLG9uUl3jJVjHnn1bSkOUB2sXiL5sv99c1ZO8gzq//dR3tVayvxnpbkdm7csm1T/H9WHLVVtT7JzHBC1nXl4jS0lQ4/NI343S0uiRHcWjyLF5ntUveMYdkBOVpvKbC7g3VU7531CUksHYD7zCpf+c3m40+3Y0uLjlJaO0nkH/aAo71JNX96yri+FuI7btSwrleTAzAGXA7U2G0f7vcOIf/RLNV+y/bl9IG6vA3UH7DkWdoibJplr7QM5bR5HHvw0DqrjK3M+/hp0oF6mqvq3FJsHDhyUdA2KTOpAnVSL2REIjNJPfBU4DVK3Udp+0facx2X6Hs5g7ie/lt4Vpfl2Rt9j6tscY/Ol9HB1Mll0l1lv61bpjdGSpZr2yOo3pLYTq7sUEiUM6v9/q3wOwlP7khJ8VbRtcGtS/X8UH6b1Hzj/QS31vaRddpgWHCk5MLF5pPb70mub+fBvN0341oAwwueAwjA9AlmD5QK+pxrjy9q+9yUETU/TtO9xiTt6Lg8HXw76H9dAurv+eyTtYmmdJi38+6EmHPiH7S7VtOvtMz+vZ9tMukryj2Oc5rNZ+7vLSrffnLwz8c4j2FJNlGx/bh8I2/cO7ibJdcuxrkC11j6Q0+Zx5MFP46A6vjJH9ZdrMuhAvUzLfywtaarswYEPSN4H+2pSm03qQN22bdLyCOT2EweF3u/uK/k4E/RuTS+LNuVjokc0/fxICBTfoWnfu/rAKJ8nD5QulcKg3E6a/r20fZKvbdYxjwPEf21Z+Cil/UJyXUexQf3/b1WQY4Z4kMi3QNwmdW1nUv0/14ejsFjxegafXTx2wFov1bKzpOXS2dI3pb9qyf94pZ0g2dkO5Jz3LZIDuxpsFMDu5MskP+Hnszrfn+ofS2y5PHwPi+/7NbfzJbPziUM8chrKPbbJE5j6x7eHdKLk+4IvlH4iHSR5lG6cZl+nJyvx9kq335c/fXb60Wgjpds/Sh9wNd4mfTFudMf0tkqfk66WvA2PRHs+nHDU2gfUhKkYfpoK9nlvdBR/+X73OcnPNdzaTJ+TbNkn4x+SvL88TwqjVtsl+Tz7SmlO8tUu1+PyZn7YLVpeF5ssgdx+4uOu87ZpWVLl+2v+MMknNh5Y+ZrU5nvf7rZPk8d9yjGPg9Vca7vcHtb19tpGOdvKzun/D9aKb5dcR9f1p5LjLV/tTW3S/T/Xh2k9mc8kAOBMUD3ORh+ow7n4qQ4/hVrir7r8Na3a0k+mRb7cdjuf+i+3CUqCAAQgAAEIQAACEIDAPAjkPok9j6JZBQIQgAAEIAABCEAAAvMnQKA6f3asCQEIQAACEIAABCAwRgIEqmOES9EQgAAEIAABCEAAAvMnQKA6f3asCQEIQAACEIAABCAwRgIEqmOES9EQgAAEGgKf0X8/gbwpRCAAAQhAAAKzQoBXY8yKJ6ZXD/rA9NiPsuVcPz1MhTpvm/x+xTZ7UpS/LVD1B0+OlJZLfjej31/43LaCWtL8Pse2ury/JW+fknL91ac205bRCUy6n6ymKvpd7343vH/Hfhe532P+9x1Vf06Tz+8u9cd3Xi+FD+2EVZ6hCX/kyO9XD+/5fZOmVw0Zov/eB32syet3vPrDBI9cQL6WVSeeNGkfTryB094ggKftgelvnz4wfR/k1CDXTw5U/RW93VoUPpoRb88HnTOlr0jeRhqorqU0v1zeH3kIB57nadrf995ZGmYOVPeT0vr4M9V9tlx/9ZkBbRtOYNL9xL/vW6W/iKrmLy66Hv6QTmx/rhl/qSp8DWqppv3FqdrZyW4AACAASURBVLdGmRx4et0DpHAF3F+cvF7yR31i877mNMkfIPC+xPP+rKs/BhN/NSs3X1z2NKcn7cNptnUq2wbwVLDP1EbpAzPljs7K5PrJgWr8yd3OApsFL9H/k6SuT936oORtp6Me/jLcoM8Jh+06UN06zCyi/7n+WkRIaGoLgUn3k0eoDvGXDkOVLtaEA8jYfMJ7dJLm0dgbJZ/A2hyo+hPn6W2aH1Sa2+b9UTCf4DotPhn216t+IzlgHTVftMpUJ3nh/1Txs3EIQKDPBHyQOEjae0AjPfL5O8mfKY7NlwI3lto+zZhkZRYCEJgRAstVj/Qyv0cwV5eujuq4oab9iVSfxMbmeX+q/FlN4q/1f13ptpWz3e3KZj6+3cgjt7+SLojy3qzpMyQvC5abL1plupNplD7d2rB1CEAAArNPYD1V8dPSdyXfN/ZJaZOWajtAPVX6XsuykOTvz/tAZsUWDkwOVofZ7spwuuR73L4l7SXl7NsdSPtAN0xt98INqxPLIVATgVUyfgf+ndxvxEatqfz/LvkS/79G6zpItTmwjS3Mh+Ve5nVT8wnszyXvf4J5nbQ8L3PaBlKoe26+P5Y85amcndmUq8jmIQABCMwMAd87anuv9MRGvtz2HWmLOxat+OtRkNdI+0ZpbZMOYu8lpfeuPrbJvEbbSlHaDZr2SI0fuHiM5FsJ9pMOH7KeF+8vXZehN2aURRYI1Exgx4zfgX8rXxqhkT6R9WX7p0m+LB9fNVmnKcf3msYW5tdO0uNZr/t86e3SLdECp6flebHTfCIcbifIzRcVPd1Jn0VgEIAABCCQR+AqZdssyuqDwKukZ0sHSuEhCl/yP0QKl+iiVVaadB6PgB4s7Sr5wOYHo7Zqct20Uu67zrwuSfKlw/dI75DeJ/nJ4y47VAty7rdtG6XpKpN0CNRIwCeaT82ouIPVXPOJ7P9v70ygJinKdI1H3EVRwAVQGgTGC6KijopwbVScwWVc8AKj4jKIXgW3gVFRmSuMKKCiIzqIIx76arvMdRw9qGyiaKuDKC6AyCLSDYILAuKCuKB937fN0Oggsyr+/4+qysh64pz3VGZkZCzPF1X1ZURkpmctniN5xuOl0vtzT+5I58FF39V/suT16XMRcFTnwsw0EgIQmCAB3/zgdWHhpiaPrD5eypm297mPlo6QPG1vx9Rryjwae5LkJwIsNJzTnOD6jHJU7UTbMR4XxjnL487nOAT6TsAXnN/OqGQ8gpmRfAOvEbVj6UfUvUv6uOR1p2G96kZJJmEG5bqOzN+peD9dxMt90uA80/ycxnl61id813PTpfmzP1AC7hyE+SZAH6jD/rl28pozT9WnwSOZ4Y/gn7R9jbQmkv8cXIYfFeP4faVRwY6qp/U9ItMVbq0DYTovTmPH12V5pHZUOLpJ57SjdNioTGZ0LNdeM6oexfaEQG4/2XPMdyB8P84c0y7/NrQNAL6iyX+X5nzfTOU8D0zye0QT71mVNHiG5NNS15rxlTrm3500nKoIP3UghNx0aT6z2s+14azqV325AK7ehEtuAH1gyQinkkGunVaoNgckNfIfh/8gRv2J+RyXka5F9R2+eyT5efcM6T1JvJ3ke0Rxy7R9VZLGu14O4LJ2azkWR/kGi90ztNWYfGZxONdes6gbZfaHQG4/8QVfznfBsyWjwpE62HZh9zbFuy6+CSqE87XxsWjfm4dKnmVJ16i+XXGpk+qlBE+Ozt9L2y7Da9VD8G+TR3Djx1Plpouymelmrg1nWsmaCwdwzdYrU3f6QBmOk84l104rVJFLpa2aCnlU09NxnhL0SGZX6HJUt9QJnh7cuTnRNz14NNUjIOGGi5Cn7+r3qO0dm4hl+nS9XyOFpwbspG2voz29STPUj1x7DbX9tCuPwLT7iR1VP7Q/dmh31b5nR05Jqvw32vej6ZY38f5N8Z38viEyDsdqxxfCL5A80hr0KW0/P0ro34BVkt9GFWZ9vFbdS3zaHvg/Ll2U9Uw3p23DmTZ2FoUDeBbU+1UmfaBf9uiqTa6d7Ai+W7pA8oiI15DaKewavfSf1BopnfoPzqbXj3lU5QrJeXqdnG+wikdOtbsueArPacIbsPxn9CLJLwe4ULpY+p7kG7k8UjvkkGuvITOgbeMJTLuf3E9Veot0nuTfh/Cd9pMz2r6TT1H8N5u0F+nzECl+VJ1nPdyGLj1fx+LgR2idKPli2vnZOY5HcUPa3HTrZT6jnWnbcEbNnF2xAJ4d+76UTB/oiyVG1wM7jebTt6PYq28W6Wd96Cf9tMtCasWbqRZCi7QQgAAEIAABCEAAAtMj4GdyESAAAQhAAAIQgAAEINA7AjiqvTMJFYIABCAAAQhAAAIQMAEcVfoBBCAAAQhAAAIQgEAvCeCo9tIsVAoCEIAABCAAAQhAAEeVPgABCEAAAhCAAAQg0EsCOKq9NAuVggAEekrAb5byG6P8jEI/I9EP4T9euldLff2sQr/n+5ImvR+wvV1LOv8O+6H9zsvPXvy65Fc6EiAAAQhAAAITJcAz3CaKt4rM6QNVmGndA7Vzgh/I74do+0H9Dn7jyzek1dKdmzh/hLfEOK1fY+h9v8bwail+S4zT+m02V0pbeEfhSdLvpOXNPh+3JJBrr1ueScw8EaCf1G9tbDhhGwJ4woAryJ4+UIGRVMVcO9lRfXDSpGc05z87in96E+cR2BBur42fS/F7tz0S69co+r3dcfDbrs5J4tj9C4Fce8FsvgnQT+q3PzacsA0BPGHAFWRPH6jASKpirp3CO7TjVu3SnB87mysV5/dzp8GvQb0sijygOXeHJKGXArhOW6YZsL+OQK69wDXfBOgn9dufN1PVb0NaAAEITJGAp+TTEN6l/cXowAO1vTpN2MRto887NcecziFNG/bD8SYZHxCAAATmiwA3U82XvWktBCBQloDXnr5Q+pDkm6tC2FQbv4j2w6bjfM7dmwinu1m6KUkbzt2kJQ+iIAABCMwNARzVuTE1DYUABCZA4JXK03f3HzSBvMkSAhCAwNwTwFGd+y4AAAhAYJEE9tF5B0p+lJRvkorDtdrZKInzrp8W4HVz1zfHnG5DyTdaxSE8VeC6JJ5dCEAAAnNFAEd1rsxNYyEAgUIEfKf/G6XHSVe15OnnoXotahq2VsTl0o3NAadzSNM6nUM43uzyAQEIQAACEChHgDsOy7GsNSf6QB2WW4id9lKT/BD/+0ZN853/b4j2ncZ57hjF+XmqN0htj6dKlw6cpnQ8niqCl2wuxF7duXBk6AToJ/VbGBtO2IYAnjDgCrKnD1RgJFUx1052QH3j0+uk/SK9RdsroqaGB/77bVThkVZHafuHUtsD/69Q/ObN+U/QJw/8j2C2bObaq+VUouaIAP2kfmNjwwnbEMATBlxB9vSBCoykKubayW+Qcto2rUia6pusTpQulfzKVb+lKjzKKk7qJViHNmk81X+uZGeV0E0g117dOXBkHgjQT+q3MjacsA0BPGHAFWRPH6jASKoidqrDTqGW2Ksue82qtvSTWZEvVy4P/C/HkpwgAAEIQAACEIAABEoS4K7/kjTJCwIQgAAEIAABCECgGAEc1WIoyQgCEIAABCAAAQhAoCQBHNWSNMkLAhCAAAQgAAEIQKAYARzVYijJCAIQgAAEIAABCECgJAEc1ZI0yQsCEIAABCAAAQhAoBgBHNViKMkIAhCAAAQgAAEIQKAkARzVkjTJCwIQgAAEIAABCECgGAEc1WIoyQgCEIAABCAAAQhAoCQBHNWSNMkLAhCAAAQgAAEIQKAYARzVYijJCAIQgAAEIAABCECgJAEc1ZI0yQsCEIAABCAAAQhAoBgBHNViKMkIAhCAAAQgAAEIQKAkARzVkjTJCwIQgAAEIAABCECgGAEc1WIoyQgCEIAABCAAAQhAoCQBHNWSNMkLAhCAAAQgAAEIQKAYARzVYijJCAIQgAAEIAABCECgJAEc1ZI0yQsCEIAABCAAAQhAoBgBHNViKMkIAhCAAAQgAAEIQKAkARzVkjTJCwIQgAAEIAABCECgGAEc1WIoyQgCEIAABCAAAQhAoCQBHNWSNMkLAhCAAAQgAAEIQKAYARzVYijJCAIQgAAEIAABCECgJAEc1ZI0yQsCEIAABCAAAQhAoBgBHNViKMkIAhCAAAQgAAEIQKAkARzVkjTJCwIQgAAEIAABCECgGAEc1WIoyQgCEIAABCAAAQhAoCQBHNWSNMkLAhCAAAQgAAEIQKAYARzVYijJCAIQgAAEIAABCECgJAEc1ZI0yQsCEIAABCAAAQhAoBgBHNViKMkIAhCAAAQgAAEIQKAkARzVkjTJCwIQgAAEIAABCECgGAEc1WIoyQgCEIAABCAAAQhAoCQBHNWSNMkLAhCAAAQgAAEIQKAYARzVYijJCAIQgAAEIAABCECgJAEc1ZI0yQsCEIAABCAAAQhAoBgBHNViKMkIAhCAAAQgAAEIQKAkARzVkjTJCwIQgAAEIAABCECgGIFbKae1xXIjIwhAAAIQgAAEIAABCECgCgJcBFRhpolWkj4wUbzFMsdOxVBOJSPsNRXM1RdCP6nehBusZeq/fiPSAghAAAIQgAAEIDBIAjiqgzQrjYIABCAAAQhAAAL1E8BRrd+GtAACEIAABCAAAQgMkgCO6iDNSqMgAAEIQAACEIBA/QRwVOu3IS2AAAQgAAEIQAACgySAozpIs9IoCEAAAhCAAAQgUD8BHNX6bUgLIAABCEAAAhCAwCAJ4KgO0qw0CgIQgAAEIAABCNRPAEe1fhvSAghAAAIQgAAEIDBIAjiqgzQrjYIABCAAAQhAAAL1E8BRrd+GtAACEIAABCAAAQgMkgCO6iDNSqMgAAEIQAACEIBA/QRwVOu3IS2AAAQgAAEIQAACgySAozpIs9IoCEAAAhCAAAQgUD8BHNX6bUgLIAABCEAAAhCAwCAJ4KgO0qw0CgIQgAAEIAABCNRPAEe1fhvSAghAAAIQgAAEIDBIAjiqgzQrjYIABCAAAQhAAAL1E8BRrd+GtAACEIAABCAAAQgMkgCO6iDNSqMgAAEIQAACEIBA/QRwVOu3IS2AAAQgAAEIQAACgySAozpIs9IoCEAAAhCAAAQgUD8BHNX6bUgLIAABCEAAAhCAwCAJ4KgO0qw0CgIQgAAEIAABCNRPAEe1fhvSAghAAAIQgAAEIDBIAjiqgzQrjYIABCAAAQhAAAL1E8BRrd+GtAACEIAABCAAAQgMkgCO6iDNSqMgAAEIQAACEIBA/QRwVOu3IS2AAAQgAAEIQAACgySAozpIs9IoCEAAAhCAAAQgUD8BHNX6bUgLIAABCEAAAhCAwCAJ4KgO0qw0CgIQgAAEIAABCNRPAEe1fhvSAghAAAIQgAAEIDBIAjiqgzQrjYIABCAAAQhAAAL1E8BRrd+GtAACEIAABCAAAQgMkgCO6iDNSqMgAAEIQAACEIBA/QRwVOu3IS2YbwIfVfPXSg+Ybwy9bz126r2JqCAEIDAPBG6vRh4hfVc6X7pI+nfpXi2N319x50kXS1c06e7Wkm43xX1O+r60RjpV2qElXR+j7EDkhJVK5LRdumOUSS6P++icD0mrpUulb0hPjfIZtXmiDrbV5V9HnbTEY/vp/HOlCyT3m89ID2nJs7b25/YBN/WR0umSvz/m8DVp7xYGIepR2gh2anNUa+sDI5o68UPYaeKIixaQay9/L94j+TfF3yl/t46X2v6TilaQzHpBILef3E+1PVb6ZiP/Z35eekxLKzZW3PukS6TwX7VdSzoPBL5GCv7Q17W9Z0u6SUYNof/n2jCb43uV8gbp/s0Zm+jTzqgNdKsol1dr+7fS/2ziNtLnl6SzpVtH6XbV9u8kG9vBebxDulbyn3DfQy5gO6pvkeysxfqI9v87amQuj7vrnB9In5Ru15z/dH3+QXpylF/Xph3VN0hpfR7adcIS45+p883Knw4bSidJP5NiO9fY/tw+4B+6X0n+Ew0zHS/Qts9/ipQGfxe+Kn2qSZM6qrX1gbR9097HTtMmvrTycu31bRVzinSXprjN9OmL9tXSnZdWBc6ugEBuP3mp2vJDadumTfZD7Gv8Rtopaqd/d1dJ7lP+b/X+MdLVkvtWHI7UzpXSFk3kk/Rpf2b5+skmujeE/p9rwyyQNtjPpf+bpD5Q+y4oXHHYuL+UPNoXBzutTvf3UeRntW1Dx0sU7qT9X0gnxCf3dDsX8FGqv52wNJyriOdGkbk8Xq9zYuYhi89pw1eA44IdVY/uTSucrIKuSArzqLnb8MIovsb25/aBg5v2bp1wuEb76XfFSZ4l+Yr/gOa81FGtrQ8kzZ76LnaaOvIlFZhrL/9RPzgp6RnNd+bZS6oBJ9dAILefeCDnJUmDtmz6iQfWQnA65xn/3nom2b6PHdYQPGLvwTg7wHHwjNk5SVzbri+szpLSvuu0dqI9iDVqti3kOYT+v7bkGlUbzyN2Hg2LQ9j3MYe/knwl62mYOHipgEM8euQRPA+b/zFKeKO2v5+kiw5Xufla1forSc3/Wvt2Wv5fFJ/Lw+n8JflekqcZe7R7+yR+1rs3qwLj+o3rONT2u21m4JBy8I9S+O40STbwD+ObpENCRMtnbX2gpQm9jMJOvTRLZ6UeriP+s46DR84c2paarZ+SvXkh8Ak11EtE4hBG4a+NIn2R81PpO1GcR1098+ljITxZG7eVPJgQB++7T9oJHhV+rYMekDtDCjPUTu8BQQ8keXR2jSPGhEH0/5KOqnkdIdnR3KWBt5U+fUXxAenyJs6OpkM8xe/94IzGRnHaNF1Ie29thI60LsOBhRerPSdJ/hKEkMvD6dyhrTi0MU6S/Hl3f219SfKFwtnSy6XS/SUU9jZt2JYvk1xnj5ofLrns2FEfavvVzA1WSpc17b6DPs3aS17CFJTThGAH9YvSt+LIZLu2PjCiKb06hJ16ZY6xlfFUaxrChbq/QwQItBHwINFx0iopntF6oPZXt5zguG0k/3c5OJ1Dmjbsh+NNslt8+IJ4H8mDS2dKy5oUrtO+kh1hL6kcF5ba/zdWAeN013GV6OPxg1SpX0q+ajXsd0nxKJH/eL328ONJ5cPUv/+sQ/CU8I+k20RxYerfI7jjrkqi02ay6TouJrhjeL1iWC4R8sjlcbBOcNnx2hrn4al/x+8XMuz49NqcN0u+icuO42Ol6yT/SU8qLFfGvpjx1audc0/z+2IkDjW2fyF94L5q7BekmyTz9oi4b5iKg6eUfixt3kQeoE+X8YD1k21QYx9ImjDVXew0VdxLLmwh9ooL8+/Zl6VJ/pYtuXFkUIzAQvuJ/3Ovknzef0n3TGpiv8b/TWk4WhE+5z7NgQ/r8/dpIu3v2aR7Tsuxtij7Ox6t9SzyuyXPlD6hLWFm3EL6v2fu3KZxsp83ybBQG46ti53SH0g7Nyn9Z+opbV+5ehg8BDuzbtzeksH5z9ejdnbOLgiJ9On1Gb4i8Iibzzc4r021I+zKbyL1OSwW8CvUqLYvQy4PO5hrpLOkTSWPzj1XCtyeoe2FhkN1gtvz0IWemJHe6y091eErSNfVI4qehnFf2jY6v8b25/YBO5q+KDtWup0UbGYuT4sYvF/bh0f7XY5qbX0gatJMNrHTTLAvutBce6UF/KMiPG1b5ShQ2hj2xxJYbD+5u3L2f5DvEXhYVMq0HVUX7YEr/xe6Lf69X0pYSP/3f9DuGVq+lAplnNtpQ6+jsNOYyp59V7AD4wwPTBI8oolPFyr/g+LtnF4seYp5L8lD2ack5+/WxHl0yXdrej2nR/xcN4Psc+gEPKbSF+m4ebSFXB4enTtJMrfzJTv4z5dcJ69bWWh4THOuLzK6whE6kPaZsN/1xxBG2OMpfudvZ+0G6T+Swvrc/jYuuX0gjBabRxxO1Y5HUB0eJF0p2QkNoctR9fFZ9IGoalVtzpudFvNd7ZNBc+0V19kXwv497PtMXJ84116XxfST0Gb/Fl8mxX6P/0u/2gLleMV5aV2Y+j9O2y7bg2txcB90/BOT+FG79ql8n4J/++0jLXbJ42L6/7hpfx/v+m8f1aaFHOu0ob/IHslKFYa12wp5niKd4R7JQS9Yd7yvTsYFT/seNi6RjnvZwJkZ6WadpBPwiIrZIbxa2nBEmvRQLo+X6USPqqZfnjg/fzl9NZmGRyvC7fFa1a7gEe60z4T9rouKrZp8j2zJ9DzF2WkfF/rS/rZ65vaB1Tr5yy0ZvFNxzsNTUP8k+Qp/TSR/Z3zcfcbx+0qjwqT7wKiy+3xs3uy0mO9qn+yXa69QZ88iXSL54o0wPwRy+4ln8Ty7m4ZPKCK+T2Sl9v0bnAYPKNipDeEAbbjsHZKEr2nicy+WvETATur/ljxD7SUAq6R4sCIponV3Mf1/kFP/Xjdhw7wgweTpWscfHsV79DWssQvRXovnDrFVlM4/Kh5FioOvWK6Xxv0hJ6fNZDf3SxJXziOLHu1oC7k8/KXboyWDMxSXXjD4augeUdpl2r6q5VxPGbg9HtEsGTZSZjdLH0wytcNsJ+wLUfwk2u8fjPhLv0z7Jduf2wfOUbm+Yk5/LD+pOH8vPMLcFsIPYrpGtaY+0Nauacdhp2kTX1p5ufZyKZ6dSp1U3/D7hqVVgbMrIJDbTzxI0Pbfdq7iPd0fgvuS89wxiguzf8dEcV7O6PWk6QzkaYrzb31OcFn+b3xVlHiZtn8gnS7FyylH5bfY/t/7qf9Rje46ZmjfleIfhDtr31caP5eWRSeeqG3fSbdhE+eRWo+evTJK4839JI+ohRE+OxQrJV/l1BByvyShLe7cN0ldV1u5PHy+nZudm4zt/Hgk7TJp0yYufNhmdvyDs7ZM2663r/yC07STtn8k+csxieB1l/5SL28yd7n/IrkevhIMoXT7zcnl+scjhGXaKNn+3D7gK+dQbqjL32rjZsnTSF2hy1GtrQ90tW9a8dhpWqTLlJNrL/9J+zf1dZJ/P4Leou0VZapCLj0mkNtP7Kh6pDIetPF/ps9/ddQ+/zc53Wek4CgepW07s5tF6bx5pHSFFAblPJjne26WJ+nadu3zeNncG1sO/pXifiK5T48LQ+j/uTYcx+LPx20oT1Xa+TlfspP5H9L9kxyerX1fqayWviG5k/yvJI13HyKdKdnY35ac9rVS/BQAp+trWCjgw9QQj6B1hVweXsPyMcncLpDM7gQp/hKGMnwh4TSBqb98L5I+J10oXSx5XdebJI/STSK4bF+kuJ7fkdxvzpLsqMWhdPs9/emr0/dGhZRu/0L6wN+pHv4RdPvN4VuSr8jDBV1UzXUviFgjpVP/4YKjtj4Qt20W29hpFtQXX2auvTxL4bRtWrH44jmzEgK5/WQ3tcf9wf95HjSzD+PfYt/wnYaNFXGidKnk3+pTpO3TRNr3iOShTRr7Q/Z57KzmhlGPsHJ5o5bwhTKG0P9zbZjLlXQJAQDTJegDdfQB7FSHnUItsVdd9ppVbeknsyJfrtyib6YqVy1yggAEIAABCEAAAhCYewIemiZAAAIQgAAEIAABCECgdwRwVHtnEioEAQhAAAIQgAAEIGACOKr0AwhAAAIQgAAEIACBXhLAUe2lWagUBCAAAQhAAAIQgACOKn0AAhCAwOQJfFRF+A7k9MUMky+ZEiAAAQhAAAIdBHg0RgeYOYqmD9Rh7Fw7+UUKTtsmP1+xLfiteyF9m6PqF574BSirJT+b0c+LfmpbRi1xfp5jW13+tSXtkKJy7TWkNtOWhRNYaD95porwc939Hbxc8luk0mep+nv+PskvN/JzVP3w/+2kNHgg0C/OCc+V/7q290wTsT+WwNq2B4mPPYsEEIAABOaYgB/e/daW9t/YEuc32bxd+rT05JbjfgPNf0v+Y/SLUfymtKdL/yXZWfV548LhSuB3gMfBf6AECEAgn4BfJuQ3Ifp7d7Xkl798RFou+QU6Dv4+nyz5rVF+IL/fNHW09AXpwdJPpRD+RRvPlXaRnN+TJJ/7eOmLIRGfEJg1gYVezc26vpRfngB9oDzTSeSYayePqMav3B1Xl2cpweelrlfdvl7HXHY6IuM3w+U4mx5RfeS4SgzweK69Bth0mrQAArn9xG96+r1kZzMOnu2I43wR6TzjmRG/IcqviT8mOtGvQ/dF50ujOG+eLnmUlpBPgAf+57MiJQQgAIEFEfAf2JukQ0ac9VAd8x+aX1McB4/aeoS17dWMSVJ2IQCBJRJ4ns7/seTXeMfBr9iO4zzi6lFTv+I6hN9ow7MiPhaCZ088IuuL1Dh4/+GSL3gJmQS4mSoTFMkgAAEINAS20KenBL3mzOvUPijt0ELHDqqn+L7VcixEebmApxOtOPyx2bGzOi7srwRfkrwW7mzp5VLOb7sdaa+3G6fbjasAxyFQOQGvI79Merb0FeliyWtVn5m0y9P9q5M47zpuG+lOzTGnC/HN5nr74Xh8jG0IzIRA7rTDTCpHoVMhQB+YCuYlF5Jrp3urpAskj4Q63EX6gOQ1aw9q4vzhqT+P0GzexHVN/R+s4y57p+hcb3rq3/H7JfHp7jsU8WbpjpKd3cdK10kr04Qt+15b5zLG6bCWc2cdlWuvWdeT8mdLILef2En1d3iVdA/JF3petuMLxoOiJvxQ25+N9sNm+C55qYDDhyUvJUjDnopwnZ6THmC/k0CuDTsz4MBoAgAezWcejtIH6rDyUuxkJ9HO4aeipr5f24dH+12Oqs9dI50lbSr5D9I3YPxScp3i6UTtZoVDm3ODM911kkeAds/QVl0ZzDB+KfaaYbUpesoEcvvJVaqX0z4sqZ/v6L9WunUTj6M6ZQPaLtz1P33olAgBCAyLwK/VHK9ZCzc1eWTVd/bmTNv73EdLR0ietr9J8nq3l0knSV4jt9AQbtZwffw0ga7gP93ruw5G8a4TAQJDJhAuDL02PA5etvNEaWvJo652WjdaP8m6Pc+s2NEN3yens3/l5TVewxqC0zn4wpaQScBXH27duwAAGxZJREFU7wQIQAACEMgjcFcl800SafiDIsKoi51U/0F5zeiaRp4adPBdv47bt9n3x5XSP0i+899r114s+c/QU5HpH6ei/hxcnh9vlQbXxSHUJz0e9g/Xxs8y9KquDIiHwEAIeE1q21rx8F0KvpK/j56JSIMd2cul8Ii68L1N0zqdw6jvdZo3+xCYKIHcaYeJVoLMZ0qAPjBT/NmF59pphXL0NH4cfLPRNdKZSXy82zX1fwcl2qPlvDMU954k3k6y18+FsEwbnrJMwz8qwu3ZLT2Q7DP1PwYQh6snkPu93r/5zqRT/x9XvEc/w0XfXk26HSMy/v7fILU9nipe3+pTTpN4PFUEL2Mz14YZWZGkjQCA26jMVxx9oA5759pphZrjt0dt1TTLf2DvlHzjhKfwu0KXo+rH1HhqcOfmRI/qeNrf04xesxoHj9B6atHrWh2WSa63337j8xx2kn4keeR2yCHXXkNmQNvGE8jtJ7dRVn4MlW+UCt+vx2nb3+vY2fT3bJXktathZuUobXsZzWZSHI7UzhVSuKHyCdr2CwKWJ+nYHU0g14ajc+FoJwEAd6KZmwP0gTpMnWsnO4Lvlnznv6fvvIbUTmHX6OWuOrZG8po1l3F1sx/+DL1m7WOS/9Ccp/8sT5DikVPtrgunSk7jP1UH/1G+SPITAi6UPH35PcnPbvVI7ZBDrr2GzIC2jSewkH5iR3OF5KU4fuyc16fu11KEH+d2ouQLVr+U4xRp+5Z0Xi5waJPGvxXnSnZWCQsjsBAbLixnUq8jAGA6An2gjj6AneqwU6gl9qrLXrOqLf1kVuTLlcubqcqxJCcIQAACEIAABCAAgZIEwp1sJfMkLwhAAAIQgAAEIAABCCyZAI7qkhGSAQQgAAEIQAACEIDAJAjgqE6CKnlCAAIQgAAEIAABCCyZAI7qkhGSAQQgAAEIQAACEIDAJAjgqE6CKnlCAAIQgAAEIAABCCyZAI7qkhGSAQQgMEcE7qe2Hit9s5Gfpfh56TEtDPy8xfdJfiajn7foh4T7Nalp8O+wH9rvB/r7eYtfl/ZME7EPAQhAAAIQKE2AZ7iVJlpffvSBOmyWa6eXqjl+C822TbP8Zqp3SH67lF8GEEJ4g40fBu5XLHrfr1j0A//b3mBzpeK3aE5+kj55g00Do+Mj114dpxM9JwToJ/UbGhtO2IYAnjDgCrKnD1RgJFUx105PV9qXJE3ya1B9/qujeKdz3AOiuNtr++dS2zvB7QDHwW+74p3gCZRoN9de3TlwZB4I0E/qtzI2nLANATxhwBVkTx+owEiq4lLstENz/v5RU1dq+5qWpvs1qJdF8Qc05zqPOHgpgOtkJ5hwSwJLsdctcyNmqAToJ/VbljdT1W9DWgABCMyQwNYq+zhplfShqB4P1Pbqlno5bhvpTs0xp3NI04b9cLxJxgcEIACB+SLAzVTzZW9aCwEIlCHgm6Kuki6XfiHtI/02ynrTJj4tzWm9XvXuzQGnu1m6KUnodA6bJPHsQgACEJgrAjiqc2VuGgsBCBQi8D3l42l5O5I/kS6QHlYob7KBAAQgAIGGAI4qXQECEIDA4glcr1N9I5RHQL0EIIRrtbFRtB8276INr5vzeQ5Ot6HkG63i4HQO160fzR4EIACB+SKAozpf9qa1EIDA0gjcQad76j4Of9COR1QfEkWer22vRU2D17R6ucCNzQGnc0jTOp1DON7s8gEBCEAAAhAoR4A7DsuxrDUn+kAdlsu105fVnN1amnSu4vx81RD20obz3DGK8/NUb5DaHk91UJTOm6dJPJ4qgRLt5tqrOweOzAMB+kn9VsaGE7YhgCcMuILs6QMVGElVzLWTHVXf4X+PqFkva86Pn6MaHvjvt1Hdtkl7lD7tzLY98P8KxW/epHuCPnngfwOj4yPXXh2nEz0nBOgn9RsaG07YhgCeMOAKsqcPVGAkVTHXTh5NXSFdKJ0n+bWndlz3ltLgV6ieKPk1q36Fqt9StX2aSPtegnVok8ZT/R6dtbNK6CaQa6/uHDgyDwToJ/VbGRtO2IYAnjDgCrKnD1RgJFURO9Vhp1BL7FWXvWZVW/rJrMiXK5cH/pdjSU4QgAAEIAABCEAAAiUJcNd/SZrkBQEIQAACEIAABCBQjACOajGUZAQBCEAAAhCAAAQgUJIAjmpJmuQFAQhAAAIQgAAEIFCMAI5qMZRkBAEIQAACEIAABCBQkgCOakma5AUBCEAAAhCAAAQgUIwAjmoxlGQEAQhAAAIQgAAEIFCSAI5qSZrkBQEIQAACEIAABCBQjACOajGUZAQBCEAAAhCAAAQgUJIAjmpJmuQFAQhAAAIQgAAEIFCMAI5qMZRkBAEIQAACEIAABCBQkgCOakma5AUBCEAAAhCAAAQgUIwAjmoxlGQEAQhAAAIQgAAEIFCSAI5qSZrkBQEIQAACEIAABCBQjACOajGUZAQBCEAAAhCAAAQgUJIAjmpJmuQFAQhAAAIQgAAEIFCMAI5qMZRkBAEIQAACEIAABCBQkgCOakma5AUBCEAAAhCAAAQgUIwAjmoxlGQEAQhAAAIQgAAEIFCSAI5qSZrkBQEIQAACEIAABCBQjACOajGUZAQBCEAAAhCAAAQgUJIAjmpJmuQFAQhAAAIQgAAEIFCMAI5qMZRkBAEIQAACEIAABCBQkgCOakma5AUBCEAAAhCAAAQgUIwAjmoxlGQEAQhAAAIQgAAEIFCSAI5qSZrkBQEIQAACEIAABCBQjACOajGUZAQBCEAAAhCAAAQgUJIAjmpJmuQFAQhAAAIQgAAEIFCMAI5qMZRkBAEIQAACEIAABCBQkgCOakma5AUBCEAAAhCAAAQgUIwAjmoxlGQEAQhAAAIQgAAEIFCSAI5qSZrkBQEIQAACEIAABCBQjACOajGUZAQBCEAAAhCAAAQgUJIAjmpJmuQFAQhAAAIQgAAEIFCMAI5qMZRkBAEIQAACEIAABCBQkgCOakma5AUBCEAAAhCAAAQgUIwAjmoxlGQEAQhAAAIQgAAEIFCSAI5qSZrkBQEIQAACEIAABCBQjMCtlNPaYrmREQQgAAEIQAACEIAABCBQBQEuAqow00QrSR+YKN5imWOnYiinkhH2mgrm6guhn1Rvwg3WMvVfvxFpAQQgAAEIQAACEBgkARzVQZqVRkEAAhCAAAQgAIH6CeCo1m9DWgABCEAAAhCAAAQGSQBHdZBmpVEQgAAEIAABCECgfgI4qvXbkBZAAAIQgAAEIACBQRLAUR2kWWkUBCAAAQhAAAIQqJ8Ajmr9NqQFEIAABCAAAQhAYJAEcFQHaVYaBQEIQAACEIAABOongKNavw1pAQQgAAEIQAACEBgkARzVQZqVRkEAAhCAAAQgAIH6CeCo1m9DWgABCEAAAhCAAAQGSQBHdZBmpVEQgAAEIAABCECgfgI4qvXbkBZAAAIQgAAEIACBQRLAUR2kWWkUBCAAAQhAAAIQqJ8Ajmr9NqQFEIAABCAAAQhAYJAEcFQHaVYaBQEIQAACEIAABOongKNavw1pAQQgAAEIQAACEBgkARzVQZqVRkEAAhCAAAQgAIH6CeCo1m9DWgABCEAAAhCAAAQGSQBHdZBmpVEQgAAEIAABCECgfgI4qvXbkBZAAAIQgAAEIACBQRLAUR2kWWkUBCAAAQhAAAIQqJ8Ajmr9NqQFEIAABCAAAQhAYJAEcFQHaVYaBQEIQAACEIAABOongKNavw1pAQQgAAEIQAACEBgkARzVQZqVRkEAAhCAAAQgAIH6CeCo1m9DWgABCEAAAhCAAAQGSQBHdZBmpVEQgAAEIAABCECgfgI4qvXbkBZAAAIQgAAEIACBQRLAUR2kWWkUBCAAAQhAAAIQqJ8Ajmr9NqQFEIAABCAAAQhAYJAEcFQHaVYaBQEIQAACEIAABOongKNavw1pAQQgAAEIQAACEBgkARzVQZqVRkEAAhCAAAQgAIH6CeCo1m9DWgABCEAAAhCAAAQGSQBHdZBmpVEQgAAEIAABCECgfgI4qvXbkBZAAAIQgEAZAndQNidIFzU6W5/3KpM1uQyIwGL7yZfF4Abp2gGxmHhTNlQJNzel2Gl9onRaVOq7tf0SaZn0gyjem5tJ35LuJt1Rulp6o/ReHyRAAAIQgAAEZkjgMJU9zsn0/9UFUR0P1vaTpPtLv5a+KG0s/ThKM63NZ6qggyQ7Rf6f/an0NuljUQVct7dKj5b+KF0uvVL6XpTGm/5/f5X0PMn/+b+V/lmK/++dbh7DNPvJbgJ8pPTieQRdos3/qUz2jDK6rbb95VwrvX5EASfq2G9GHJ/nQ2ZHmG8C9IE67I+d6rBTqGWOvR6nxP5vsiO6SUvzdlbc0Um8HbdPRnG30/atWs6ddNRrVcC50hZNQf4//rjkwaMQXK9V0ilSqOcx2vagkQeS4mDn6Eop5Gdn/HfS8iTd0Hb72E9sC0ZU83vaejZ8p86ztx/CM7TxLumSRtGh9TZxVLvI/MnJ7z7KkXkgkPNDOQ8c+t5G7NR3C61fv1x7PVmn2SH7hnTXliaelMR9VfsfbUk3zajtVdjvpQcnhd4niXu69s3hAVG622v755Id1hA8quwR1JdGcd48XToniRvabh/7CY7qwnrZSBuerLx2kA6RnPBRHXnjqHaAabh1H+XIPBAY+SWbBwCVtBE7VWKoppoLsdc+OsfT3V5veuekmf9D+54Wv590lWSHzlP+3l4jzSK8SYWmS+3a6rFSkde0HDhVcZdF8Qdo27z8fx6H1zTxWybxQ9qddT/xxcWnJPcpj3T/H8n2ZUQ1v5d12vCeyuNzTT6eMrlJ+veOfHFUO8AouhNw9ykcGRgB+kAdBsVOddgp1HKh9nqeTvQaTq859T0VXWEpI6p2gr1mdJxu3VV4E3+WPq1nS1+RLpa+LHnNahzO107biOjxindb79QkPk6f5uW1rnGwA+9435sy1DDLfuILINvou9J2kke7XyGtlhbjqPr8cX3Lx70MZEih04ZeUP6sqKUf1PYNkkGlAUc1JfKX/U7A3adwZGAE6AN1GBQ71WGnUMvF2Ms3Bvu8M6SuP/OlOKo+1/mPU7zEro26R0N/JXn96T0kOzz+P7bz6ZurQvihNj4b7YfNo7XhOng0z+HDkpcSpGFPRTjdc9IDA9qfZT/Zu+H71ISnR/YX46gGu47rX4cNyH5uytoNOxrkhdZPiI6doO39JK+J+UjHOURDAAIQgAAE+krgPaqYR1PfJv2ntJfU5sCl9X+aIjxNvkt6INk/UPt3GZPGh+OnDLQl94CQR0M9YBSm9u1seoT1CMn/x39oO5G4IgRK9ZPQX+yYxsHrpT3CGsLm2via9NfSj6L4dNOz2jlPaVidnlj7fpuj+pAG2KVJ4/yFfr6Eo1q71ak/BCAAgfkkcKyabSfQDp+3X56BwY6GH704Lvg/s+0/NT3Po6Wjwi910KNmnjaOgx8H6Wn6rSWPunpUbqP1k6zbs7Ps869vjjmd62UHOH5CT3Cqr2vS8fEXAiX6yb2b7H6WgPXsdBx8MfJqKVyUJIf/vOsR9GDTrjSO91LNwQff/b9rSyu9ANhXcVskx0ZN/XvKYhaP9mip/kyiFjPtMJOKUujECNAHJoa2aMbYqSjOiWe2FHv5maRnSXb40tCHqf9PqFJuX7o8wc614/1UAAdupmpAjPiYZT95u+rl8n3PTxz8iDGm/kcYLTl0CxveRgm+I9nBTMMjFOETDk0OjHJUP620e6QZzdH+LQDPUdtp6p8I0Afq6AnYqQ47hVou1l73VQYnSZt2NDd1VB+odF4H6vLGjZZ6NnL3DLU9Jiuuzv5NeQ+LI7Xt56h69DPcjOWlC67XjlE6O7cesWt7PFW8vtWneBq57WasKLvqN2fZT8IaVS8diYNvkAuOqn2tT0oeBR3nK22jNLtnaKu4sAFs38KGXoNqx7MteGTU6ycuSg7iqLbR+lPcLQB3J+XIQAnQB+owLHaqw06hloux14N08vukcDd8W4tTR9VptpVc3jhHtS2/xcR5wOjbkh1kr6l18MsLvPwudjb9n7xK+ozkFwI4HCV5irjtgf9XKN7rIR18D8rvpOXN/lA/ZtlP7IR6+caFkp1M2/XFkp9zm46oXqW4cY6qksxlWGfDfZume1rBV2JeA/H+BIev4NZI9vp9kjv845u4sJ7Gx1P52WHzDH8xXxIhIwyIAH2gDmNipzrsFGq5UHvZ0fOytjZn0yNfD5fWSH6O6o3N9iv16TBtR9Vl2tFcIV0pXSJ5fapvaE7DxorwYJHXx3oQ6RQpLA2I09pp8myo09h5OleKb5iO0w5pe9b9ZEvBPFmyL+SBvuMkj3Z7GeUa6bGSA45qA6LlY6E2bMmCqFEEADyKznwcow/UYWfsVIedQi0XYi8/2unwEc1LB2bSpLNwVNM6sL84ArX0ExzVbvt2Pp6q+xSOQAACEIAABOog4Lup/RzLk6QDWqrsEcn0ruyWZEQNnAD9ZOAGpnndBBZyNdedC0dqJkAfqMN62KkOO4Va5tjrrUrsdOP0mDFNZ0R1DKAeH66lnzCi2t2JcmzYfTZHxhIA8FhEg09AH6jDxNipDjuFWubYy4+h8t394+SbkrrCTjpwquTyfNd9epNS13nE94NA3/uJ1w775RNew+ob43bvB7Ze1SLHhr2qcG2VAXBtFitfX/pAeaaTyBE7TYLq5PLEXpNjO6Sc6Sf1W3OtvXkCBCAAAQhAAAIQgAAEekcAR7V3JqFCEIAABCAAAQhAAAImgKNKP4AABCAAAQhAAAIQ6CUBHNVemoVKQQACEIAABCAAAQjgqNIHIAABCEAAAhCAAAR6SQBHtZdmoVIQgAAEIAABCEyZwFYq70uSn2tK6AkBHNWeGIJqQAACEIAABCAwMwJ/r5K/KG0+pgaP1PHTpe9KF0hfk/ZuOecyxfnxWKme1pL2KYr7hnS+5HwPltqe75ubrqUIoiDQToBnuLVzmadY+kAd1sZOddgp1BJ71WWvWdU2t5/cThX8gnRfyQ/g7xpR3U7HfiUdL4WBvhdo2+XYiYyDHc79WrRlku5vtP87KbwhbZm2fyK9fpHpktOq3821YfUNnVUDADwr8v0plz7QH1uMqgl2GkWnf8ewV/9s0sca5fYTj14Gx3OUo+qRTue5ddLYa7T/oSTuO5lAzlM6lxmH12rHb6u6exSZmy7JqvpdHvhfvQlpAAQgAAEIQAACSyFg5/OPGRnc3KTZMEl7a+3/IeP8NMm2inig9PnkgPfvID2xic9Nl+Y/iH3WqA7CjDQCAhCAAAQgAIEJE1ip/L329HDJjqR9qNdIdlTfIcXBx46VzpYulU6TguMZ0tlJdVgdIpL9cDw3XZLNMHZxVIdhR1oBAQhAAAIQgMBkCVyv7B8nbSF5+6fSAZId0G8lRd+g/a9Lu0o7Sp+SPi29MEq3abP9iyjOm2F/kyY+N12SzTB2cVSHYUdaAQEIQAACEIDAZAk8QNmfI/kO/Y2lzaQ3SmdK6d38j1LcRyUvKfi99G/SGdIx0m0kQiYBHNVMUCSDAAQgAAEIQGCuCby5af2r9flbyU7oByQ/1uqEDDJ2cu8mbd+kvbb53Cg59y7N/nULTJdRhfqS4KjWZzNqDAEIQAACEIDA9AnspCK/L6U3TnkN6j0buVZev3rnluqF87ym1cHPTXXYpvkMH+GpAuF4brokm2Hs4qgOw460AgIQgAAEIACByRLwY6j8rNX0YfxbKc4jrF6X6rCv1DbC+lDF3yjZsXXwjVl+aUB4hmoTvW7/JunUJiI3XTifTwhkE8h9hlt2hiSsjgB9oA6TYac67BRqib3qstesaruYfjLqOarPUUOcp+/0D+FvteHHVh0XxT1f27+RYgd0H+17qcDronTe9AP/7eQub+Lt9P5Yanvgf066JPvqdxdjw+obPc0GAHiatPtZFn2gn3ZJa4WdUiL93sde/bZPX2q3kH7yflV6jeQRTzue3v5mS0P+TnGrpIskP9Tfd/sfJMXPVvUygH+WzpU8bX+55Buw9pfawlMU6bKc1vkeIqWjtj4vN11bGbXGLcSGtbZxpvUG8Ezx96Jw+kAvzDC2EthpLKJeJcBevTJHbytDP+mtabIrxpupslGREAIQgAAEIAABCEBgqgS4mWqquCkMAhCAAAQgAAEIQCCXAI5qLinSQQACEIAABCAAAQhMlQCO6lRxUxgEIAABCEAAAhCAQC4BHNVcUqSDAAQgAAEIQAACEJgqARzVqeKmMAhAAAIQgAAEIACBXAI4qrmkSAcBCEAAAhCAAAQgMFUCOKpTxU1hEIAABCAAAQhAAAK5BHBUc0mRDgIQgAAEIAABCEBgqgRwVKeKm8IgAAEIQAACEIAABHIJ4KjmkiIdBCAAAQhAAAIQgMBUCeCoThU3hUEAAhCAAAQgAAEI5BLAUc0lRToIQAACEIAABCAAgakSwFGdKm4KgwAEIAABCEAAAhDIJYCjmkuKdBCAAAQgAAEIQAACUyWAozpV3BQGAQhAAAIQgAAEIJBLAEc1lxTpIAABCEAAAhCAAASmSgBHdaq4KQwCEIAABCAAAQhAIJcAjmouKdJBAAIQgAAEIAABCEyVAI7qVHFTGAQgAAEIQAACEIBALgEc1VxSpIMABCAAAQhAAAIQmCoBHNWp4qYwCEAAAhCAAAQgAIFcAjiquaRIBwEIQAACEIAABCAwVQI4qlPFTWEQgAAEIAABCEAAArkEcFRzSZEOAhCAAAQgAAEIQGCqBHBUp4qbwiAAAQhAAAIQgAAEcgngqOaSIh0EIAABCEAAAhCAwFQJ4KhOFTeFQQACEIAABCAAAQjkEsBRzSVFOghAAAIQgAAEIACBqRLAUZ0qbgqDAAQgAAEIQAACEMglgKOaS4p0EIAABCAAAQhAAAJTJYCjOlXcFAYBCEAAAhCAAAQgkEsARzWXFOkgAAEIQAACEIAABKZKAEd1qrgpDAIQgAAEIAABCEAglwCOai4p0kEAAhCAAAQgAAEITJUAjupUcVMYBCAAAQhAAAIQgEAuARzVXFKkgwAEIAABCEAAAhCYKgEc1anipjAIQAACEIAABCAAgVwCt1LCtbmJSQcBCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgMCfCPx/uI48qm1rrvcAAAAASUVORK5CYII=)
So now, we have
∑fidi = 18500 and ∑fi = 600
Mean is given by
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mean = 549.5 + 30.83
⇒ Mean = 580.33
Thus, mean is 580.33.
Question 7.The number of shares held by a person of various companies are as follows. Find the mean:
![](data:image/png;base64,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)
Answer:This is a grouped frequency distribution.
Notice the data in ‘number of companies’, is small and the class in ‘Number of shares’ have equal intervals. So, we can use direct method for ease of calculation and can rely on the answer for accuracy.
So, create the table again as we need to represent midpoints and frequency. Re-creating the table ensures ease of calculation.
The calculation is done on a table and we can easily extract data from it.
We have,
![](data:image/png;base64,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)
So now, we have
∑xifi = 7000 and ∑fi = 20
Using direct method,
Mean is given by
![](data:image/png;base64,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)
⇒
[Using values in the table]
⇒ Mean = 350
Thus, mean is 350.
Question 8.The mean of the following frequency distribution of 100 observations is 148. Find the missing frequencies f1 and f2 :
![](data:image/png;base64,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)
Answer:This is a grouped frequency distribution.
To find f1 and f2, we’ll need to find mean of the following distribution by direct method and equate it to the given mean of the following distribution, 148.
This given data is in inclusive type, and we need not convert it into exclusive since it won’t make a difference in the calculation.
So, let’s construct a table finding midpoints and stating frequencies.
![](data:image/png;base64,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)
So now, we have
∑xifi = 8869 + 124.5f1 + 274.5f2
And ∑fi = 62 + f1 + f2
Mean is given by
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGcAAAAuCAMAAAACyPdvAAAAAXNSR0IArs4c6QAAAIpQTFRFAAAAAAAAAAA6AABmADqQAGZmAGa2OgAAOgBmOjoAOjpmOmY6Oma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZmY6ZpC2ZpDbZra2ZrbbZrb/kDoAkDo6kGY6kLbbkNu2kNv/tmYAtmY6tv//25A625Bm27Zm27aQ2/+22////7Zm/9uQ/9u2//+2///bluTKjwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACUklEQVRYR+1WaVfbQAzcNQEDbRKOcJm2djFH1nj//99jtNrD1+Olsfyt+kA2zvMOGkmjUep/DBiodYz1iBz7S+vx06M4tIV+ohdtNb7RFmeqFsJRTX7yQkDtZnRjk7t/QShqfeZuqkY4hlMVisAcQWm92qNifL3JUTpBJKOZOQLKSmWLcLdsPpQGM4duKJBP5E8ap91Eepr8x89YD2kcVYMuH/5Yr/YoEMG7k0x0Wrq9uXXFWgSnCuVR9rlsN/GbMG91bDdLM2QgDAb9zbzxSSLS1GOSMuRDmka8GTc+UvUhEXNRR75CffixUD6Btc9UlzEOJcnTC7U4SlmJHB/d91MWfAJQ+DwKBiWZwmny7Dez6U/tdudmzJxeHYVzaCO12z+0N2zxwOujudLZPQnV24XWUBDQ8vSa02letNuyQvub1YfDafJH9Y7thCbaWxJfPLksUby58g4cmqZqzdpRoVixUd1g+D+eVCwYH0nRDkoUOLi3OX9xOAmMSxhwJnZyuD21wTcn3LwFKye7NUNQmyNApH2/xjY8AOegbBgHrVcGHM8P1Wcqnzm8oSpQDJdPLI3hFhDMZ+M7iUtg9KOyr/eAWKvPHeE4baevsyLqDqusUpiV7A5C8RfT84F13FCVwo/fQA1sqaAR7YP2bamoEe0D9WyprBHtA3VtqfDC7gF1bKm0Ee0n1LGlS+bTtaXL4iRbuixOsqXSRrRfoKTqy+IkW7oob8mWChvRoSDE3S5rRIcCN7SlUkZ0IDvezCdbugjOhC1dAmfCliZLOmtD/tPLX2b2OGiKyNUOAAAAAElFTkSuQmCC)
⇒
[given, mean = 148 and using the values from the table]
⇒ 148 × (62 + f1 + f2) = 8869 + 124.5f1 + 274.5f2
⇒ 9176 + 148f1 + 148f2 = 8869 + 124.5f1 + 274.5f2
⇒ 274.5f2 – 148f2 + 124.5f1 – 148f1 = 9176 – 8869
⇒ 126.5f2 – 23.5f1 = 307
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ 253f2 – 47f1 = 307 × 2
⇒ 253f2 – 47f1 = 614 …(i)
Since, there are 100 observations.
⇒ Frequency = 100 [Frequencies depict total number of observation]
⇒ ∑fi = 100
⇒ 62 + f1 + f2 = 100
⇒ f1 + f2 = 100 – 62 = 38
⇒ f1 + f2 = 38 …(ii)
Multiplying 47 by equation (ii), we get
f1 + f2 = 38 [× 47
⇒ 47f1 + 47f2 = 1786 …(iii)
Solving equations (i) and (iii), we get
253f2 – 47f1 = 614
47f2 + 47f1 = 1786
300f2 + 0 = 2400
⇒ 300f2 = 2400
⇒ ![](data:image/png;base64,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)
⇒ f2 = 8
Putting f2 = 8 in equation (ii), we get
f1 + 8 = 38
⇒ f1 = 38 – 8
⇒ f1 = 30
Thus, the missing frequencies are f1 = 30 and f2 = 8.
Question 9.The table below gives the percentage of girls in higher secondary science stream of rural areas of various states of India. Find the mean percentage of girls by step-deviation method:
![](data:image/png;base64,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)
Answer:This is a grouped frequency distribution.
In step deviation, we need to mark the assumed mean in xi. Step deviation also calculates deviation of each xi values from the assumed mean using a formula.
The assumed mean is the value from xi closest to the central value.
So, assumed mean is
A = 50
Here, class interval is given by
h = 10 (∵ 25 – 15 = 35 – 25 = … = 85 – 75 = 10)
We need to represent it in tabular form:
![](data:image/png;base64,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)
So now, we have
∑fiui = -29 and ∑fi = 35.
Also, assumed mean, A = 50 and class interval, h = 10.
Mean by step-deviation is given by
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKcAAAAuCAMAAAB6d/nOAAAAAXNSR0IArs4c6QAAAJlQTFRFAAAAAAAAAAA6AABmADqQAGZmAGa2OgAAOgA6OgBmOjoAOjpmOjqQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZmY6ZpCQZpC2ZpDbZra2ZrbbZrb/kDoAkGY6kGZmkLbbkNu2kNvbkNv/tmYAtmY6ttv/tv/btv//25A625Bm27Zm27aQ29uQ2/+22////7Zm/9uQ/9u2//+2///bZOZt5gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADe0lEQVRYR+2Yf1vTMBDHk4pURTaECbKpuA4pIku3vP8X590ld03brB3zodnj4/1Bu620n3zvR66n1H/7JxQotdgEFmS/ao3HozO70HOEsgXy2cWpKo+SU1X5mwcE3U6Br8oJ+tjMfrtXqtSnxFUAp3Hidqw6T4q+opD0nodTk0OwEqnR2RLUFWy6MpWVTkijnefplPUsgTP4aBfpAqJ6Byjkce/5EMw0OZWRtYyuauHkxBRiGWs925x2kcrzIiekEoonfi9P1qCs6Ekf4YtUgvrnk56sFekZ56wvGtfxwXMlAILEafsdotjpOrYRCFlZexT1NBqBqvx8vbmSj+h4+YdRUYUu2IMMlU8XECudXf/GAsrxUeUpMskuvBtxS3eycvrXgeu+b1/4ynKWuMWIbaeM572+4S8EjMOC45ICFGqYL2LQaR0ssKgUW3MjwNiL6Gpv/NQdeqqCVgSgBA7HgzHdthxYY7trcPqKDpt7m7PKs+/BLeqPrspuL2Z0NG8vD+csPjeDfZDzJbHGnHdYbu3ii6u61aXObuBof33QGtoqcND8Mcez3bb99JPTw13U4vyxkpiSLWh/UueC7cUSA8CcPBNnld+qJ+haIR3XtkClq/xsCc1iX98CKRsUww6nPrt3t8Isfnk1FE48KSZuo8DkkpJBJc7/8UFRSFjVD0T1mh15U09cI3caf8MJXNX7B+KsYSkGhLN3l60+BmuDbo3Nr4TyiNfBnHUa9Z2RC0RPcNps4hCxTIFBINinK+iyWc9eTvfuGPY13Txqc+4fngEn1IAlc3r/YnzG9Iz4HSJcVu0f/0qcCjsXkkxCs3YWKdGnp/H1l/e/br4Hft/1xtajr69LU5/JDsXoW2Ufb0DKidrMEJHu3NMM+KVtp4Hjd+fRoZyyb+IJgkKtzK5hg4KSd/4MLwbw8qfn/GNk1fgTCIqHGjTkhAKcLekuLjWbu8kecxG3b45s0odIJA/ORZI0yp2OZXAuIikzrqLNjQt3qIG5SJo+ufsaEZ2LBNoleu/oVrjoXKQGTRKe6OfO+2NsLiKcqd6LVTBn8DCxuYhwJpsz0ObXtMhchC9IN7fpChqbizBnOjmDN2EPE5uLxBqacQsoPK05fY3ORTxT0jmtork32465CP2ceO4dOnBwLjK6t+MPZK/vnIscB+fwXOQoOIfnIkeBuTfEH/yBZdV9sVUZAAAAAElFTkSuQmCC)
⇒
[using the values from the table]
⇒ ![](data:image/png;base64,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)
⇒ Mean = 50 – 8.29
⇒ Mean = 41.71
Thus, mean is 41.71.
Question 10.The following distribution shows the number of out door patients in 64 hospitals as follows. If the mean is 18, find the missing frequencies f1 and f2 :
![](data:image/png;base64,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)
Answer:This is a grouped frequency distribution.
To find f1 and f2, we’ll need to find mean of the following distribution by direct method and equate it to the given mean of the following distribution, 18.
This given data is exclusive, grouped frequency distribution.
So, let’s construct a table finding midpoints and stating frequencies.
![](data:image/png;base64,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)
So now, we have
∑xifi = 608 + 16f1 + 20f2
And ∑fi = 35 + f1 + f2
Mean is given by
![](data:image/png;base64,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)
⇒
[given, mean = 18 and using the values from the table]
⇒ 18 × (35 + f1 + f2) = 608 + 16f1 + 20f2
⇒ 630 + 18f1 + 18f2 = 608 + 16f1 + 20f2
⇒ 20f2 – 18f2 + 16f1 – 18f1 = 630 – 608
⇒ 2f2 – 2f1 = 22
⇒ 2(f2 – f1) = 22
⇒ f2 – f1 = 11 …(i)
Since, there are 64 hospitals.
⇒ Number of hospitals = 64
⇒ Frequency = 64
⇒ ∑fi = 64
⇒ 35 + f1 + f2 = 64
⇒ f1 + f2 = 64 – 35
⇒ f1 + f2 = 29 …(ii)
Solving equations (i) and (ii), we get
f2 – f1 = 11
f2 + f1 = 29
2f2 + 0 = 40
⇒ 2f2 = 40
⇒ ![](data:image/png;base64,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)
⇒ f2 = 20
Putting f2 = 20 in equation (ii), we get
f1 + 20 = 29
⇒ f1 = 29 – 20
⇒ f1 = 9
Thus, the missing frequencies are f1 = 9 and f2 = 20.
Find the mean of the following frequency distribution:
Answer:
Since, this is a grouped frequency distribution, this is solved by creating a table and using certain formulae. To find mean, we need to create a table showing class intervals, midpoints, frequencies and product of those midpoints and frequencies.
Now, we have
∑fi = 100 and ∑xifi = 14850
The formula of mean by direct method is given by,
⇒ [from the given information]
⇒ Mean = 148.5
Thus, mean is 148.5.
Question 2.
Find the mean wage of 200 workers of a factory where wages are classified as follows :
Answer:
This is grouped frequency distribution.
We shall represent them by creating a table having columns of class intervals, midpoints, frequencies, and product of these midpoints and frequencies.
So now, we have
∑fi = 200 and ∑xifi = 64300
For grouped frequency distribution, mean is taken out from the formula:
⇒ [from the table]
⇒
⇒ Mean = 321.5
Thus, mean is 321.5.
Question 3.
Marks obtained by 140 students of class X out of 50 in mathematics are given in the following distribution. Find the mean by method of assumed mean method:
Answer:
We have grouped frequency distribution and we need to find mean by assumed-mean method.
Assumed-mean method is given such name because in this method, we actually assume a mean from xI (usually a centre value) and the formula of mean is also based on that particular assumed mean.
By using assumed-mean method, we can avoid the risk of miscalculation. Also, by using assumed mean method, we’ll be able to solve the question with ease and more accuracy.
So, let us assume mean from the midpoints. Let assumed mean, A = 25 (a value quite centrally placed).
So now, we have
∑fidi = 120 and ∑fi = 140.
And we have assumed mean as, A = 25
Mean is given by
⇒
⇒ Mean = 25 + 0.86
⇒ Mean = 25.86
Thus, mean is 25.86.
Question 4.
Find the mean of the following frequency distribution by step-deviation method:
Answer:
This is a grouped frequency distribution.
In step deviation, we need to mark the assumed mean in xi as similar to in assumed-mean method but the formula differs. In step deviation, we calculate the deviation of each value from the assumed mean value. This brings more accuracy when values are large.
Here, class interval is given by
h = 10 (∵ 50 – 40 = 60 – 50 = … = 100 – 90 = 10)
And let us assume mean as A = 65, which is the closest value to the centre-most value.
We need to represent it in tabular form:
So now, we have
∑fiui = 7 and ∑fi = 52
And assumed mean, A = 65
Mean by step-deviation is given by
⇒
⇒
⇒ Mean = 65 + 1.346
⇒ Mean = 66.346
Thus, mean is 66.346.
Question 5.
Find the mean for the following frequency distribution:
Answer:
This is a grouped frequency distribution.
We can find the mean of the data using any of the methods. Since here we have small values of classes, we can find the mean using direct method easily.
We need to create a table using the values, representing class, midpoints, frequency and product of midpoints and frequencies.
Also, this is an inclusive type of data, which needs to be converted into exclusive type of data.
For conversion, we need to subtract 0.5 from the lower class of each interval and add 0.5 to upper class of each interval.
So now, we have
∑xifi = 3735 and ∑fi = 200
Mean is given by
⇒ [Using values from the table]
⇒ Mean = 18.675
Thus, mean is 18.675.
Question 6.
A survey conducted by a student of B.B.A. for daily income of 600 families is as follows, find the mean income of a family:
Answer:
This is a grouped frequency distribution.
We can find the mean of this type of distribution by either direct method, assumed-mean method or step deviation method.
But let us try doing it by assumed-mean method since it assures accuracy of the answer when data given is large.
Also, notice given data is inclusive-type of data. We need to convert the inclusive type of data into exclusive type by subtracting 0.5 from lower limit of each class and adding 0.5 to upper limit of each class.
Let us assume mean by taking a value from xi’s closest from the central value.
Let assumed mean, A = 549.5
So, we have
So now, we have
∑fidi = 18500 and ∑fi = 600
Mean is given by
⇒
⇒ Mean = 549.5 + 30.83
⇒ Mean = 580.33
Thus, mean is 580.33.
Question 7.
The number of shares held by a person of various companies are as follows. Find the mean:
Answer:
This is a grouped frequency distribution.
Notice the data in ‘number of companies’, is small and the class in ‘Number of shares’ have equal intervals. So, we can use direct method for ease of calculation and can rely on the answer for accuracy.
So, create the table again as we need to represent midpoints and frequency. Re-creating the table ensures ease of calculation.
The calculation is done on a table and we can easily extract data from it.
We have,
So now, we have
∑xifi = 7000 and ∑fi = 20
Using direct method,
Mean is given by
⇒ [Using values in the table]
⇒ Mean = 350
Thus, mean is 350.
Question 8.
The mean of the following frequency distribution of 100 observations is 148. Find the missing frequencies f1 and f2 :
Answer:
This is a grouped frequency distribution.
To find f1 and f2, we’ll need to find mean of the following distribution by direct method and equate it to the given mean of the following distribution, 148.
This given data is in inclusive type, and we need not convert it into exclusive since it won’t make a difference in the calculation.
So, let’s construct a table finding midpoints and stating frequencies.
So now, we have
∑xifi = 8869 + 124.5f1 + 274.5f2
And ∑fi = 62 + f1 + f2
Mean is given by
⇒ [given, mean = 148 and using the values from the table]
⇒ 148 × (62 + f1 + f2) = 8869 + 124.5f1 + 274.5f2
⇒ 9176 + 148f1 + 148f2 = 8869 + 124.5f1 + 274.5f2
⇒ 274.5f2 – 148f2 + 124.5f1 – 148f1 = 9176 – 8869
⇒ 126.5f2 – 23.5f1 = 307
⇒
⇒
⇒ 253f2 – 47f1 = 307 × 2
⇒ 253f2 – 47f1 = 614 …(i)
Since, there are 100 observations.
⇒ Frequency = 100 [Frequencies depict total number of observation]
⇒ ∑fi = 100
⇒ 62 + f1 + f2 = 100
⇒ f1 + f2 = 100 – 62 = 38
⇒ f1 + f2 = 38 …(ii)
Multiplying 47 by equation (ii), we get
f1 + f2 = 38 [× 47
⇒ 47f1 + 47f2 = 1786 …(iii)
Solving equations (i) and (iii), we get
253f2 – 47f1 = 614
47f2 + 47f1 = 1786
300f2 + 0 = 2400
⇒ 300f2 = 2400
⇒
⇒ f2 = 8
Putting f2 = 8 in equation (ii), we get
f1 + 8 = 38
⇒ f1 = 38 – 8
⇒ f1 = 30
Thus, the missing frequencies are f1 = 30 and f2 = 8.
Question 9.
The table below gives the percentage of girls in higher secondary science stream of rural areas of various states of India. Find the mean percentage of girls by step-deviation method:
Answer:
This is a grouped frequency distribution.
In step deviation, we need to mark the assumed mean in xi. Step deviation also calculates deviation of each xi values from the assumed mean using a formula.
The assumed mean is the value from xi closest to the central value.
So, assumed mean is
A = 50
Here, class interval is given by
h = 10 (∵ 25 – 15 = 35 – 25 = … = 85 – 75 = 10)
We need to represent it in tabular form:
So now, we have
∑fiui = -29 and ∑fi = 35.
Also, assumed mean, A = 50 and class interval, h = 10.
Mean by step-deviation is given by
⇒ [using the values from the table]
⇒
⇒ Mean = 50 – 8.29
⇒ Mean = 41.71
Thus, mean is 41.71.
Question 10.
The following distribution shows the number of out door patients in 64 hospitals as follows. If the mean is 18, find the missing frequencies f1 and f2 :
Answer:
This is a grouped frequency distribution.
To find f1 and f2, we’ll need to find mean of the following distribution by direct method and equate it to the given mean of the following distribution, 18.
This given data is exclusive, grouped frequency distribution.
So, let’s construct a table finding midpoints and stating frequencies.
So now, we have
∑xifi = 608 + 16f1 + 20f2
And ∑fi = 35 + f1 + f2
Mean is given by
⇒ [given, mean = 18 and using the values from the table]
⇒ 18 × (35 + f1 + f2) = 608 + 16f1 + 20f2
⇒ 630 + 18f1 + 18f2 = 608 + 16f1 + 20f2
⇒ 20f2 – 18f2 + 16f1 – 18f1 = 630 – 608
⇒ 2f2 – 2f1 = 22
⇒ 2(f2 – f1) = 22
⇒ f2 – f1 = 11 …(i)
Since, there are 64 hospitals.
⇒ Number of hospitals = 64
⇒ Frequency = 64
⇒ ∑fi = 64
⇒ 35 + f1 + f2 = 64
⇒ f1 + f2 = 64 – 35
⇒ f1 + f2 = 29 …(ii)
Solving equations (i) and (ii), we get
f2 – f1 = 11
f2 + f1 = 29
2f2 + 0 = 40
⇒ 2f2 = 40
⇒
⇒ f2 = 20
Putting f2 = 20 in equation (ii), we get
f1 + 20 = 29
⇒ f1 = 29 – 20
⇒ f1 = 9
Thus, the missing frequencies are f1 = 9 and f2 = 20.
Exercise 15.2
Question 1.Find the mode for the following frequency distribution:
![](data:image/png;base64,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)
Answer:Observe that, from the given data:
The maximum class frequency, here, is 15 and the class corresponding to this frequency is 20 – 24.
So, this implies that,
Modal class = 20 – 24
Mode of such grouped frequency distribution is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the modal class = 20
f0 = frequency of the class preceding the modal class = 7
f1 = frequency of the modal class = 15
f2 = frequency of the class succeeding the modal class = 1
c = size of class interval (the class intervals are same) = 4
∴ Substituting the values l = 20, f0 = 7, f1 = 15, f2 = 1 and c = 4 in the formula of mode. We get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 20 + 1.45
⇒ Mode = 21.45
Thus, the mode is 21.45.
Question 2.The data obtained for 100 shops for their daily profit per shop are as follows:
![](data:image/png;base64,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)
Find the modal profit per shop.
Answer:Observe that, from the given data:
The maximum class frequency, here, is 27 and the class corresponding to this frequency is 200 – 300.
So, this implies that,
Modal class = 200 – 300
Mode of such grouped frequency distribution is given by,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOgAAAAuCAMAAAAVxqXjAAAAAXNSR0IArs4c6QAAAKJQTFRFAAAAAAAAAAA6AABmADpmADqQAGZmAGaQAGa2OgAAOgA6OgBmOjqQOmY6OmZmOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmY6ZmaQZpC2ZpDbZra2ZrbbZrb/kDoAkGYAkGY6kGZmkLbbkNu2kNv/tmYAtmY6tmZmttv/tv//25A625Bm27Zm27aQ29uQ29u22/+22////7Zm/9uQ/9u2//+2///bmvA16gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAECElEQVRoQ+1a2XbTMBCV3QRitmxQltaUgANVU0rtWP//a8yMLCeOLY048dZD89DopBNJd5Y7iyPE8+tZAy1qQN0EwcK9n4dIixfqaCsVz4R0A/UQ6ehybW6bRdfcdh4i3Ba9/V99+2U5Kw1YoB4i2bw3KO6DtjbnTKMgYKB6iAhhPaBfBciZ9TwPc3mICBWzjtED5OzVj66BivTitgckzBGJ3aCiZq4EfFm/wkI9PhYFkzI5qgc1uAxaB1q/kBfQMZhUTh/t6tQo1JYzOhQN4WeXVfLl0CZ134CA3r1bc0Dl7NHpGUIkLn324LgiNbHWeFjhlw5eJu/Ol9dcGLrP6QGpdPFhWqRRZwKCTJuvgJlcpCZEFg3ruyr2cSmXRdEYHkCxJD7nBTpnc7EsU0H9pHzpcz4LlHddPkjzpcEimzomH3Z3xIeXR6nkpYOZUXtANQwZiYStGQApuRe8N7i5T/NQAVotx3z0BArmmtJ8HYRXbs+UTtbTAXBJMumL9TBAzwmtw3dLoPkHXQ7ui/dSJF99x2yr4i866WbrIHhDfRWu3lLHCCtHwnZYlNdzOzDBToZMVDxBpPnSNG8IIwQUQGno3+n0DwHNoiuxj9HhcaW+4vdxdW/vkccFFEwGoXhgQQIEbIZAURvJQhcxlK4oMqnYIEXhquTvhrr7ODyqMTqARdE5pw/rmeG3smYCoAAie31LQDVa/KtXCLnQgDUjlhat68AALZuSLhbk/ce0p2LNr/g61KCYjeXFZYFMf47mOwZK17Py98hcF69vA5pF4H2MRQ1rPBHXNSatWpQikz7SNRs6rA5K9AiuvDozj7bDuwc2MGSknfdweWwNjrw5hbJhT2hluBH790hGaQD8e2dtCCtVwb8XDC0DLcrrknYlXv4nOmxRAuIC43MHo7k5akNtg3D+O6KWMQrCTya8Ty8G9fAR7VaBNpWA/OidlxA1kbIE3H/UF82Kd7z8ZNOONu27lHpV95C2J1iB8aN3XqJhk4E777JNS8CB9ktdh3D9EC9R34Tjka4tColLV55Uh0gd8BxQXqK+iVeb1CXaCiMjAn70zks0bDL4KKUyHCPC4O3FSzQMhH0mGV1aVByNO3Xs8TB4idomw487xWEyUIzT+el8HWitGjsVGcMzCTO9M7zI24uXOLXoGB5JlCZNisaJn86ThHs4TyIPkJp1dz0Gg0JSoUEgxWoKpRc/nScJ93CextqrjdhRTTaOx4b6OS2FqkoMUAO/kQc9hvPGuzUDjORBsMBH+wWdLMCgura2z3JJwj2zNpvoX3qM5tF+o9mYobXHcB623Y3l1wuODM0B9RjOC/kEcLLTeY/hfAo4U65w7rQa4jfnp/P8cB4baPM4hT/xv5H4C5XCeQKTyIMAAAAAAElFTkSuQmCC)
Where,
l = lower limit of the modal class = 200
f0 = frequency of the class preceding the modal class = 18
f1 = frequency of the modal class = 27
f2 = frequency of the class succeeding the modal class = 20
c = size of class interval (the class intervals are same) = 100
∴ Substituting the values l = 200, f0 = 18, f1 = 27, f2 = 20 and c = 100 in the formula of mode. We get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJQAAAAgCAMAAADDuaGFAAAAAXNSR0IArs4c6QAAAKtQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGZmAGa2OgAAOgA6OgBmOjoAOjqQOmY6OmZmOmaQOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZjqQZmY6ZpC2ZpDbZra2ZrbbZrb/kDoAkDo6kGYAkGY6kGaQkLbbkNu2kNv/tmYAtmY6tmZmttv/tv//25A625Bm27Zm27aQ29uQ29u22/+22////7Zm/9uQ/9u2//+2///bNzOKsAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACeUlEQVRYR+2XC3PSQBSFd1NF4qtCAK0WUrWSKimtksf+/1/mOXfzApMGMiPJjN6ZppeG3f323Mdulfpvw1YgnmvnUwXx51zrCT6HWmunJ/TUW6rYXam7FQDSD7t0dqu2zhpQ/ENPFl1slAqmKl2s8AMYWPyyZygCJP4YKi2uwSUWTrPwMYy9GHLnck6K2OUTts1ZYrcXIrtoOkO4CqXCQh/jt0BFWv+tzEsoFPOJeaUiMEUrZW7W0E6lXr4uFM2UrJBGR0CZB9Tzc8lW80XrNz/2vdp9G//ZEi++cxSrDxTkMHfoCHiBz6MdX3k1TFK3bRbopUo81pPxR7vE3/fy0cZvn6lYKZ1dsUGo6IUk3oEdBYUqQtdjEDiTiFt6HaG+eaAx/jV/oRwQCxsBem9FqcP+W6OdoAQUKfUAWXododacIRr9EqjYRSwkAvTMZ65F76EljpyD0SPUaFd6Bf+J4Vtzl8E0FaiAsZCgBVzBCgDPsNXRAqakmEQ9MxlhUfgsvc5QWDB+tREoS8an9bhYRivl0GDG55cbof7YSLGxWsf2sPDiKqOwAJSlCiVDGdJGJpExD9q44nVWCnogFC1K5bPXhS8YWxWz9Ma+Sq9rottMEii7WQbNJhFzqkinJqFCyT6Mtn2Bj9LrBuVlTc3GK0ILTYQsdG5VsrDLoA7vq3eyPTy5cxhcRA4Kz26wC1RxzNAh1dbFHZCToeU7k0eXVPeudj425nkWUA5O0NreyRdLL6M6qSU0l9Q//uaYw+zcEpmb1ycc1meiC5en3CDOAxVNhlcE6fuN8ZdfnzjEzqPN3ir8/1Pbi+agbHjhgzyP7hOn/aDkGxjMb1mpU6yIhBPHAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 200 + 56.25
⇒ Mode = 256.25
Thus, the modal profit per shop is Rs. 256.25.
Question 3.Daily wages of 90 employees of a factory are as follows:
![](data:image/png;base64,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)
Find the modal wage of an employee.
Answer:Observe that, from the given data:
The maximum class frequency, here, is 33 and the class corresponding to this frequency is 550 – 650.
So, this implies that,
Modal class = 550 – 650
Mode of such grouped frequency distribution is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the modal class = 550
f0 = frequency of the class preceding the modal class = 12
f1 = frequency of the modal class = 33
f2 = frequency of the class succeeding the modal class = 17
c = size of class interval (the class intervals are same) = 100
∴ Substituting the values l = 550, f0 = 12, f1 = 33, f2 = 17 and c = 100 in the formula of mode. We get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMkAAAAiCAMAAADCmw12AAAAAXNSR0IArs4c6QAAALpQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGZmAGaQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmY6OmZmOmaQOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmY6ZmaQZpC2ZpDbZra2ZrbbZrb/kDoAkDo6kDqQkGYAkGY6kGZmkLbbkNu2kNv/tmYAtmY6trbbttv/tv//25A625Bm27Zm27aQ27a229uQ29u22/+22////7Zm/9uQ/9u2//+2///bv6933AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADf0lEQVRYR+1YaVvTQBDOVkCJB2pPxANTRSRI06KVHPv//5Zz7ZGmSQO0+OR5uh/IlCQz8847MzubINivfQS8COQ/blbikQ7uuhih7M1Vxe3kZNY9KMXoKzi9nCg1QOf19TFekqPusRKj58X4Mlj0gJv5+wkh0dGwa6RkL01uiZQQkiB91rX8IkpoJcyCIOkcKVmIVYJrQWVikQRJx0ix/iYCxHASOIzbLJhUKRO6TWrntqU6qeGdWHpUCkBStKHjF9y1itHDar4YGWcTpaoq0hZIslDBwgbkpEBfKPV2deNzyIoRlwmaJwfAutjXUUMjvj3lgDn1TgJd9CZc18SiDdXuGSehO3nkZ7yOfHazsD7wcW2h5BPF95x6z1AxPsNwBunzyRaRpKizRGgZSRPXCfkDsf3A/TiXa5D1b6S8nHrPUDH+iYmpoy+cnxlsupwWKL2jFgNS73Nt0q/jhOJqUojzocRJGyQ6OkQoxcj0BPghSJx6z1AxvsJf6dFfQpKF5wGnBUr6O+YwSre2a1YQrUHCuV6MvIwvIzFxXxeexNQmaSmFQ5A49b4hQIIBiofcM2jDIt+ou1DsUNKR7GQxliYtSQJ4+iRUh5gRVmIDpdptj8TxBQqWk2N/EGNOnHrfECABL7NXM0LCcPAvS4hJINZ2FD1FGhGXlVaQVNEbTmxYWCCKvMzTEbcjuzYgAc7OxHX2GgnwkZCV5q3XNSOUDOl2InlInZAjDUgw73xDwAlEHiK6gRMTlmp86Y5LZ5KkEL1ueP+KpyxaTkqklCse1HuGEAlVByFhjJhTXBjItC2Rmu4VcxqiWitR1TZ04aZ9yu4npuK9/BIkTr1niA88UhxofQhJj3CS3mWQn7JH0MXmtW04BkK53TkJ21Z5s77HzigsyPul5iX15dT7kkwrODdgSBcwe9BpWl+r3uBPiFDmoep9qj3LAVyl+rgFOSmA7Vj1/VfKSBp4trfyj/x+JlcYUXAuOsCQOvUVQzWZs7N/mwmyaqBpkNmZO49QTFMGrPlrGh+gScGiVmfuPEL5k74qs7ue8jlef4PNd0rg6tl6UgfbG3MfUcyJHo8q2ELbnoja29rtk9bj/OKcLAklHfxMJC7H6oCRpFQl3aMEC0JmGR6zmZLOfVmRdBrc8ayESIgSPfXOIrvN7u1q/z2jTRe3OqYk/7VdA3tt/zUC/wA7GY2hbPYydQAAAABJRU5ErkJggg==)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 550 + 56.76
⇒ Mode = 606.76
Thus, the modal wage of an employee is Rs. 606.76.
Question 4.Find the mode for the following data:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAj8AAADFCAYAAAC7OpNhAAAACXBIWXMAAAsTAAALEwEAmpwYAAAgAElEQVR4Xu2bCbhuR1WmjSaIGGRQEJnSQAAbGcL4QEAGUYOINAgoICICtiihVegOItGEuaWhUYKAIM2VQVAD2IQAkSABAgYIYzABDOSEBImKzKOA8XvDv/NUKv9Qde5/7jl17rueZ92zd+21q9Z6a9hr1/7vd32XIgEJSEACEpCABCQgAQlIQAISkIAEJCABCUhAAhKQgAQkIAEJSEACEpCABCQgAQlIQAISkIAEJCABCUhAAhKQgAQkIAEJSEACEpCABCQgAQlIQAISkIAEJCABCUhAAhKQwFYROKCh4gsbbDSRgAQkIAEJSEACu4aAyc/O7MoR+mUEH1t7dzfF0hozdsbdQ2t8W/t7/D7siWC/7e/v7qGkrQQkIAEJSEACEhidgMnP6D2o/xKQgAQkIAEJdBEw+enCpbEEJCABCUhAAqMTMPkZvQf1XwISkIAEJCCBLgImP124NJaABCQgAQlIYHQCJj+j96D+S0ACEpCABCTQRcDkpwuXxhKQgAQkIAEJjE7A5Gf0HtR/CUhAAhKQgAS6CJj8dOHSWAISkIAEJCCB0QmY/Izeg/ovAQlIQAISkEAXAZOfLlwaS0ACEpCABCQwOgGTn9F7UP8lIAEJSEACEugiYPLThUtjCUhAAhKQgARGJ2DyM3oP6r8EJCABCUhAAl0ETH66cGksAQlIQAISkMDoBEx+Ru9B/ZeABCQgAQlIoIuAyU8XLo0lIAEJSEACEhidgMnP6D2o/xKQgAQkIAEJdBEw+enCpbEEJCABCUhAAqMTMPkZvQf1XwISkIAEJCCBLgImP124NJaABCQgAQlIYHQCJj+j96D+S0ACEpCABCTQRcDkpwuXxhKQgAQkIAEJjE7A5Gf0HtR/CUhAAhKQgAS6CJj8dOHSWAISkIAEJCCB0QmY/Izeg/ovAQlIQAISkEAXAZOfLlwaS0ACEpCABCQwOgGTn9F7UP8lIAEJSEACEugiYPLThUtjCUhAAhKQgARGJ2DyM3oP6r8EJCABCUhAAl0ETH66cGksAQlIQAISkMDoBEx+Ru9B/ZeABCQgAQlIoIuAyU8XLo0lIAEJSEACEhidgMnP6D2o/xKQgAQkIAEJdBEw+enCpbEEJCABCUhAAqMTMPkZvQf1XwISkIAEJCCBLgLbkfw8Jh6eH70weo8ubzWWwGICj8ylr0Yfvtjk4iuXzdFG9DMNtpsxOSQ3vT3KOG+RV8aI+XDjFuNN2Nw595wXfdkm7t2KW3r5bIUP1jkWga2es5uhsdXzFp/217g30x9rv4dFuVVuFMM90U9EPxX91+hbo4+PXic6yaE5MPkpgGzisLVfrpi6Xxj9aPSs6InR6ze0N/UR7czTpzfU0eIjD+R59U9ll1vRzlVy/XXR987qaUl+Hjez7Ul+WmLB1ftHN6Ifj7YkP4fPfKH+1uTniNi+JkqfnhH9UPSo6PdGSzkoJ0+Nfjj6lehmkp+WuPH7eVHGF/6cGX1u9GrRWnr5lPe3xs09D4qeHsWfadzfonZmyfm6475t2jopCht8enf0fkvaLy/dKSd/HqWfPxD9WPQvotet7ifmeXOJe1qlJe7rpbJnRt83U/z5u+hdqkaumfN5/lDGutQjy+Zsz7hY1GZL3OW9y+Ztz3xY5M9UvixubB4a/WD0I9Fzoy+IXmm6ueHvOuOmuTtE3xxl/duIviFKXtAiPeOXte7oKOs+45vY3xi9SUtDsWmKu8kolTGRWWDZ2fn+mQOXyd9fjn4p+u+zMv6Y/BQwNnnY0i8HpO63RV8fZbBw/odRElOShmVCH50dZUCW+uCcs8Py08tunl1r8ZEHMolU3c4rUvbOhjZ+Pza/EWXBob1Vyc8Px+bTURbrdSc/MD4leu3o8dFVyQ/9cVr0hCi+tyQ/PDSwfUJ02rm9eY6/GP3raCk8FEhCvi9KrFuV/LD4MMZ+YNY4Y4tF6ZzowbMy/vTyKW696GHZGvcDZrb8RQ6Mvjj6uei1ZmWr/rSM3da4edn4cpS+mPrsYTmmjXuuciTXGUtvik58r5BjdhZ5yWRnYBLmELsR9Vy6e2Gz6rAl7iNTyT9FWSOQ74k+K/r1aPnwuWbOeTDX/nBOYt4qy+Zsz7hY1l5L3NP9q+Zt67hY5g/XlsXN9aOi34j++Kyiy+cv4+Lvo/RJi6wz7tunQZ7zj501DCfGBWtPy7xrHb/MIZKq/xedxv9Vc0zCdd9oizTF3WJEZve16B8saJUH5reKayY/C0B1FLf0y71TH3blQ5XB8oUoSdAyYbC+fI7BPVJ2dpSBvUpafHxaKmHS1HJ6Chg3q2Sa5MRIe6uSH96MjomSCDApW6UlFphMDzceWKuSnwfGhiQMn+t+WuQXi/1ni3Ymu+NmdfDAmaRcAIl1K5Ofw4p2ObxPlJh+qSjv5VNW2RP3a3PjuZU/rFH482tV+aLTlv7mIdcS96NnbV+nauxfcj5vjtU+kejerirkQYGPtynKKfvd+ubO85a4WVd44SiFcce9PJAnoYy38b2VZXO2Z1ws86Ml7un+VfO2dVws84dry+LmRYJNhXr8kAgRCzusLbLOuEnQPxmd1kDaZyOEF7PnNzjTOn5/NXX9cxQGpbCze42GdjC5sHSy8Z65Zkw4FloW4HnyVyn8//MuFGVMFDqbNwW2UxlAx0brAH8iZe+Y2bANzCcPHsiTXDcHfBKgnvdHsWXx2R+FBxCfHvnsMQlvZ+yocG2ZnJeL5YNrsmXR+9Noz6RZ1g7buvRRKbfOCQ8Kxs0q+fYqg+I6b6V3i/6fjnt6TGHyH403kIQ+JfqYRvvJ7PM5uNqcdngTR3gYTNLDprit+5AHMPO1lMmfKxWFPXxqJ3ri/lZuPrCqYDpfJ5PWuPEHqX1izWzx55jY8TZfyrQL9G9V+b44ZX193gJ/el4oWnxdNWd7xkVLe6tsWuZt67hY1taquG+Ymw+OnlFVwjMRadlRrG5detoS9y1Tw5nRcg3kaxA7Muv0h5fFk6LsepVC3vCpqmzh6bqSHx4oH4myrTxPeOCuetgeFhve3g+PksHdMXrnKG89k7ANeEL0SVFsuId2j7zY4jsPTMpuFr15lE8qPGT2R7lpgj5nTuCUkSROnyfnmMwtOiSld46+eO7V9RU+YtYG42ad8n9TGbuTX11npZusi6TnrVES9F5ha7mWG6TgguhH6wv74HyRPzRNjOuSRe3UcT8jDZIcPCp6QJRxfmyUhbkloY5Zkyzyh5vLuNlxOzt6bJRPkKy7fBog+eGzQI8QD7tAvHCye8uDpRTWzzdGSUZ5EMKiTEAvab2eM15Unh19W7TeieBN/BXR90QZmy+NsgvXKi1zdlE/1OOitc1ldi3zdpE/1Ns6H1bFTVKBlLu7nE+Jx4/Orq/rT0vc+FT7M/n0IzlgTq6SVeP3oFRwq+j50WOjJDz/GGVzhZfmtcqqN/zLpTVs/raj1UNn95Q7NnyvrH+H8rCUlW8SPzm7j4V+Et6Cf312Ahg6/78X1znkzWm3yap+IV7evtmKrOV/p4D7+bTVI0+NMQt5q7T4WNfFzgW/j7h+fWHFOYkz7T18gR1jjYkyJfzEUY6tBbddXNwby/G5kwk6TxizLMxXn13EZ+onhs3ID+WmL0QXxU6dxNrTd5MfvXFzHw/oU1e0t4zP1Paqv8vivlNu/kSUuEmimQcswK2y7rivnYZPifLzAHZrWLBZ6HuEnVju5eH65Ohlqpv5vcNro1Oc18vxe6NnRVlfW6QnbuYoY5x7Xh3l5bQU/GBngh0BhIffS6LMb15OV8lm5+yycbGozZa4NztvW+ZD6VdL3CQZbDa8qgpo+uxFst0i64ybsffpKM/hSabPXrTD151l0jJ+qYO6GEN/HOXL0GWjx0WZ59NYy+FSaYl75eeNKfk5aWlTl7x4aE5pnE6ehIfSkdF3RT8Z3YjyyQa7KWMkOWKb87zo/4oeEq3lnSkgAyVzbgVR1zHCeUvntSQ/ByZYEo5JF+0GsdDynfX2HXBafKyr+60U1Albi48kDrQ3LwHgfh4Ady4ae1mOeTC2Sm8syx7uL0qjxxYN4zP1E0MpZb9cobo2nTJvXhPljXqZECsx90pv3NT/O9EPRxf5jM0yPnsb9wNTP7t7vxCFD7stfKZh3Tg02iLrjJt+5aHwzCiLNT49OIqP9yqcaYkb8xtE3x4lmeeeZXLbXCQW3txbZDNxXzkVw5ffMN1qRSM8L0jgTijs5sW92TnbOh9qN1vibp23dd2L5sPexv3INMQn1ftFSbBIzv4+SmJA0tki64z7sDRIYv6MKM8LkpLnR78UpZ0fjCLz4p5dutSfevwyf6mL9Yy5NAltMa5YC1ukJe6VyQ8NkaR8sKXFmc0UwD2Ke47O8TejPxulI5EHRXGSTH4SJv6eKB3MNbYRy7cIFlw+c/Hg5/rHoiyCu01aOo9t79PmBP7clLFDRqJztyh1TfrGOfYU3T9KfT3S4mNdH0nKz1eFLT7ygKE9EolaHpWCv6kKSQSYQK3SG8uihztjleSeh8Ak85IfJnPZL7zVzBPeeF4XLd+25tkR675Ifphr7GqsestbxGdv457eiOvPWyyUn4/+5Tw4c8p6+3tZ3NMbMb6V8oacXDAraI17uv+QHODjUy9Z5aXOSCJ4QP71pa7ML+iNe6qF2Nht4OVzlbBm88xAFsW92TnbOh9qH1fF3Tpv63oXjYt1xf2raZCE5yNREmLWzvdEX187suB83XHfYdY2awC7jo+LPivK85rEdFHcC9y76Hdy5fhldxGfT51zA2XnzymfV3QhFa9DAP2AKIkH2++1kOkB5R3Rz9UXZ+ds6eL8iQuuT8UkMw+JHhn9xeiTo+w6sa1M1kn7j4/y246fij4p+soo930guj8JycpPzwn4OinjkwA7ZKdF2SqdZFH/8ENnsvitlLukcnb5eFiU0urjIt/umgu3iW4UBiTU7AhMZXfK8bnF9a06ZEyyAJxZNHDw7JhxzAvAY6M8vMt+IVmthUWFvrxPlPu2W/CD+Qbv1kWo9vkbKdibuEm6WG+Y76VQL/1706p8Haer4r5JGuG3Od+uGsPHu0VZ0Nk1WRQ3ifJXq3uJhWTulkU5O+NTUjEV86BA68Srqq7rlHlDMl4+OIntjOjPFDXxPPhalHW5FGwnfxb192bm7FbOh9Z5WybXy8bFuuJ+cViipbwgJ/wGZh3SGzfP8LtXDfNpjjWcNWxR3NzSMn75+sAzikSqFsbVvPLarvl8VWZIRTeMMjkft6DWp6Wct122wpBDo9Rb7vzw1vCW2fXpz1Ezu2nn5/Y5/7XK5qEzm2vkLw/OZ1fXrzu7TnK1m6SlX3gLwO7HisCnN+A/7IBxo9h+KXr5jnswbfGxrJIH/hM625jMl+38zKvyZSncjp2feb48fMaKGFqFz7rs+JRbv7wQlHOqrItYiblXWvuQsfbRKC8hk9wuB8csaPD4lG8mQVoVN2OUN8WXVu3ysIXBKQv8qYvXGfe7Ujnr3wFVI+xGkkSUfVj7cWAKWFuntXO6zlrHYv8XxQ0bOWZtLeXmOSGWo6vyRactcfOA42W2ltNTwI77JHtywNguhVhJ9E6uyltOl83ZVeNiVf0tcdd1LJu3vfOhrrs8XxQ3ie/VqxsPzzlj6pBlFRbX1hk3c/9mVbt8XfhslI2KVbIRg5bx+5LY8YmrnBPMExKj1qSvKe4mozR6r+gXo2xX8maL8PcxUba8fnJWxh8CpN5yoSZrZ9Ga7P5Ljnm7wW5Kfu6b43OiU4ezoL0oypYfgh1vwHecnfPnIVHePkiCdpO09AuL7dui7KZNA4VElAWKLLtVjovhZnZ9WnycfLhaDugn3tw3IyQOtMeC1CKLFpRF9/bEQh09D3d8pn5iaJFnxogHyMOiDyr0hBw/ZEEFW5n8sNDTd79X+fP0nO9Z4E8Pn6mK1rhZE3jDvNPsRubBE6Mw5m28RVr6uzXuX561zY7eJEfkgPWuflmrfWNRx5c/jk5JEjtBjF92VMokZCPnvGXzwEGuHGX+fyo6raGzSwv/tMR96qzeqxa1sO5zLy+sk+zJAbtbh8wKWK+Jo16jL75hxcGiOds6LpZV3xJ3ff+ieds6Lur6Fp0vivvPcsPLo4wR5FpRfn7y27Pzlj/rjJu16Kwo4w6ZxulrWhyJzUa0ZfweGju+8Dy5qPeYHJP0kRC2SFPcTUaz1tghoKPOiW5EPx7lzaTMBkmGzo9SL5kaD1aECfvc6AVRJsxJUQY1drw1kVzxYHxO9MNRPmH9Q5Rv2VNic1COfz/63tn1D+Xv26N3ie42ae0XPgEwSWDKwHx99AYdMOgXttcP67hnMm31Efujo7wJ98pNcsNGlAWe9njIc/7g6Dxh/HGdhJw3Z45fO8+wKmuNhQcvdfJJkYcbx++r6ppO2cnkOj5TPzFwzqKxSBjr2C7Sh1Q3Mkc2osRKzBwzz1qlJW7m5yJ/9lQN9fApb+2Jm3WABwBrBGsF4/4t0SMqX5adrjvun0tjJCL4gk/vjz4yOj24lvnCQ4UXmDOjPNyo49XRW1c38cmJ3VPsaIN+eUm03I2rbrnUaUvcJFx7oowt/KE9YrtfVRtzk/X6jChr8XlR1nXu75Flc7ZnXCxrsyXu6f5V87ZnPizzaVnc3MfXjNOj50R55p0ave+yCudcW2fct0j9J0fZtGDu4RNfg5iPLdIzftnRpK2NKD/heFP0Ni2NzGya4m4y6mhU0/UQGKFfRvCxtTd2UyytMWNn3D20xre1v8fvw54I9tv+/u4eStpKQAISkIAEJCCB0QmY/Izeg/ovAQlIQAISkEAXAZOfLlwaS0ACEpCABCQwOgGTn9F7UP8lIAEJSEACEugiYPLThUtjCUhAAhKQgARGJ2DyM3oP6r8EJCABCUhAAl0ETH66cGksAQlIQAISkMDoBEx+Ru9B/ZeABCQgAQlIoIuAyU8XLo0lIAEJSEACEhidgMnP6D2o/xKQgAQkIAEJdBEw+enCpbEEJCABCUhAAqMTMPkZvQf1XwISkIAEJCCBLgImP124NJaABCQgAQlIYHQCJj+j96D+S0ACEpCABCTQRcDkpwuXxhKQgAQkIAEJjE7A5Gf0HtR/CUhAAhKQgAS6CJj8dOHSWAISkIAEJCCB0QmY/Izeg/ovAQlIQAISkEAXAZOfLlwaS0ACEpCABCQwOgGTn9F7UP8lIAEJSEACEugiYPLThUtjCUhAAhKQgARGJ2DyM3oP6r8EJCABCUhAAl0ETH66cGksAQlIQAISkMDoBEx+Ru9B/ZeABCQgAQlIoIuAyU8XLo0lIAEJSEACEhidgMnP6D2o/xKQgAQkIAEJdBEw+enCpbEEJCABCUhAAqMTMPkZvQf1XwISkIAEJCCBLgImP124NJaABCQgAQlIYHQCJj+j96D+S0ACEpCABCTQRcDkpwuXxhKQgAQkIAEJjE7A5Gf0HtR/CUhAAhKQgAS6CJj8dOHSWAISkIAEJCCB0QmY/Izeg/ovAQlIQAISkEAXAZOfLlwaS0ACEpCABCQwOgGTn9F7UP8lIAEJSEACEugiYPLThUtjCUhAAhKQgARGJ2DyM3oP6r8EJCABCUhAAl0EDmiwvrDBRhMJSEACEpCABCSwawiY/OzMrhyhX0bwsbV3d1MsrTFjZ9w9tMa3tb/H78OeCPbb/vazV88w0VYCEpCABCQggeEJmPwM34UGIAEJSEACEpBADwGTnx5a2kpAAhKQgAQkMDwBk5/hu9AAJCABCUhAAhLoIWDy00NLWwlIQAISkIAEhidg8jN8FxqABCQgAQlIQAI9BEx+emhpKwEJSEACEpDA8ARMfobvQgOQgAQkIAEJSKCHgMlPDy1tJSABCUhAAhIYnoDJz/BdaAASkIAEJCABCfQQMPnpoaWtBCQgAQlIQALDEzD5Gb4LDUACEpCABCQggR4CJj89tLSVgAQkIAEJSGB4AiY/w3ehAUhAAhKQgAQk0EPA5KeHlrYSkIAEJCABCQxPwORn+C40AAlIQAISkIAEegiY/PTQ0lYCEpCABCQggeEJmPwM34UGIAEJSEACEpBADwGTnx5a2kpAAhKQgAQkMDwBk5/hu9AAJCABCUhAAhLoIWDy00NLWwlIQAISkIAEhidg8jN8FxqABCQgAQlIQAI9BEx+emhpKwEJSEACEpDA8ARMfobvQgOQgAQkIAEJSKCHgMlPDy1tJSABCUhAAhIYnoDJz/BdaAASkIAEJCABCfQQMPnpoaWtBCQgAQlIQALDEzD5Gb4LDUACEpCABCQggR4CJj89tLSVgAQkIAEJSGB4AiY/w3ehAUhAAhKQgAQk0EPA5KeHlrYSkIAEJCABCQxPwORn+C40AAlIQAISkIAEegiY/PTQ0lYCEpCABCQggeEJmPwM34UGIAEJSEACEpBADwGTnx5a2kpAAhKQgAQkMDwBk5/hu9AAJCABCUhAAhLoIWDy00NL251A4JA48fbo+TvBGX2YS+CVKb0weuO5Vy3c3wjs73N2t8yH/a4fWcSWyVVykQfRV6LYclzrF1P2P5dV4rVuAqv6hQp5+Dwvelb0jOiZ0edGr8bFOfKAlJ0afW/0E9F3Re83x661qMXH66WyZ0bfN9OP5e/fRe8yp5H7p2wj+vHovk5+1hnLNeM/9c3TK86JezuLWuIu/Tu8iKtOfnrH4whx3zZOnhRlbjHH3h2t58xui/tlRR/PG8OXKzpuO+dsz/hpGeebmbfL5kOPf1tl2xI3bbf24x1i++Yoa/RG9A3RG1HBDpOmuJuMEtifRb++IMAnp9zkZwGcTRa39MsHUvfroz8wa4NElcTmnOjBVbuPy/np0WvMyi+Tv6+KPqey6zlt8fHIVPhP0UNnFX9P/j4ryli6SdHY9+b4lOi1o8dHd2Ly0xoLi+gHow+aowelbCdJSx9O/h6Qg9OiJ0S5r05+esbjdjNoifv6cfLLUV4opl30h81iv2cRwG6Lm+Tn6dF6/L4iZe8s4t7uOVu4svKwpb975+2q+bDSqX1g0BJ3az/ePv7+e/SxM7+Jn7X8M9Fr7YNYeppoifuiRaxFliU/PMRu2FKJNs0EWvqFRfewqsb75Jx7f6kov0GOvznHlgFb319Vt/S0xcd7p4bfqGqZ3rCOKsqZSNMDZqcmP62xEN8bl5LbORdb+nDy9oE5YNfu4VHum5f81ONp3njcCdG3xP3oWZzXqRz+l5y/vChrnYejxP20OMqDrhZenh5cFG73nK39W3be0t+983bVfFjmz7661hJ3az++KU5/Mlr+nOb7c86Xn+fvq4Aa27lwq3/zc3AcIetjO/ij0UdEgY3ywHtilIWCcx5oCLsUvEltRPkEwueQ8i0KG4S6NqJ8bntP9I5R6vlc9MToXaPsDlD221GEuikjO93znaKL/13Vbu07CwBtfSp6dFUXp8T+7OhG9ENRGBwXZYfjtVF8YHcDf6ZtYn7LQjwwu0N0b+U2qYCFtxR2WZArFYW/kuMLorXteXPKitvWcvia1MKnuVKmnSo4TEI//sclzXbcWWssO87xNTh02dTxlOhjltTVOh6XVLGjLn1r5s2BlVfsXn67KNttcbNL/I4q5lvnnCTwr4ryEeZsFcbaTlvmw9oa2+KKWvvxlvGDz7/lOs3zjE9g857hW+z23ldP4C0yb+dnSn6m+y+fA3aAqJOk5pgou0IkCSQ/LBpMKh7C08OZN0MWkrtFJ+GbOnWw0DLI2H4+dVZ25MVW3znAbkp+pkvUv6ewa2m39P303Ps7UXx/apQ2fryq72055xPTFMchOSZR+t2Z3Qvz91+jBxX3cUiSxBvGKmntl7qeX0kB95aflN6Sc5TdIPh/JApPfgO0N7IZH1lAT46+Ncp26zxhrJA07ktZZyz0L/38iiiJOy8GL40O+208vj8+uieKPDwKrxvPzpf9mTcel9nvq2st/X3lOPOP0ZdHvy/KyyRb/p+P3nyFoyPHPS+0F6XwGfMuzMq2Y84ucedSl1r6u2febnY+XMqxLS5oibt0YVk/8rLM7k8tPAdpZ3qpra9vx3lT3E1G8Z7kB9taP1NFRrKCzeuKcn6LQnIzJTV8PiiFB/FpRcE/5Pj9lc0ROafezSQ/re1OvjMAJiFx4rv/HxRl980xvtyjKOPw96LTb5/Y2cHmXoUNb0/zBk9VzUWnrf1S3sv2JSxfVlV4ds6JgYTtqlEWcbZsyeAfWdn2nPb4SAJLQsM9r47+8JKGlk3AJbft1aV1xvIj8YTkhzclhEXhJVH64Gazsp3ypyXuq8XZC6JXnzndmvwsGo87IfaWuPGT36CdEv1a9N+iJEOHc2GJ7Ia4y/CumBPGLnN4kWzHnF3ky7zylv5unbebnQ/z/Nrqspa4Sx+W9SNfND4dLV/op89etNPyUr/V8U71N8XdZJQaSX74jFPKwTlZlPywdVoL3wVpr37wHZcyHsTsvvCgwIZPY6X80Kx8M8lPS7u0NSU/0w+6pvZZ8P6kcGZRfZdwOCdsB/Kgn4Q6HlQbLThv7ZfydnarPhy9QlXnlHTcqio/Mef0HwneZmQzPvI2zWcwPofW/kw+LJuAm/Gz5Z6timVqm0+fPDxPaHFmH9q0xM1b/7GFT63Jz6LxuA/DW9hUS9w3zt0s9s+MskvJSwO/eflqtHypqRsZPe46nt9KwaqXtu2Ys7Wfy85b+nve/fPm7Wbnw7z6t7qsN+5l/XhYnOXnHM+I8h9meF7yLPxSlHZ+MLpTZMt/8/OVRLpoK5/fy9RCAoPwX6w3CmVnhh9NkVGTfSP1/Ww1b1Za2i3r/kLVEJ/lygRhqu+zKxziU8fPRhkUDBaOy2Roxe1dl38h1r8ZZYet9n8anPw2qRR21/CNT1H7SmBGAkt/8zl0ZOmJhQcmieltBwuYnaqfij690+9l47Gzqm0z55M3clT0G1Fe0NjB45Mti/482Q1x13E9IgX17/Zqm916Xs/bzSmkNzIAAAeCSURBVM6H3cCHn5P8RJRnPl9n+AnFuVE2RsgF6md2irZPDtzipsn2eINvFXYZkJtGefjNE3Z+EHYISmHrdZ6wILHNXMrB1XlLu/PqXlQ21cfvfZbFz0LJ57L7R/ls8JYok2ndcp9U+KToXaPs8tTykRT8aLTmRFKH8Ea7VcJvJb4eLd9AaPeM6M9sVaNbVG9rLOy88ZmEt6RS6iR6i9xca7UkPrzhnVnUOs2vk1L2zSg7pX9ZXF81Htfq4BZWxu/m2L2d5snU1MdywEsGO9j/XLS/W+Iukd4lJ6zJfPLY7dIybzczH3YTt1MTzN2rgF6V89OiPIuHktZtsXmfveYFykJJnbwt1MLiwDV+D1MKmeQLigKySrLMUhh03MuuQSlsSz+lKODTGQ/bPUVZa7uLfCd5KN/07ptzfKkHwf9IWf257+0pe3f0hOido63S2i8/nwr5QS2/TZjkdjk4pjh/aI6pr/7MxKDlU8xWfvZistT9jWunR6f/mcZ5KcfnZF4SV9ut87yFd2sse+IYn4ZK4bMJifLJVfl2n7bEXfu47LNXy3is69uO85a42aH+ZLR+afiblLHG0KeT7Ka4i7Au+t9dTygLFhxvx5xd4Mrc4pb+3pM7NzNvl82Huc7sw8KWuEt3lvUjzxh2vkrhNz/sgP9iVb7dp1v+2as3QBYNtoyfFmXXBGFH57joebNz/hwbBTLfzvlcdEj0N7kwR96Wsv8WJWtnB4MfHde7Sq3tzql+btFrUkpSc2x02pG6QY7ZHv/b6o4/z/mto/81SuzrFBbcl0dp445Rfk+E3jt6naIhPr99MAr3y83K2SW6Z5SdqfrNtrh1LYd8PrhqUdOjcnzL6B+tpfZ9W0lrLIwFxi1Ccvn0KGP+ibOy3findTyOEvtz4ui1ovTlJEfk4B5RXtb4FIbstrhnYV30M4Sfi75wKtgP/u6P87a1W3nGvDJ65dkNPEv+NMpzrdz5ba1v2+1WZYZXiYcb0S9FseX4zQu85jPGuTM7dhSwnZKc6Ra2zHnoce1D0fdFHx09YDKY/f31mQ3t8sbNpzLar3d+WJz4MR7tvTfKZGXX6MvRs6OTrGq39p2EbIqdrf3Jj6m+y+fg2dGNKInFO6MsjLVMW6lPqi+sOF/VL9zOWyl283RPVT+xUMY97BS9P0qitDfS4iO7Pnui7ObBic8nJKz3m9Pwi1K2EeX78bdmx4yPfSHrjOUmcZgH5xlRxjiJPZ+I5u2A7YvYlrXREvd0/+1zsBH9TJT7PjU7nxLqnvG4zKd9ca01btYTxutZUX6zxbzhf0geWDi5G+MmvKOjvDguk+2cs8v8qq+19HfvvF01H2oftuO8JW78aunHW8Tu5CjPeJ6xPG/50nEQFewwaYq7yWgHBMZig6918rMDXFvpAg/866+0uqTBCP0ygo+t2HdTLK0xY2fcPbTGt7W/x+/Dngj22/7mM5CyvQR+LM1/Lsp/l1ckIAEJSEACEthiAiY/Wwx4QfW3Sfme2bXH5C/fRRUJSEACEpCABHYIgRG2xfh9yPlRfGUX5cQdwm6RG+z2XBDltx78IJkfvPbKCP0ygo+t3HdTLK0xY2fcPbTGt7W/x+/Dngjs7yW09lc4S5DsiEsj9MsIPrZ25m6KpTVm7Iy7h9b4tvb3+H3YE8F+299+9uoZJtpKQAISkIAEJDA8AZOf4bvQACQgAQlIQAIS6CFg8tNDS1sJSEACEpCABIYnYPIzfBcagAQkIAEJSEACPQRMfnpoaSsBCUhAAhKQwPAETH6G70IDkIAEJCABCUigh4DJTw8tbSUgAQlIQAISGJ6Ayc/wXWgAEpCABCQgAQn0EDD56aGlrQQkIAEJSEACwxMw+Rm+Cw1AAhKQgAQkIIEeAiY/PbS0lYAEJCABCUhgeAImP8N3oQFIQAISkIAEJNBDwOSnh5a2EpCABCQgAQkMT8DkZ/guNAAJSEACEpCABHoImPz00NJWAhKQgAQkIIHhCZj8DN+FBiABCUhAAhKQQA8Bk58eWtpKQAISkIAEJDA8AZOf4bvQACQgAQlIQAIS6CFg8tNDS1sJSEACEpCABIYnYPIzfBcagAQkIAEJSEACPQRMfnpoaSsBCUhAAhKQwPAETH6G70IDkIAEJCABCUigh4DJTw8tbSUgAQlIQAISGJ6Ayc/wXWgAEpCABCQgAQn0EDD56aGlrQQkIAEJSEACwxMw+Rm+Cw1AAhKQgAQkIIEeAiY/PbS0lYAEJCABCUhgeAImP8N3oQFIQAISkIAEJNBDwOSnh5a2EpCABCQgAQkMT8DkZ/guNAAJSEACEpCABHoImPz00NJWAhKQgAQkIIHhCZj8DN+FBiABCUhAAhKQQA8Bk58eWtpKQAISkIAEJDA8AZOf4bvQACQgAQlIQAIS6CFwQIPxhQ02mkhAAhKQgAQkIAEJSEACEpCABCQgAQlIQAISkIAEJCABCUhAAhKQgAQkIAEJSEACEpCABCQgAQlIQAISkIAEJCABCUhAAhKQgAQkIAEJSEACEpCABCQgAQlIQAISkIAEJCABCUhAAhKQgAQksJ8T+E9JJFxpZ6AZogAAAABJRU5ErkJggg==)
Answer:Observe that, from the given data:
The maximum class frequency, here, is 82 and the class corresponding to this frequency is 28 – 35.
So, this implies that,
Modal class = 28 – 35
Mode of such grouped frequency distribution is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the modal class = 28
f0 = frequency of the class preceding the modal class = 42
f1 = frequency of the modal class = 82
f2 = frequency of the class succeeding the modal class = 71
c = size of class interval (the class intervals are same) = 7
∴ Substituting the values l = 28, f0 = 42, f1 = 82, f2 = 71 and c = 7 in the formula of mode. We get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 28 + 5.49
⇒ Mode = 33.49
Thus, the mode is 33.49
Question 5.Find the mode for the following data:
![](data:image/png;base64,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)
Answer:Observe that, from the given data:
The maximum class frequency, here, is 31 and the class corresponding to this frequency is 80 – 100.
So, this implies that,
Modal class = 80 – 100
Mode of such grouped frequency distribution is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the modal class = 80
f0 = frequency of the class preceding the modal class = 21
f1 = frequency of the modal class = 31
f2 = frequency of the class succeeding the modal class = 27
c = size of class interval (the class intervals are same) = 20
∴ Substituting the values l = 80, f0 = 21, f1 = 31, f2 = 27 and c = 20 in the formula of mode. We get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 80 + 14.29
⇒ Mode = 94.29
Thus, the mode is 94.29
Question 6.The following data gives the information of life of 200 electric bulbs (in hours) as follows:
![](data:image/png;base64,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)
Find the modal life of the electric bulbs.
Answer:Observe that, from the given data:
The maximum class frequency, here, is 82 and the class corresponding to this frequency is 80 – 100.
So, this implies that,
Modal class = 80 – 100
Mode of such grouped frequency distribution is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the modal class = 80
f0 = frequency of the class preceding the modal class = 42
f1 = frequency of the modal class = 82
f2 = frequency of the class succeeding the modal class = 71
c = size of class interval (the class intervals are same) = 20
∴ Substituting the values l = 80, f0 = 42, f1 = 82, f2 = 71 and c = 20 in the formula of mode. We get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 80 + 15.69
⇒ Mode = 95.69
Thus, the modal life of electric bulbs is 94.29 hours.
Find the mode for the following frequency distribution:
Answer:
Observe that, from the given data:
The maximum class frequency, here, is 15 and the class corresponding to this frequency is 20 – 24.
So, this implies that,
Modal class = 20 – 24
Mode of such grouped frequency distribution is given by,
Where,
l = lower limit of the modal class = 20
f0 = frequency of the class preceding the modal class = 7
f1 = frequency of the modal class = 15
f2 = frequency of the class succeeding the modal class = 1
c = size of class interval (the class intervals are same) = 4
∴ Substituting the values l = 20, f0 = 7, f1 = 15, f2 = 1 and c = 4 in the formula of mode. We get
⇒
⇒
⇒
⇒
⇒ Mode = 20 + 1.45
⇒ Mode = 21.45
Thus, the mode is 21.45.
Question 2.
The data obtained for 100 shops for their daily profit per shop are as follows:
Find the modal profit per shop.
Answer:
Observe that, from the given data:
The maximum class frequency, here, is 27 and the class corresponding to this frequency is 200 – 300.
So, this implies that,
Modal class = 200 – 300
Mode of such grouped frequency distribution is given by,
Where,
l = lower limit of the modal class = 200
f0 = frequency of the class preceding the modal class = 18
f1 = frequency of the modal class = 27
f2 = frequency of the class succeeding the modal class = 20
c = size of class interval (the class intervals are same) = 100
∴ Substituting the values l = 200, f0 = 18, f1 = 27, f2 = 20 and c = 100 in the formula of mode. We get
⇒
⇒
⇒
⇒
⇒ Mode = 200 + 56.25
⇒ Mode = 256.25
Thus, the modal profit per shop is Rs. 256.25.
Question 3.
Daily wages of 90 employees of a factory are as follows:
Find the modal wage of an employee.
Answer:
Observe that, from the given data:
The maximum class frequency, here, is 33 and the class corresponding to this frequency is 550 – 650.
So, this implies that,
Modal class = 550 – 650
Mode of such grouped frequency distribution is given by,
Where,
l = lower limit of the modal class = 550
f0 = frequency of the class preceding the modal class = 12
f1 = frequency of the modal class = 33
f2 = frequency of the class succeeding the modal class = 17
c = size of class interval (the class intervals are same) = 100
∴ Substituting the values l = 550, f0 = 12, f1 = 33, f2 = 17 and c = 100 in the formula of mode. We get
⇒
⇒
⇒
⇒ Mode = 550 + 56.76
⇒ Mode = 606.76
Thus, the modal wage of an employee is Rs. 606.76.
Question 4.
Find the mode for the following data:
Answer:
Observe that, from the given data:
The maximum class frequency, here, is 82 and the class corresponding to this frequency is 28 – 35.
So, this implies that,
Modal class = 28 – 35
Mode of such grouped frequency distribution is given by,
Where,
l = lower limit of the modal class = 28
f0 = frequency of the class preceding the modal class = 42
f1 = frequency of the modal class = 82
f2 = frequency of the class succeeding the modal class = 71
c = size of class interval (the class intervals are same) = 7
∴ Substituting the values l = 28, f0 = 42, f1 = 82, f2 = 71 and c = 7 in the formula of mode. We get
⇒
⇒
⇒
⇒ Mode = 28 + 5.49
⇒ Mode = 33.49
Thus, the mode is 33.49
Question 5.
Find the mode for the following data:
Answer:
Observe that, from the given data:
The maximum class frequency, here, is 31 and the class corresponding to this frequency is 80 – 100.
So, this implies that,
Modal class = 80 – 100
Mode of such grouped frequency distribution is given by,
Where,
l = lower limit of the modal class = 80
f0 = frequency of the class preceding the modal class = 21
f1 = frequency of the modal class = 31
f2 = frequency of the class succeeding the modal class = 27
c = size of class interval (the class intervals are same) = 20
∴ Substituting the values l = 80, f0 = 21, f1 = 31, f2 = 27 and c = 20 in the formula of mode. We get
⇒
⇒
⇒
⇒
⇒ Mode = 80 + 14.29
⇒ Mode = 94.29
Thus, the mode is 94.29
Question 6.
The following data gives the information of life of 200 electric bulbs (in hours) as follows:
Find the modal life of the electric bulbs.
Answer:
Observe that, from the given data:
The maximum class frequency, here, is 82 and the class corresponding to this frequency is 80 – 100.
So, this implies that,
Modal class = 80 – 100
Mode of such grouped frequency distribution is given by,
Where,
l = lower limit of the modal class = 80
f0 = frequency of the class preceding the modal class = 42
f1 = frequency of the modal class = 82
f2 = frequency of the class succeeding the modal class = 71
c = size of class interval (the class intervals are same) = 20
∴ Substituting the values l = 80, f0 = 42, f1 = 82, f2 = 71 and c = 20 in the formula of mode. We get
⇒
⇒
⇒
⇒ Mode = 80 + 15.69
⇒ Mode = 95.69
Thus, the modal life of electric bulbs is 94.29 hours.
Exercise 15.3
Question 1.Find the median for the following:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAeQAAADFCAYAAACFKYHeAAAACXBIWXMAAAsTAAALEwEAmpwYAAAgAElEQVR4Xu2bB7QtRZWGQUEMqJizgHFGMYdBQcecdczjjAFnZC0TulRc5pxQRpeKWWDmqhgHw9IRdZkQEypmETNXMIsJs6LM/2G31mvO6a77Xt+6F/n2Wv873V11au/zdXXtqur7tttOk4AEJCABCUhAAhKQgAQkIAEJSEACEpCABCQgAQlIQAISkIAEJCABCUhAAhKQgAQkIAEJSEACEpCABCQgAQlIQAISkIAEJCABCUhAAhKQgAQksCWB7SuAnFpRxyoSkIAEJCABCawzARPyOgM+Eze/2fqW8Yx3RvnIZ5zAeKn9Z4LPWcbLLZWABCQgAQlIoAUBE3ILyvqQgAQkIAEJTBAwIU8AslgCEpCABCTQgoAJuQVlfUhAAhKQgAQmCJiQJwBZLAEJSEACEmhBwITcgrI+JCABCUhAAhMETMgTgCyWgAQkIAEJtCBgQm5BWR8SkIAEJCCBCQIm5AlAFktAAhKQgARaEDAht6CsDwlIQAISkMAEARPyBCCLJSABCUhAAi0ImJBbUNaHBCQgAQlIYIKACXkCkMUSkIAEJCCBFgRMyC0o60MCEpCABCQwQcCEPAHIYglIQAISkEALAibkFpT1IQEJSEACEpggYEKeAGSxBCQgAQlIoAUBE3ILyvqQgAQkIAEJTBAwIU8AslgCEpCABCTQgoAJuQVlfUhAAhKQgAQmCJiQJwBZLAEJSEACEmhBwITcgrI+JCABCUhAAhMETMgTgCyWgAQkIAEJtCBgQm5BWR8SkIAEJCCBCQIm5AlAFktAAhKQgARaEDAht6CsDwlIQAISkMAEARPyBCCLJSABCUhAAi0ImJBbUNaHBCQgAQlIYIKACXkCkMUSkIAEJCCBFgRMyC0o60MCEpCABCQwQcCEPAHIYglIQAISkEALAibkFpT1IQEJSEACEpggYEKeAGSxBCQgAQlIoAUBE3ILyvqQgAQkIAEJTBAwIU8AslgCEpCABCTQgoAJuQVlfUhAAhKQgAQmCGy2hHzWxLsa/So6ZiL2jSzeLc7fFR0bfT16/UYGsw2+9893vxOdGt1upJ29UrYanRI9d6TeehbtmsY/HBHvZrAzejxvCETu+x7rBPOMzmedsPy1WfmME95sfMajbVjKQ7vMdksBA+Sfoz92xxcdVD4w5ydFv4neMyhbdnpYCjZzQn5v4ntLF/wu+SQpb6SdL86/F91/K4K4XL4zlZD7ZrnXcybksb5V/pR75GQ1+ma0LCGTWF4WHRd9Mfpy9NJo2B9zaanNGc9l4+V50Wc6fS2fH4huvNT76QvmjKds/fo5oW20loQ8ZzyXLGLoY+k/eaZqbM54en//loOPRJ+OvhV9IrpbTTCpM2c8jIFDLuX5OStimjMe3O0ZMYbzbPGMfTKqZcP3545n77T5/ohxYTVikXQlHFVaTTxrGVfotwdHX40Yh94ZXb4yFqrVxFNViYHmdxGJYZEdkIsPX1Sw5NpmTsjbJ+bfRg8rYj/Hkt/R6vK54+jo6O5b4XCzJ+Sd8puOjC4dHR4tS8ifS9kR0Xk6BhfKJ4Pq8dHO3bWpj5oHojae/eKMSRJ8MXZ/nh/xnFyluzb1MWc8vS/6L33lHRHtz52Qa/mQkD8f3WuBduyDnficm89j4++Y6BKd37Pl883Riyfi6IvnjIcxkMXMkM/rc+1jGxAPiYWdSya5/c7q/XLMb77DBsTDrt0fokd3vunXPF8nRZeaMZ7acQX/R0WMQTwDnD8n+m7EWFRjNf2nKiHvE2809qAFXrl5x0cXXlC27NJmTshn737rA5YFfwa7vtkTMh27HwCmEvLVB+zv0t2re1bek5oHojaeO8XnAwd++1XhozYgnt7lv+eACfS+HZu5E3ItH1i8u5LDsmpz3q8rxAm7fMM+xOA+vNYiHhYxJJ2hMWG4z/DikvM5+TwiPmhv94GvH+X8tUv8Dy/PGQ+7lCdE5WvXc+X85OjlQ8dLzmviISEP7/+icYXnnfbK54lc8YuIxFxjp871DpmBktnTfRd4vVmufSHixtHB3hp9ttOn8skW0ZixNcOq6PfR24qKbJ38Mlpd8OVb5xptf70rPzify1bv5dd3zslB3XfYYmRbZp+iArPVb3TnPDDExYx1aMyQmBlxg7ghbF1gbJ/ynVMiylk11TDp3/fR3j9Fb4r47Zw/Jer5UK+3HXLwjIhVImI18upo2RYuv30l+lmnl+STDjVlV0yFt0er0fER20ZXnvrSGsr5jbwSmbLrpgIPT2msULGae7/lN5ef1cZDP2cLvbR+9c4sfi6rjQd/3M9nRvvP5XxBO2uJZ8HXZ79UG88+8fyDaNiHTlxwbVuCrI2H1fpHB46uk3MSIs//XFYbD2MWxrhSGmPYnwbXtuW0Np5rxQlb5+XY8Oucs31du2KvibN2XCFJ/zj6UtEou2HsZlA2mwGoxlZSibrDwfh1uXbnroHn5pNthX4icLkc/zC6VVfefxyWA2aCpR2ZkzIhU/aCaHWLWtttd9uc00H+s7vOdi5Q+IOgsQkIHeuoCL/9AH6DHLM9/ZCoNwY1fucDimvLDnmXQLIq7eI5Oba4UMOELQ8GDPx+MGJiwLbnR6L9uraOzmeZkEmwP40u05Xz+/4rggWrmN64B7TL5IP7wAN304iJxHCm+Z1cI97eWOWQXP4ngi3tMqHh2sX6SiOftX2rb+LwHBBDrfXM5twiLn2vJR4G0vdFH4qYsNXY3HweH6crneN980n7e9QE0tWZMx76Dn2OCS2TZ56V10RzvwMsf97Y/eK5QveMSIRfiXi+phYMZftz8inb7Y8PzUH5/C2qs17xnD8Ns8BhNcwrOp53tot/Hl2jdDpyPCcfJkqskofG4gM//eR3WF6erzWe/rv7dD7KcYVFJ39vMDS2+Jk0nGtYsOC8Kp6qSmn8RhF1GfR7O28OToh4F4OxOmPFWxoPIQ9KaduSkEl2rAZLu1lOiG2Y+Ms6d+3qkNBLe3VOSE593GtJyI/L9/4Yldv1j8k5s9/eapkQO7/hkcV32UrpO8UwIfPA7FbU5fCyEW2Ug3CfkJkolXZgToi9fB8zTMisoqnDhKE3JkC/iZ5dXFt2WNu3+u+PDahDH0wOGFDpS7W2HvFcPs7hRtv8IeBFaoPpvrOG6qPv2OlnP4iYEGL7RsO+0BUt/ZiTDxM2EjIrHYwBlGeNnbarddemPuaMh50vfB8V8bzy/LC9z2D64KlAuvI54xm63CUXiI/+VGtzx8PfcRwZsUj5SUSC5g8Ea23OeFjofD/asXBO0js5wg8Tvilbazy0t2xcYTdu0QSBcRA/Ne+1Z9uyJlBm/t+OWL2xGsP+NWJVy8t37PfR0yJmEyTq1eiO0WWiOYxBhxk2q8DS2CLHWPktM5I2xmy9tE/mhMGC7aK1GgMMDzZMert3Drje21qZlNtYbK8xqC0yBhK2k+kkq52O7Cou4n3MoBEY7hBde3C9PIUnA9mPi4u/zDHbRmOsR5qcrehhaYlBrHYwnc3xoCEGLQaHC0TsBnG/xpiuVxzPTMPseDBwbAZjMGUyyYoGYyB9QMTz8IzuWssPJtoM6I+IfhTx/Lwu4hXMU6N+TMvhhtg+8frxiP60EcYknhUg94vnikn40yN2fRjDW9uT4pBn6oCIBR/373kRCRNj0rAetq7jCsliLmMWQKIhKbKaw+hEK90xH/8bsRIlUTPb2i16Y9SvoHO4TXbB7ttsM60WohOxymXbZZn13+Udamls+2J9+Zal42esjOiwcMCuF50Yfbc752OtTIbxFU1tcfjPOTsi4iG+QrRbhH9sEW/4lNb/7n5FNSg+7RQmu0erA7H6qdkyOq2RdbC7p80HRfTD4e9aB3dVTcJzv4jEc1DVN+arxIrz5hG7HpvZ2Fn5UrTnBgTJRJIxjMVCaUzmGfjp5xtpTFZetoEBPKvz/ah8MmliwsJ4z0KMiV5rYzFyk4gFGLuiLFRYEB4S/TqqHSdTtdrGxpWT0gq7g0NjHKRf9ePpsHyLc1ZAc9qr0tgTo/+I+KMoAvxM54CtOlZNT4mO666t5YP3wtsPvrDz4Bwo2H9HzHTXYv13SdqsZHrrk3hfvpY2qbsSMdO+ZgQXznvbViZFU6c7vEeuwOxp0SmnKz39hfMOLjEIYWMrKpicEPHbNovdJYEwc6evMSHaKOM92+8iHsbeuB+skG9dXGtxSDJmBfHlwln/7Lwn13jt8OiIyXEro7+xiul3z3q/MNqI1ehX4vcfouEYQzzYnIuXrsnqjxunJgP726u/MX9FdjPY+ep59B4Y55n4MpaV4+b8EZy+xY/k0m0Gl9+c86MjJgxz2tS4wkTuFgsc7p5r34qYJEza3J2MGwak20ckRBJ0bzsWx+Xh2AqsrMc20nCVyuyotB/khBn2VQfXOX1KxMC0zFjJYsOtac5ZZQ23spe1M7z+1u77D8znLaO3FRW2lcnQV3m+qO0x1sOkyrshEvkxI07YDr9sdM5BnbvlnK2d1nbnOGQmz31mooCxK/Dk7rjlB2z2WuDwUrlWNVte8N2tvfTcfJH3orsVekzXGH2S6y2TMa5fGN2ni6H/2CkHe0T9JH5QvK6n7+haJ/GURjzcL8a2jTLGDlZ+NRPr9YqR8ZddzeGEZddcY8X88/VyvKRdYmHnpzReOTB5OXjJd7b2cs248pY0zjb+lQsn9GfGHyYJs1k5w69p9H6pxHeYdTNrKo3tn9WIm4gxcNLJSKKlHZaTYSKgU7Li6H8wkBh0V7f45l9mKfhme6E36rJaGib08qvMyo+K8Hu+rmDvfLKN9pCiIisNfh9bSLX2iu47i7Z2apkwC8Uvs/hFxqzwDUXBv3T1SUY8RHTWI7prdy3qXa67xlY6W0BM0m4UMQkZxgtDBvfeSPBMgg6K+lUN8XFfbvTXWssP1tq3Dk9Ty1a93GNWXI+L7lWIbdqV5SFsUTJnPExM6U8kwt7oR/hg26/G5oxn6G/fLhYSTq3NGc9KnLK62rVzTv8hSfPs3rAyoDnjYQLLNigTqX6CyS4L8Tx4A+LpXV40B/TrS1bGUFabk8+90zDtsZPSG5M5xm+e/xqbMx6e8eOi83eOuWfkDRZAtVYTT+24whjL8/7OqH8leECO2WEkUddYTTxbbLnVNMrWCsvzfsZZfucyOSHgn0V0/tdErBjZtlqNLtF9/iqfzLq4xgoMY7bxyoiZ2lejx0cviOgQq9G1o954kD4WHR8x28bHP/6teOkRW+x0rtWIwYLtxfsWte+Z429HgPtJtBrtWZQvO6QO31lUd4oJD+RTI7aDaOO7EduMvcFnNYIX3Dnuk+NDc8zMnk4Bj/0j2oDhs7tzEhzX7hfRmbk36CXR2SNsr2g1gvVwtwD/zABPjGD94eg2UY1VdcA0dGi0GvH7+vs9XEUxCaC9RVrJ9RqbMx4mc/g9Nvp8xHYxD+zdagLp6swZT++2v5cn5ULfn1ZzPNzlWBTmnPGwEn1xxDP2hYj+Q7+GW63NGQ8+GThXIvoSYwyTZQb+Wps7Hvw+ISp31Wpjod7c8dw+bdKHSYQsouDDZGUHnFXYnPFcM/7eFzEek0s+HT02WrQzuCy0mnjWMq7sEkeHROQOGLEAusIy5wuu18RTfVMXtO8lCYwSqOqAoy3MW2g84zzlI59xAuOl9p8JPmcZL7dUAhKQgAQkIIEWBEzILSjrQwISkIAEJDBBwIQ8AchiCUhAAhKQQAsCJuQWlPUhAQlIQAISmCBgQp4AZLEEJCABCUigBQETcgvK+pCABCQgAQlMEDAhTwCyWAISkIAEJNCCgAm5BWV9SEACEpCABCYImJAnAFksAQlIQAISaEHAhNyCsj4kIAEJSEACEwRMyBOALJaABCQgAQm0IGBCbkFZHxKQgAQkIIEJAibkCUAWS0ACEpCABFoQMCG3oKwPCUhAAhKQwAQBE/IEIIslIAEJSEACLQiYkFtQ1ocEJCABCUhggoAJeQKQxRKQgAQkIIEWBEzILSjrQwISkIAEJDBBwIQ8AchiCUhAAhKQQAsCJuQWlPUhAQlIQAISmCBgQp4AZLEEJCABCUigBQETcgvK+pCABCQgAQlMEDAhTwCyWAISkIAEJNCCgAm5BWV9SEACEpCABCYImJAnAFksAQlIQAISaEHAhNyCsj4kIAEJSEACEwRMyBOALJaABCQgAQm0IGBCbkFZHxKQgAQkIIEJAibkCUAWS0ACEpCABFoQMCG3oKwPCUhAAhKQwAQBE/IEIIslIAEJSEACLQiYkFtQ1ocEJCABCUhggoAJeQKQxRKQgAQkIIEWBEzILSjrQwISkIAEJDBBwIQ8AchiCUhAAhKQQAsCJuQWlPUhAQlIQAISmCBgQp4AZLEEJCABCUigBQETcgvK+pCABCQgAQlMENh+opziUyvqWEUCEpCABCQggXUmYEJeZ8Bn4uY3W98ynvHOKB/5jBMYL7X/TPBxy3ockKUSkIAEJCCBJgRMyE0w60QCEpCABCQwTsCEPM7HUglIQAISkEATAibkJph1IgEJSEACEhgnYEIe52OpBCQgAQlIoAkBE3ITzDqRgAQkIAEJjBMwIY/zsVQCEpCABCTQhIAJuQlmnUhAAhKQgATGCZiQx/lYKgEJSEACEmhCwITcBLNOJCABCUhAAuMETMjjfCyVgAQkIAEJNCFgQm6CWScSkIAEJCCBcQIm5HE+lkpAAhKQgASaEDAhN8GsEwlIQAISkMA4ARPyOB9LJSABCUhAAk0ImJCbYNaJBCQgAQlIYJyACXmcj6USkIAEJCCBJgRMyE0w60QCEpCABCQwTsCEPM7HUglIQAISkEATAibkJph1IgEJSEACEhgnYEIe52OpBCQgAQlIoAkBE3ITzDqRgAQkIAEJjBMwIY/zsVQCEpCABCTQhIAJuQlmnUhAAhKQgATGCZiQx/lYKgEJSEACEmhCwITcBLNOJCABCUhAAuMETMjjfCyVgAQkIAEJNCFgQm6CWScSkIAEJCCBcQIm5HE+lkpAAhKQgASaEDAhN8GsEwlIQAISkMA4ARPyOB9LJSABCUhAAk0ImJCbYNaJBCQgAQlIYJyACXmcj6USkIAEJCCBJgRMyE0w60QCEpCABCQwTsCEPM7HUglIQAISkEATAibkJph1IgEJSEACEhgnYEIe52OpBJYR2DUFH46+s6xC4+vG0xj4NrrbbPdrG3+OX5+DwBwJ+ULdoPTrfJ7aHTNIlTo554+cI2DbONMROKzrV/StRTrnBhC5R3x+KLr4hO9dUn5w9NXouOid0eUnvrM1xTXxXDINL+LHNeKc02riwd+e0XuiL0dfjD4Z3W3OQNLWHtHLIvjjA18vjS66wM9mul+E1yqevePr/dE3o9XoXdGVCGCDrEW/qP1pl03F50Wf6fS1fH4gunFtA3PX44GtsUNS6XdLKj4j103IS+CciS/X9C0S8oHRvQZ6fc4/NjO7mnh2is8jo0tHh0fLVsjbp+yo6IiI73D+nOi7EZPYGpszHhLy56MhR853rAkmdeaMh4nJryKSY78wuF/n4w4zxvO5tMU9OE/XJuw/HR0f7Vz42Wz3q1U8e4XBH6JHdyzw+/zopOhSBZ85Dmv6zxz9ojbWmnj2S2Pfiy7XNXrWfMKHXHeVWkeV9WriqXoI8TeWkAn8ipVBWe3MQ6CmAx4QHAwaQzsmF+4zvLiN5zXxMGD1CWQsId8p9WiPFVpvZ8/BLyISc43NGQ8J+d01TkfqzBnPI+KH9nYf+PtRzl87EkNZVBMPCfnqg/bu0vm+Z3F9s92vVvG8NwxOiMrd0nPlnF3Nlw+4betpzf2ao1/UxlkTD/fhgYMGeZb47qNqHVXWO3WOLesxX8xAmWmxVcS23QMifgjiRz4t4gHknMENYybLrHk1YnuArYJFM2baog5b5Z+KbhjRzs8itgZvGrF64drDIoy2ucaMcOUvl/7675TfYewkCnyx4nnCoC1O+e0HRavRFyIYvChipvX2iBiYZRFPv+3KO0l+D8z2jrTttntsIHx0AOI6OWcgf9MGAKI//bnCL4P+j6MvFXW536zqKZvLauOZy99UO7XxnNI1tMOgQVYgf5pysoby66YuSbk0VjzY+YqLm+1+tYrnWmHANn7ZpxmD2L5eNO4WyNblsFW/qA3+ranIK4/S+t0WxunmxgNWY4tWyH1C7r9/7hywUqZNEu2TI1bPJC4SMg8jgy8PUP+w0DF5QG8V9cZ7JtrYP2LVwTbHR7pr+/211l8OyoTcF9H+SlGvxm8Z+zH57sMjYn9WhI8bDNpju5Ktsf537Jpjkvdjunq8W2TA3rH4HodfjJiBnRmstm8NWRyaC88dXpzhfK3x0GeXbVkzCfvEgpiYbDL4sQqZsjnjoU/Rt14fMYFlgvyaaC3vCueM5/zx/fXotdE5IhYHbJv+PLpGVGNrjadvc58c8N1yy3Gz3a9W8ZwYDqySh8bYBaM++QzLt+a85n7N0S9qY6uJZ9gWC4H3RR+KdhoWbuN5VTxVlRIICZm6Qw1nESRQ6vxfETzvdUi4faJlm6A0ku3RxYVjc/zZQZ1b5px2tyYh1/rtY2cg7o1kzruwJxXX7ppjYrldcY3Dx0X9u3RWwNS5Y1GHld+ih2PQzN/NaW3fKn/wLjmBN5OwuW2t8YwlZFZhi+7ls3MdPzXv5+aM52LxSUJmRYQx0L46guXVumtTH3PGgy/ewx8Z/Tb6SUSCvj4FlbbWeGiWVw6MJ4cNfGy2+9UqHnbrvh+VC4N+yxq+cy4Oau/XtvaLwa1delobDw0w3jD55jtviS6ytNWtL5h9y/r3iYUO34tV5TL7aFHASpH3W2wzY2zrlUbyZeuJ9hhImNV/fMsqp61Gt9Zq/JZts8LojdU7Hbq8QTfrCst6XGI13a/sGBS+Fd2nq8vHfaNXFecenp7APrnEvWfw1uoJ0EdZEfbPyck55jUMz+wz6puZreYeaYkdBOJhksWk/OkRq49ykjqbw66hh3X+Hjx3w2fQ9lhIXCA6IDpbxKLjeRFjOMZkqaVtVL+Y+o2MN0xOYPXDiMnttae+tNby9X6HzLuIZVtivH8d2gW7Czyoq4VYwTKAXDRipo8Nv89W19Zajd+y7V8MHJGUWSn31rf304mA2DK8bcRN5mHgmNmXtpwASWT4Tmd57Y0rYWdo0YSUCSWz7Km+0SLy38TJl6I9Wzgb+GByivGHMUwK2MZnxc5W4Nx/THSao9jdowdF7MYNn+HNdr9axcPru5tEjNPsPLJQ+nbEjifj93CczaV1tY3oF2v5QTy3+0Xko4PW8sWaujvUVNqGOgw8/NFWrdEJsatG/OBFxoCG8a6hNGbZi4wHvZ/t9eU7DyrW+F3U9rJrfXu8Px77/QxAzFDvEf0g+mDEIKktJnDjXOb+s8222e0LCfAWC4LcPdfYGWGwa2nnjTNWO/wxYWnDyWSrmFit84dD+C+NP+QkYbLjxEpkLrtLGmIFzm4YW49D22z3q2U87NbdZgDkzTk/OmL8bGmt+8XUb+PvG/hjzHJ7mz7LCvnWU19ea/l6r5DXGk//zo2EXBqzt1d2F0jU/FXg9QZ1lv0hCAmxX7HyFVYtw/ciNX4H7kZP2XbDhlsaD801/mq4NwZmZqRsw943crv6b2wWHT0wF5m5n7KocJNde0viYRv2ykVcO+WYfstg19peGIfl6xH8E88e0WdaBxN/PJeXjoaT5V1zjRXztux4DX/OnXOBldfNoxO6Qu7Dk4uKm+1+tYqHezD8GwLeITP5Pbjg0+qwZb+o+U3khr0WVORvQH664Pq6XypnBmPOGCiZSUwZ7yhok63HobHte2T04aj/62RWvu+PnlhUZgubNh4esdXLQ/zW7hrbCaW9MSdsy7FCYALCuxJu+kpRqdbvsti/krbKbTbaOyr6ZNSv3K+QY2bm/R/V9O73zQG/5RvRcHDq6/y9ftb2LX4/rytY4Q0nU3OyWUs8+D08WrTaoox7SR94Z0Qfxeh734tI1DU2Zzwrccjqk2cFo4+SpP8Y3bC7NvUxZzz3jjPae3Th9JY5ZrJ10FQgXXlNPCRj+g1/UHmvQgfmeKXws9nuV6t4YHJcdP6OxTnzeVjEeDq31dyvOfpFbdw18bB7wHN84aLRh+SY7/K6ZU6riWeLpfoi5wwuq9EvIxrkmAS6yFjifzui3k+i1ahPvH19tpNf0JWxbcPs/RHRMFndv6uDX6CxqqbdYUJmJsMsB3+fjm4f8d7kVxFJsLcpv8PYX5Qv9r+dQa2Po2+PlTgDy2r0+ehjEQPO0PqtRLbTzmxW1QE7KE/I59vWGVBtPIcmjtWIbWcSCMeLVplMxg6JSIQMekdETMxqbc54rhKnL47YauO5OjF6T7R3bTCpN2c8uOVZZLCDDZPmz0b8sdUOFFZYTTysiKm3SCsDH5vpfhFai3iuGT/vixiXGRcZI9nFK//qmljmsJr7hZ9t7Re1sdbEw/OxEh0bMY6zO0ufZVE4t9XEU/0Qzh3cWtvjIeYHDRPyWtvZiPrc5MtvhOMN9lnVARvGaDzjsOUjn3EC46X2nwk+bOFqG0uAd4z8JePXNzYMvUtAAhKQwEYSMCFvDP3rxu1K53r/fL5iY8LQqwQkIAEJnJEIbLZthkXs2M/nj2uIldUmf0izmY1VMf/Nifd4r434A5szo222vmU8471QPvIZJzBeav+Zgc9mgzj+kyw9IxHYbH3LeMZ7j3zkM05gvNT+M8HHLetxQJZKQAISkIAEmhAwITfBrBMJSEACEpDAOAET8jgfSyUgAQlIQAJNCJiQm2DWiQQkIAEJSGCcgAl5nI+lEpCABCQggSYETMhNMOtEAhKQgAQkME7AhDzOx1IJSEACEpBAEwIm5CaYdSIBCUhAAhIYJ2BCHudjqQQkIAEJSKAJARNyE8w6kYAEJCABCYwTMCGP87FUAhKQgAQk0ISACbkJZp1IQAISkIAExgmYkMf5WIKTSlYAAAGmSURBVCoBCUhAAhJoQsCE3ASzTiQgAQlIQALjBEzI43wslYAEJCABCTQhYEJuglknEpCABCQggXECJuRxPpZKQAISkIAEmhAwITfBrBMJSEACEpDAOAET8jgfSyUgAQlIQAJNCJiQm2DWiQQkIAEJSGCcgAl5nI+lEpCABCQggSYETMhNMOtEAhKQgAQkME7AhDzOx1IJSEACEpBAEwIm5CaYdSIBCUhAAhIYJ2BCHudjqQQkIAEJSKAJARNyE8w6kYAEJCABCYwTMCGP87FUAhKQgAQk0ISACbkJZp1IQAISkIAExgmYkMf5WCoBCUhAAhJoQsCE3ASzTiQgAQlIQALjBEzI43wslYAEJCABCTQhYEJuglknEpCABCQggXECJuRxPpZKQAISkIAEmhAwITfBrBMJSEACEpDAOIHtx4tPKz21oo5VJCABCUhAAhKQgAQkIAEJSEACEpCABCQgAQlIQAISkIAEJCABCUhAAhKQgAQkIAEJSEACEpCABCQgAQlIQAISkIAEJCABCUhAAhKQgAQkIAEJSEACEpCABCQggRkJ/D8Cbv40F7svPwAAAABJRU5ErkJggg==)
Answer:Here, we have ungrouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
![](data:image/png;base64,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)
We have added up all the values of the frequency in the second column and have got,
Total = n = 100
Since, n (=100) is even then the median will be the average of
and
observations.
We have
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
And
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Note that, in the above table:
50th observation = 15 &
51st observation = 16
[∵ 50 and 51 lies between 50 and 70 in the cumulative frequency column]
Taking their average, we get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Median = 15.5
Thus, the median is 15.5
Question 2.Find the median for the following frequency distribution:
![](data:image/png;base64,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)
Answer:Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
![](data:image/png;base64,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)
We have added up all the values of the frequency in the second column and have got,
Total = n = 60
Now, we just need to find the value of n/2. So,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, look up for a value in the cumulative frequency just greater than 30.
We have, 37.
Corresponding to this value of cumulative frequency, we can say that median class is 12 – 16.
That is,
Median class = 12 – 16
∴ we have almost everything we require to calculate median.
Median is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the median class = 12
n = Total number of observation (sum of frequencies) = 60
cf = cumulative frequency of the class preceding the median class = 25
f = frequency of the median class = 12
c = class size (class sizes are equal) = 4
Putting the values, l = 12, n/2 = 30, cf = 25, f = 12 and c = 4 in the given formula of median, we get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Median = 12 + 1.67
⇒ Median = 13.67
Thus, the median of the data is 13.67.
Question 3.Find the median from following frequency distribution:
![](data:image/png;base64,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)
Answer:Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
![](data:image/png;base64,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)
We have added up all the values of the frequency in the second column and have got,
Total = n = 400
Now, we just need to find the value of n/2. So,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, look up for a value in the cumulative frequency just greater than 200.
We have, 210.
Corresponding to this value of cumulative frequency, we can say that median class is 200 – 300.
That is,
Median class = 200 – 300
∴ we have almost everything we require to calculate median.
Median is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the median class = 200
n = Total number of observation (sum of frequencies) = 400
cf = cumulative frequency of the class preceding the median class = 126
f = frequency of the median class = 84
c = class size (class sizes are equal) = 100
Putting the values, l = 200, n/2 = 200, cf = 126, f = 84 and c = 100 in the given formula of median, we get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Median = 200 + 88.09
⇒ Median = 288.09
Thus, the median of the data is 288.09.
Question 4.The following frequency distribution represents the deposits (in thousand rupees) and the number of depositors in a bank. Find the median of the data:
![](data:image/png;base64,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)
Answer:Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
![](data:image/png;base64,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)
We have added up all the values of the frequency in the second column and have got,
Total = n = 2776
Now, we just need to find the value of n/2. So,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, look up for a value in the cumulative frequency just greater than 1388.
We have, 2316.
Corresponding to this value of cumulative frequency, we can say that median class is 10 – 20.
That is,
Median class = 10 – 20
∴ we have almost everything we require to calculate median.
Median is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the median class = 10
n = Total number of observation (sum of frequencies) = 2776
cf = cumulative frequency of the class preceding the median class = 1071
f = frequency of the median class = 1245
c = class size (class sizes are equal) = 10
Putting the values, l = 10, n/2 = 1388, cf = 1071, f = 1245 and c = 10 in the given formula of median, we get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Median = 10 + 2.55
⇒ Median = 12.55
Thus, the median of the data is Rs. 12.55 (in thousand).
Question 5.The median of the following frequency distribution is 38. Find the value of a and b if the sum of frequences is 400:
![](data:image/png;base64,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)
Answer:Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
![](data:image/png;base64,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)
We have added up all the values of the frequency in the second column and have got,
Total = n = 202 + a + b …(i)
But given is, sum of frequencies, ∑f = n = 400 …(ii)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Comparing equations (i) and (ii), we get
202 + a + b = 400
⇒ a + b = 400 – 202
⇒ a + b = 198 …(iii)
Also, given that, median = 38
Corresponding to this value of median, we can say that median lies in the class is 30 – 40. [∵ 38 lies between 30 – 40]
⇒ Median class = 30 – 40
Median is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the median class = 30
n = Total number of observation (sum of frequencies) = 400
cf = cumulative frequency of the class preceding the median class = 80
f = frequency of the median class = a
c = class size (class sizes are equal) = 10
Putting the values, l = 30, n/2 = 200, cf = 80, f = a and c = 10 in the given formula of median, we get
![](data:image/png;base64,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)
⇒
[∵ given that, median = 38]
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ a = 150
Substituting the value, a = 150 in equation (iii), we get
a + b = 198
⇒ 150 + b = 198
⇒ b = 198 – 150
⇒ b = 48
Thus, a = 150 and b = 48.
Question 6.The median of 230 observations of the following frequency distribution is 46. Find a and b:
![](data:image/png;base64,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)
Answer:Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
![](data:image/png;base64,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)
We have added up all the values of the frequency in the second column and have got,
Total = n = 150 + a + b …(i)
But given is, sum of frequencies, ∑f = n = 230 …(ii)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Comparing equations (i) and (ii), we get
150 + a + b = 230
⇒ a + b = 230 – 150
⇒ a + b = 80 …(iii)
Also, given that, median = 46
Corresponding to this value of median, we can say that median lies in the class is 40 – 50. [∵ 46 lies between 40 – 50]
⇒ Median class = 40 – 50
Median is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the median class = 40
n = Total number of observation (sum of frequencies) = 230
cf = cumulative frequency of the class preceding the median class = 42 + a
f = frequency of the median class = 65
c = class size (class sizes are equal) = 10
Putting the values, l = 40, n/2 = 115, cf = 42 + a, f = 65 and c = 10 in the given formula of median, we get
![](data:image/png;base64,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)
⇒
[∵ given that, median = 46]
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ 730 – 10a = 390
⇒ 10a = 730 – 390
⇒ 10a = 340
⇒ ![](data:image/png;base64,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)
⇒ a = 34
Substituting the value, a = 34 in equation (iii), we get
a + b = 80
⇒ 34 + b = 80
⇒ b = 80 – 34
⇒ b = 46
Thus, a = 34 and b = 46.
Question 7.The following table gives the frequency distribution of marks scored by 50 students of class X in mathematics examination of 80 marks. Find the median of the data:
![](data:image/png;base64,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)
Answer:Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
![](data:image/png;base64,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)
We have added up all the values of the frequency in the second column and have got,
Total = n = 50
Now, we just need to find the value of n/2. So,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, look up for a value in the cumulative frequency just greater than 25.
We have, 31.
Corresponding to this value of cumulative frequency, we can say that median class is 30 – 40.
That is,
Median class = 30 – 40
∴ we have almost everything we require to calculate median.
Median is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the median class = 30
n = Total number of observation (sum of frequencies) = 50
cf = cumulative frequency of the class preceding the median class = 15
f = frequency of the median class = 16
c = class size (class sizes are equal) = 10
Putting the values, l = 30, n/2 = 25, cf = 15, f = 16 and c = 10 in the given formula of median, we get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Median = 30 + 6.25
⇒ Median = 36.25
Thus, the median of the data is 36.25.
Find the median for the following:
Answer:
Here, we have ungrouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
We have added up all the values of the frequency in the second column and have got,
Total = n = 100
Since, n (=100) is even then the median will be the average of and
observations.
We have
⇒
And
⇒
⇒
Note that, in the above table:
50th observation = 15 &
51st observation = 16
[∵ 50 and 51 lies between 50 and 70 in the cumulative frequency column]
Taking their average, we get
⇒
⇒
⇒ Median = 15.5
Thus, the median is 15.5
Question 2.
Find the median for the following frequency distribution:
Answer:
Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
We have added up all the values of the frequency in the second column and have got,
Total = n = 60
Now, we just need to find the value of n/2. So,
⇒
Now, look up for a value in the cumulative frequency just greater than 30.
We have, 37.
Corresponding to this value of cumulative frequency, we can say that median class is 12 – 16.
That is,
Median class = 12 – 16
∴ we have almost everything we require to calculate median.
Median is given by,
Where,
l = lower limit of the median class = 12
n = Total number of observation (sum of frequencies) = 60
cf = cumulative frequency of the class preceding the median class = 25
f = frequency of the median class = 12
c = class size (class sizes are equal) = 4
Putting the values, l = 12, n/2 = 30, cf = 25, f = 12 and c = 4 in the given formula of median, we get
⇒
⇒
⇒ Median = 12 + 1.67
⇒ Median = 13.67
Thus, the median of the data is 13.67.
Question 3.
Find the median from following frequency distribution:
Answer:
Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
We have added up all the values of the frequency in the second column and have got,
Total = n = 400
Now, we just need to find the value of n/2. So,
⇒
Now, look up for a value in the cumulative frequency just greater than 200.
We have, 210.
Corresponding to this value of cumulative frequency, we can say that median class is 200 – 300.
That is,
Median class = 200 – 300
∴ we have almost everything we require to calculate median.
Median is given by,
Where,
l = lower limit of the median class = 200
n = Total number of observation (sum of frequencies) = 400
cf = cumulative frequency of the class preceding the median class = 126
f = frequency of the median class = 84
c = class size (class sizes are equal) = 100
Putting the values, l = 200, n/2 = 200, cf = 126, f = 84 and c = 100 in the given formula of median, we get
⇒
⇒
⇒
⇒ Median = 200 + 88.09
⇒ Median = 288.09
Thus, the median of the data is 288.09.
Question 4.
The following frequency distribution represents the deposits (in thousand rupees) and the number of depositors in a bank. Find the median of the data:
Answer:
Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
We have added up all the values of the frequency in the second column and have got,
Total = n = 2776
Now, we just need to find the value of n/2. So,
⇒
Now, look up for a value in the cumulative frequency just greater than 1388.
We have, 2316.
Corresponding to this value of cumulative frequency, we can say that median class is 10 – 20.
That is,
Median class = 10 – 20
∴ we have almost everything we require to calculate median.
Median is given by,
Where,
l = lower limit of the median class = 10
n = Total number of observation (sum of frequencies) = 2776
cf = cumulative frequency of the class preceding the median class = 1071
f = frequency of the median class = 1245
c = class size (class sizes are equal) = 10
Putting the values, l = 10, n/2 = 1388, cf = 1071, f = 1245 and c = 10 in the given formula of median, we get
⇒
⇒
⇒
⇒ Median = 10 + 2.55
⇒ Median = 12.55
Thus, the median of the data is Rs. 12.55 (in thousand).
Question 5.
The median of the following frequency distribution is 38. Find the value of a and b if the sum of frequences is 400:
Answer:
Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
We have added up all the values of the frequency in the second column and have got,
Total = n = 202 + a + b …(i)
But given is, sum of frequencies, ∑f = n = 400 …(ii)
⇒
⇒
Comparing equations (i) and (ii), we get
202 + a + b = 400
⇒ a + b = 400 – 202
⇒ a + b = 198 …(iii)
Also, given that, median = 38
Corresponding to this value of median, we can say that median lies in the class is 30 – 40. [∵ 38 lies between 30 – 40]
⇒ Median class = 30 – 40
Median is given by,
Where,
l = lower limit of the median class = 30
n = Total number of observation (sum of frequencies) = 400
cf = cumulative frequency of the class preceding the median class = 80
f = frequency of the median class = a
c = class size (class sizes are equal) = 10
Putting the values, l = 30, n/2 = 200, cf = 80, f = a and c = 10 in the given formula of median, we get
⇒ [∵ given that, median = 38]
⇒
⇒
⇒
⇒
⇒ a = 150
Substituting the value, a = 150 in equation (iii), we get
a + b = 198
⇒ 150 + b = 198
⇒ b = 198 – 150
⇒ b = 48
Thus, a = 150 and b = 48.
Question 6.
The median of 230 observations of the following frequency distribution is 46. Find a and b:
Answer:
Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
We have added up all the values of the frequency in the second column and have got,
Total = n = 150 + a + b …(i)
But given is, sum of frequencies, ∑f = n = 230 …(ii)
⇒
⇒
Comparing equations (i) and (ii), we get
150 + a + b = 230
⇒ a + b = 230 – 150
⇒ a + b = 80 …(iii)
Also, given that, median = 46
Corresponding to this value of median, we can say that median lies in the class is 40 – 50. [∵ 46 lies between 40 – 50]
⇒ Median class = 40 – 50
Median is given by,
Where,
l = lower limit of the median class = 40
n = Total number of observation (sum of frequencies) = 230
cf = cumulative frequency of the class preceding the median class = 42 + a
f = frequency of the median class = 65
c = class size (class sizes are equal) = 10
Putting the values, l = 40, n/2 = 115, cf = 42 + a, f = 65 and c = 10 in the given formula of median, we get
⇒ [∵ given that, median = 46]
⇒
⇒
⇒
⇒ 730 – 10a = 390
⇒ 10a = 730 – 390
⇒ 10a = 340
⇒
⇒ a = 34
Substituting the value, a = 34 in equation (iii), we get
a + b = 80
⇒ 34 + b = 80
⇒ b = 80 – 34
⇒ b = 46
Thus, a = 34 and b = 46.
Question 7.
The following table gives the frequency distribution of marks scored by 50 students of class X in mathematics examination of 80 marks. Find the median of the data:
Answer:
Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
We have added up all the values of the frequency in the second column and have got,
Total = n = 50
Now, we just need to find the value of n/2. So,
⇒
Now, look up for a value in the cumulative frequency just greater than 25.
We have, 31.
Corresponding to this value of cumulative frequency, we can say that median class is 30 – 40.
That is,
Median class = 30 – 40
∴ we have almost everything we require to calculate median.
Median is given by,
Where,
l = lower limit of the median class = 30
n = Total number of observation (sum of frequencies) = 50
cf = cumulative frequency of the class preceding the median class = 15
f = frequency of the median class = 16
c = class size (class sizes are equal) = 10
Putting the values, l = 30, n/2 = 25, cf = 15, f = 16 and c = 10 in the given formula of median, we get
⇒
⇒
⇒
⇒ Median = 30 + 6.25
⇒ Median = 36.25
Thus, the median of the data is 36.25.
Exercise 15
Question 1.In a retail market, a fruit vendor was selling apples kept in packed boxes. These boxes contained varying number of apples. The following was the distribution of apples according to the number of boxes. Find the mean by the assumed mean number of apples kept in the box.
![](data:image/png;base64,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)
Answer:We have grouped frequency distribution and we need to find mean by assumed-mean method.
Assumed-mean method is given such name because in this method, we actually assume a mean from xI (usually a centre value) and the formula of mean is also based on that particular assumed mean.
By using assumed-mean method, we can avoid the risk of miscalculation. Also, by using assumed mean method, we’ll be able to solve the question with ease and more accuracy.
So, let us assume mean from the midpoints. Let assumed mean, A = 57.5 (a value quite centrally placed).
![](data:image/png;base64,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)
So now, we have
∑fidi = -165 and ∑fi = 400.
And we have assumed mean as, A = 57.5
Mean is given by
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mean = 57.5 – 0.4125
⇒ Mean = 57.0875
Thus, mean number of apples in a box is 57.0875.
Question 2.The daily expenditure of 50 hostel students are as follows:
![](data:image/png;base64,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)
Find the mean daily expenditure of the students of hostel using appropriate method.
Answer:Let us solve by direct method since the frequencies have smaller values.
This is grouped frequency distribution.
We shall represent them by creating a table having columns of class intervals, midpoints, frequencies, and product of these midpoints and frequencies.
![](data:image/png;base64,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)
So now, we have
∑fi = 50 and ∑xifi = 7260
For grouped frequency distribution, mean is taken out from the formula:
![](data:image/png;base64,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)
⇒
[from the table]
⇒ ![](data:image/png;base64,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)
⇒ Mean = 145.2
Thus, the mean daily expenditure of the students is Rs. 145.2.
Question 3.The mean of the following frequency distribution of 200 observations is 332. Find the value of x and y.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAjoAAADYCAYAAADiW0lgAAAACXBIWXMAAAsTAAALEwEAmpwYAAAgAElEQVR4Xu2dC7A0RXXHQUEUQUEFjQ8QBUwp+NYCJD5CfEWSqIhPNJbRBBUslYiIUYxAAEuCAhGfVbeCRExQYxCiFVReUoiAAgooClceCoooKIqCfvn/P6axv67Z3d77zex0D79Tde7O9PZ2n/M7PTNnumf3rrMOAgEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCol8C6GaavyqhDFQhAAAIQgAAEIFAlARKdMsM2prjgC2OsbwKMsb4Jr6x94rIybn1/alRxuUvftGgfAhCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBEh0ekdMBxCAAAQgAAEIDEWARGco8vQLAQhAAAIQgEDvBIZIdPaRV1dLV0l37d1DOjCBLaVnNNxrJzImX2qPBfZDYAgCx6tTXz+2G6Lzjvscky8do1lscx5QufJIVVySXi69RvpT6WnSd0q3kgbZWhskOhGQFWzmxuWlantZ+gOpE8xJsone+Jj0u9JLpCdJt2mp7OT47dKLpRdKvyF9Tku9eYq69OXB6tjttal9jGUoX3yCPkZqzhdJzfJD0gesYd3tO6XHJdeXGuLycCE/XHp+o9/T61ekz6gwLrm+1BCXGP9O2gnHdluiU/rxkutLDXGZx8bi45J7EdpdEbxZ6hmbezbRvJteXyn9pfR3UYRJdCIYK9zMicsGavtU6RbSE6STEp119d7p0pOl/oz3D5M6Wd1MGstB2rlS+qCm8Hl6dWyftma1ufa69MUH3wXSPVp0/cSqoXz5luww63s19pjxedIrpBtFNtYQl1xfaojLXmL/I6nPT5a7So+Q3iLdvinzSw1xyfWlhrgE9OZ+tvREqc8ZaaJTQ1xyfakhLrk2VhGXnIuQZ3J+I313iGLy+irt3xaVkehMADVHcU5cPMDC8uS0ROcFqpeeOO6ushulTniCeMbht1KfRGP5kna+npTNs9ulLz74vpjR+ZC+ODl4bGLjbto3h1dE5TXEJdeXGuJi3q9P4mK7HZd9K4tLri81xCWgf7k2PMP22iYmaaJTw/GS60sNccm1cfC4dPWMzn6Knu9+jopOBvHmf2rn8xPeC8WG9lHpBVJPHfsE+h6pZxhi+XPtfE3qOl46+YJ016jCw7T9Oanb+abUdd8avX9n2vQJ+g8ZDvsi62XGb0d1fRd7ltTvBTFnz9L5ZBOL958sdQz7klxfcvsf0hez8viOxTMJlk2jwhrikuvLGs5O2RkyLj5veEkxljDrdn1lccn1ZUoo1nhryLjYEN94HSz1isEkqeF4yfVlko9p+dBxSe1p2x88Ll0lOn5G41Lpz9u8VJkvmvEFs62a73CdoXsN9vHSp0qfLv3nqPL9tX2i9MCmjj/jfveK6jipctljpI+Tvk/qAwSZTODReuuKlrdd5sQxLEW6niWtG/bD+y1NLbTIy2qfkvr5IT9zdKzUs46xDOlLvIwbbNq22TgtMrKGuOT6YrdKj8uaI+T25wqPVOHp0uMqi0uuL7XExQmOjw3fvE6SGo4X257ji+vVcLzk2pheM+zfwq4vXSQ6G8pgP2NwrS1fC/Eg/hupn/Ox3CT1BcrTlEG8Tu7+Lm8KPFvxfqnvXix+BsNJUgzVM0mHNu/z0k7gfio271Rc5uWv+zRvuN5tUi9TxhI+e9+kfIjd3zedelw8qVHPBp0jdfIbpCRfzPh1Ul9ML0psrC0uk3ypKS7bKAZ+ns3nGfN/sdRLtkFqOl5m+VJDXLzMvLd0/ygGbZs1xCXXlxriMo+Ng57Hukh0woDzxWRtxAnOS6R+1uNK6bLUCYovnmH62MtRN0q/LH2bdEupE6yPSC23Sv2w2hHSf5U+4fbiNWaFmiJeeiSwkdreJFIvay5KfqyOnBD74V6LD7A9pb5Q+eHjeWURvrxZRpnXG+c1bs76Q/pSU1wuE1cvw/rcc53UyecT52Q9T/U+4zLLlxri4hn5D0vD8u48bNembh9xyfWlhrh0bWNurOaOSxeJzq9l3fVSZ6prI87WnaC8V+oE5qHStzQN+rkQi58j8TMBTnQOkC5LPRMU36k/V/sfkL5Ueq70e1LfkSGTCTh+G7e87QTTCewNzXuut57U6+WxhET0Z03hKXr9eaSeWRlSPEb9/NEOkRGl+OKx+Qapl3+dxMdSW1ym+ZK4tnq35LjYPo/7vaROlo9cbfHtUltcbPUkXyK37tgsKS4+tz9T6kcQZknpcZnHlzZfS4pLm30um2TjoNcXX7S6kJPVyMuk95amJ2u377vVnaVfk/oC2Cb+tsmZ0pPa3ozKnLi8WuoTkGeAfJfub/1sIfXzAu7/ndJ3S32A+Hme46X+XPoAqIoQEbhQ+qwWElupzNP3YTnR9Sx+bufiZtsvrmcJ7/+9tkPy4/LvNO8v4sVj0Etr6bMjnmaNZ5ZK8GU32eTxuYvUSyWp1BSXWb7UEJd7KAC3SOPZaY8bz+j4BipIDXHJ9aX0uPgc7hur+HyzURMIn/c9i/926aelpcdlHl9Kj4tDMI+NxV9fcpakHiGnncm9w963yCEq83JUmJnZWttud9eo7ve1/dXks/s29bz2anmK9HVJndc0dfxQlC+u8Z2Xq/qi7L6cSI1JcuIS+3uCdtoupq7zQqnbe1T0gQ20/QvpYVGZZ+28BJQusXxRZV5yXKl06cuSjHhtYoh9+YnUM01BhvbFzL8rdYIeZEdtHBDt1xKXHF+W5FfpcfGNlm/IUjlXBfGySQ1xyfWlhrik8fA48jlju+SNGuKS60sNccm1sYq45F6Enq8I3iT1Q2NhacOv+0h/Jf0LaZC2ROcIvekHXUO9h2r7h1L3HxKdF2n7CukDpRbfoX9Cemmz73rO8P2NrSCv1obv8J3wjEly4xJ8npbo+AHS06WeTQvJqJNTn9w3S6AdpH3HJcTAd7qePXlaUm+e3S59WVLHnr3bsjHAY+SD0nRc+O2hfPGB7zG5v3SPSD09v2TDGqkhLrm+2K/S4+LkwMfB5n8Mwerzmcenb7qC1BCXXF+W5FTpcYnQr96clOjUEJdcX2qIS66NVcRlnouQv8L7SamTkWXpD6T/IX2MNIgTn6ulbvc66VHNG/4K84ek10p94Hla8nCp63k2yImUHxA8WurnLbwM5SWR/5KGJGZ9bb9L6gdR/f6F0jOkz5COTXLj4kRwWerlJyeS3j6/BYaXFz8uNftLpF6O3Lal3l1Utl9Tx3x9txtP67d8ZGZRl75sr948RrzcYPuuknostd2pD+WLx7N9btMllcdSelxyfakhLh4j5u/zir/44OUSJz67xwFptkuPS64vNcQl4PeM/rL0eqmPnWuafX8TN0jpcQl2zvKlhrjMY2Pxccm9CEVjjc0FEBhTXPBlAQNmBV0QlxVAW8BHiMsCIK+gC+KyAmgL+Mgq39EiEIAABCAAAQhAYJQESHRGGVacggAEIAABCEDABEh0GAcQgAAEIAABCIyWAInOaEOLYxCAAAQgAAEIkOgwBiAAAQhAAAIQGC0BEp3RhnYNx7bUnr9m76/1IxCAwJ2PgH8d3t8KSn9kr0YSY/KlRv6jtHlMX5kbU4By4+L/+bUs9W8aTUp0/PtEbq9N/fsHsTg59k+u+zdG/Ds135D6/zStjeT44hP0MVL/xo9/I8f9+3eX/AvHqdjmj0n9y8Ou7x9C3CatpP3SfakhLg8XR//elX+byerfYfqKtO23q0qPS64vNcQlHu47aScc222JTulxyfWlhrjMY2Ppccn1Jbee4zzUOXn1AYKURyAnLv7XB6dK/W8Gpv0ysgeifyBtjxb1jzDG4l8TvlLqf7lheZ70d9KnNfsrecnx5Vtq2D9iGP6Hln+x2T8MeYV0o6jT8Cucrmv/ve9/Y+EfF2v7leeSfakhLnuJq39Be+smBv4lav/Kuf9nlH9QLEgNccn1pYa4xNzP1s6JUh9naaJTQ1xyfakhLrk21hCXXF9y6znOQ11fSHTCUVbYa05y4IMlLE/OSnT8/6pmSfj/UL4gxOJfHu77f1050Xls0q//kaQ5xP/H7AVNWXxC978i8T97bfu/XSX74hNE6XEx79cncbHdjsu+UXkNccn1pYa4BPQv14Zn2Cb924Qa4pLrSw1xybWxhrjk+pJbr7frC8/oJGfoke36YvOHDn3aVW35f2H5xBmL958s9YDuS9y+k51Ywj9a3DQqdPLzU6n/TUgQzy6cJfV7QWrwJTJ36uaQvnxOlnlJMZYw63Z9VFhDXHJ9mRqM6M0h42IznOAfLN1nisE1xCXXlylurvHW0HHJsbOWuOT4klunt7iQ6OSGYPz1vBT1KamfufGzLcdK/b/LYnl0s+PloljCfng/ebuTXS+PpRL+F9dp0Ru2IbXPb7vsYVL/TzVLDb7YztLj0uC842UrbR0pPV16XPRmDXHJ9cX1aoiLExwfG99MHaswLjm+1BKX3LFT+nksl3duvd7OySQ6U84Ad6K3ft/4+n69PqlRzwadI43/Iav/O/xtUv/n7Vj8X+st912zuNc9L8u9TuqL6UVRT7Yx2BMb4DJ/5j5NYQ2+1BQXP+zth90vb/i/WK+/jQJQU1xm+VJDXLwMsLd0/ygGbZs1xCXXlxriMo+NpZ/Hcn3JrdfbOZlEp+3Qv/OV/Vgu+8FRP9xr8QG2p9QXKj8cVqK8WUb5WwlvLNG4OW2a5EtNcblMPnvp0snudVInn0+ck0Mp1Wf5UkNcvGT1YWlY3i2F7UrsyPWlhrjUYGNujHJ9ya2X2+/c9Uh05kZ2p/nAr+Wpn3PZIfLYz1ysJ/XafyzhmYyfJeV97Xq24A1Sf63dDxnHYhs3Tsq8axs9S3VD814NvrS4sU7JcbG95ruX1Mmyl7CC1BYX2z3Jl8itOzZLiotnYZ8pfV+boUlZ6XGZx5c2d0uKS5t9LptkY03nseBbmy9tfrfV6+2cTKLTFoI7X9m95bIfMk7FU47+unCQC5sNP+sSi5/LsIT313y32z0/pHegdBdp2+8C2YbUPltgG72scrN3JDX4UkNc7iGWXhKMxePGMzqPjwpriEuuL6XHxUmOb0Yuli43emgTC39D0mUvafZLj8s8vpQeFyOfx8bSz2O5vuTWG/Sc7LtgpDwC88blBLnQlhjYsyWpv34aywba+Yn0lKgwfP0vXS7yV6D7/nq5zXih1A9K+3eBguyojQOifdcxm0dFZfblF9K2r5eX7MuSbC49LmfKxp0j1mHzXG3EyyY1xCXXlxrikobE48jHxXbJGzXEJdeXGuKSa2MNccn1JbfeoNeXeS+o6aBkvx8C88ZlVqLjX7TdsjHVszgflN4qfWpi/kHa/6H0gU35c/W6iB8M9IHvh6D9cOUekXp6fqmxxS+eXfA3fvxryGGW6hBt+6Lb9oOBJfuyJJtLj4uTA/PeXBrED8F6fO4bldUQl1xfluRX6XGJ0K/enJTo1BCXXF9qiEuujTXEJdeX3HqO81DXF34wMD3KCtnPTXQ+IXuXpV6y8TemvH1+4oMfRD5a6uUGTx9eJfUUd9udupc795P6Xyu4ru/cneysjeT4cqU6cL02XUo690PKH5f6YmQ7T5aGr6LHVUv3pYa4eIwsSb8jvUDq5RInPrvHoJvt0uOS60sNcQn4n6KNZamff/Cxc02zv2GooNfS4xJMneVLDXGZx8bS45LrS249x3moczKJTnRCKGkzJzkoyd5ptuDLNDrDvUdchmM/rWfiMo3OcO8Rl+HYT+t5lbMnBAIQgAAEIAABCIySAInOKMOKUxCAAAQgAAEImACJDuMAAhCAAAQgAIHREiDRGW1ocQwCEIAABCAAARIdxgAEIAABCEAAAqMlQKIz2tDiGAQgAAEIQAACJDqMAQhAAAIQgAAERkuARGe0ocUxCEAAAhCAAARIdBgDEIAABCAAAQiMlgCJzmhDi2MQgAAEIAABCJDoMAYgAAEIQAACEBgtARKd0YYWxyAAAQhAAAIQINFhDEAAAhCAAAQgMFoCJDqjDS2OQQACEIAABCBAosMYgAAEIAABCEBgtARIdEYbWhyDAAQgAAEIQIBEhzEAAQhAAAIQgMBoCZDojDa0OAYBCEAAAhCAAIkOYwACEIAABCAAgdESINEZbWhxDAIQgAAEIAABEh3GAAQgAAEIQAACoyVAojPa0OIYBCAAAQhAAAIkOowBCEAAAhCAAARGS4BEZ7ShxTEIQAACEIAABEh0GAMQgAAEIAABCIyWAInOaEOLYxCAAAQgAAEIkOgwBiAAAQhAAAIQGC0BEp3RhhbHIAABCEAAAhAg0WEMQAACEIAABCAwWgIkOqMNLY5BAAIQgAAEIECiwxiAAAQgAAEIQGC0BEh0RhtaHIMABCAAAQhAgESHMQABCEAAAhCAwGgJkOiMNrQ4BgEIQAACEIAAiQ5jAAIQgAAEIACB0RIg0RltaHEMAhCAAAQgAAESHcYABCAAAQhAAAKjJUCiM9rQ4hgEIAABCEAAAutmIFiVUYcqEIAABCAAAQhAoEoCJDplhm1MccEXxljfBBhjfRNeWfvEZWXc+v7UqOLC0lXfw4X2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0TZj2IQABCEAAAhAYjACJzmDo6RgCEIAABCAAgb4JkOj0Tbis9o+XOauk25VlFtaMiABjbETBxBUIzEGg6mPfF8ZpspnevFp6s9R1vZ3qTSr7x2mN8N7cBGbFJW1wpyY+JSY6ub7sIB++JL1YepH0HOnuqaMD7+f6MrCZWd3P68u0Mebk+hjpJVLHzjH8kPQBWZasfaUcXx6sblyvTTdJTPD+x6Tfldqnk6TbJHX62p3myyPUqc+/rnNrs+2yIB/Rxg3SX0mPjcqH2pzmS7Dp4do4XHp+o9/T61ekz0iMrmGMBZNfpo0zpedJL5d+XVrSuSwnLjH+acd+EqaF72b5klVJpn9cessEFw5SOYnOBDgrLM6Ni5tfV3q29ESpP1fajE6OL76I+OTsi2OYify7xp+/1mspkuNLKbbOsmMeX2aNsW+ps5Ol92o69Q2ST/JXSDeaZUgH7+f44kTnAukeLbp+ZIN9PV1qfzaQev8w6TVS+9W35PjyPzLiNuljW4zxzUKaJLRUW0hRji97yZIfSbduLLqrXo+Q+nqzfWRlDWPM5r5Deq70QY3td9PrZ6RHR74MvZkTl2DjrGO/Cl9yHZ6W6HgwxncVQzs+hv5z42JfXy71HdBrpf5cjYnOWxvbt0qC9xPtH5eUDbk7T1yGtDOn73l8mTXGfBFKL7q7NTF9RY4xa1knxxcnOl/M6OcFjd3xcXR3ld0odcLTt+T48lAZ8WvpWVJfiIK8SBu1HS/m/frIB2+G2bd9o/Iaxti2stczbemx8JCWssTlhe7mjLFg0Kxjf6GGt3SW5UtWJTXeluj4Tu36qOM9te32rB6475X6QuX9E5p6vuPzXfuy1FOUnq5su2N3W67jJbNvSJ8qdTs/l3oaeRdpmMJ9s7Ytbttlv5Mu3V50x99Z/aa2H6JPui/fxf1T0pZ37fuR0mXphVJP1x8l9V2J77Zsg+9IbM+GUssZUvtjZjs3ZZNecuPiE/AV0sdJa0503iT77XO6PPAzlf37JEgDlM+Ki2PvuLuex4VlSeq42xcndKXILF+CnTljzHetqeyoAvexV/pGD/s5vuQmOp+UfT5vpfK/Kvh+WtjDfo4v7tbnJdf1zKflnlKfhxa1XNh0O/Ul15e0kUeqwJ99TfRGDWPsYNl7VepMgfu5cck59od2L8uXrEryJCfR2Vj1PLPjNp3AHCD1bI8TAic6npL8mtSZ+aZSi+/6fi99TrPvF69luo19pAbti9+ZTVl60nS9kOhoc7W4/aWwo9ecfmPbz9Vn3iK17f8idR9/lrTnqe3zpMGPLbXtpGi/pp7X938qXT/6nDd9IvIJd5bkxuWdamipaazmROc+8uEy6XHSe0i9fPV26S+kTuJKkZy47CFjXe8ljdH31esFUr+WJDm+2N6VjrG/1Wfdh4+jviXHFx93Pv4+JfXNk5+/OVbqi2osTlD9TEUqvkH7g9QJRZ+S44v797KabxZ9nvHx49mmvfs0bAVt5/oSN+1Z3VOkp0nt4zQpbYx9VcZaPYvpa92lUl+7/MxOSZIbl5Ue+4v0NcuXrEqy2omO66Yaz+jYOScmrvOFyFOvazuRCQmMpypj8UA4Oyr4jra/mdR5tvbd7koSndx+g+1OyoI4SfKzI++Oyjw9bFt2jcq8ub80PKu0c1Pn+VGdJ2n7/5LPTNrNiYvv3K6VPrBppOZExy5sIT1V+hupZz+c+OzkNwqSnLjY3M9LfQHy2D9e+sKCfAim5Piy0jHm5RQf154dWYTk+PInMsSJzhMagzzL69lCH9+PiYz08yJtx+mhKnc/XoboU3J8Cf0/q7HpJL06OfP5qiSZxxff0F7d+PNZvd5/hiMljrHvy2aPJ98Iby71DZuXfpwgv3GGP4t8OycuKz32F+mH+8rxJa+SGsuZ0XGnIVnwA1mpfLgxKh3AR6ncA8GzKj752HDfPcVyv6Z8JYlOTr/uK9jumYRYfMH9t6hgUnvJx9b5gQp8wAZxG77bz5Gc4H1CDb0naqzmRGc7+fFj6eFS38X5BPEqqZ9DiJPFyN1BNnPiYsN8krhB6qTdMwglSo4vKx1jnhH9tvTeC3I8x5c2U7ys7KT6xOjNmhIdm/0Zqf338n5pspK4eHbqGKmXD584xaESx1hI1FK7nYh6UqCURDQnLis99qeErJe3Vq3XS7N/bPRmbabTvuFdP9+SipMVSzot7ATjJqkvDr7AWdLPewljpZLT7y+jxm9MOvLSWjxAQ3u+kE0TT4s74fOShdt/nvRt0z4wx3u+A32m9E/n+EzJVb1EaPHDh+Zt8d22p3ydWP53U1bLi2faDpB62dbJW42y0jH2Yjn7Bqm/+ZMeS6VxcCLthGyHyDBfkHzTlUq4CZt13Kef63vfy3CeMby8744W1L75+obW5zcfP22zuqWOMZ/nnUR4+TMWr1D8pdTLcp71KV1WeuwP4lffiY4D2vbQ3iRnfQKxPFrqxKZNfDKxOKuPZZNkP+x6Jij+1oHLN0rq5vQ7ofnW4tDepnp3mv++UHvJ66VSX/i+KvWJtQvxScAJ4sVRY8HvL6nsVqlnpj7dRWcLaGN79eEZsJDkhC79DMJzpJ4FvG4BdnTVhRP2F0nPkb5P6ju6muw3h5WMsd30uQOlu0h9d1uSeHbJy6L+okAs6Y2ML1JeEkrFFyknE77BQ7oj4GfybpHGswyOyUXS57Z0U/IYu1T2+uYzvSaF81q4kW9xq6iilRz7RTmQGpMzheXPtC1dpW15Pyz/7Nnypgeo+/PzK7F4VuijUYGn+/1AcSwG788604/Fyx0HRwW+E/NBsxSV5fY7yXYPXs8qBPEFzLY4Q4/lTdpJl+zOUJkvdidKn75m9al7uXGJG6l56cqzfFdK00WHeE4AAAZISURBVBOEZ3Icz1kPJU6F2eGbuXF5q/p0guMEzUsjn+3Qhq6ayvUl7m/aGPOsgh/w3SL6wI7aPqArg6e0k+PLkj5v+2PxuPLNyilRof1we4+KylzPs8qHRWV9beb4Eve9X2Pvg/syaC3azfHlTLWfXhPc5blSLyPGUvoYe42Mtc/p0pWXF30eqGnpKkFf9bd618iiU8fi/S4SHQf5VKkv/p4NsXim5svSdzX7ftld6sHiNdi7SbeUfq4pSxMdz1h46tl3a86WD5H6xLUkDZLbb26i4/ZOlzqBCTNN22rbd7BP+GO3q7fChcHTlelFPKm6xm7OCSL9/LSLUFp3kfs5vrxSBrle/HzUs7V/m/TIRRo7o68cXzwWzpN6PFn8DQx/zstwJUmOL6m9k8aYL0CeLfED+XtE6mRvKW2kh/0cX2yHZwh9PrH4OP6g1LOf8fMtPk59fHsWzucfi88rvuhu1uz3+ZLjS9z/GBId8948cmpvbZuDl7KD1DDG1pexvkn3w+wbNoZ7dtNjrLaHke8A32xMOvbTeovezzpeZlXygb0sDWuP3nZi0iaeZvyh1G06e12WhoQm1Pfyygea9zxFfL7Ud79pEvAPTR3364zfy11uN010HqIyDyr354vLX0k90H4ldXIRZFa/qe1H6YPBdw/SYEdob2Nt+AK8LL1AepbUF+ZUwnT5gekbM/ZnxSX++FO0syz1kpo/d02zHw60GV31/nauL46dT3iXSJ28el3bJ4f1ercwv4NZvrxfTf280ZC0eRz6c04EJh07+RZ0V3OWL3FPs8aYZ+PcXpsudWfyxJZyfNlenz5aepHU556rpF7mbZtN8A2Mb+6cGHk8nix1ArsIyfEl2OHZb483f8b+HLoIA+foI8cX81+S2hefS70c7/OAb3hjqWGM2V5fN5akttcznD6POfkvSXLiEuyddewP7VeWL1mVhvZE/ftiZ1vTRKcA02aa4AN3m5m11qxQS1xy3MKXHEqLr0NcFs88p0fikkNp8XWIy+KZ5/S46i45tajTKwGv8/uO67Jee6FxCEAAAhCAwJ2QAInOMEF/srpdarreR68fGcYMeoUABCAAAQhAoIbpOK/V+kFf2+rZkZMKD5tnca6Ves38OKkfepxXaohLrk/4kktqsfWIy2J55/ZGXHJJLbYecVks79zesuKSVSm3R+p1RmBMccGXzoZFpw0Rl05xdtYYcekMZacNEZdOcXbWGM/odIaShiAAAQhAAAIQKI4Az+gUFxIMggAEIAABCECgKwIkOl2RpB0IQAACEIAABIojQKJTXEgwCAIQgAAEIACBrgiQ6HRFknYgAAEIQAACECiOAIlOcSHBIAhAAAIQgAAEuiJAotMVSdqBAAQgAAEIQKA4AiQ6xYUEgyAAAQhAAAIQ6IoAiU5XJGkHAhCAAAQgAIHiCJDoFBcSDIIABCAAAQhAoCsCJDpdkaQdCEAAAhCAAASKI0CiU1xIMAgCEIAABCAAga4IkOh0RZJ2IAABCEAAAhAojgCJTnEhwSAIQAACEIAABLoiQKLTFUnagQAEIAABCECgOAIkOsWFBIMgAAEIQAACEOiKAIlOVyRpBwIQgAAEIACB4giQ6BQXEgyCAAQgAAEIQKArAiQ6XZGkHQhAAAIQgAAEiiNAolNcSDAIAhCAAAQgAIGuCJDodEWSdiAAAQhAAAIQKI4AiU5xIcEgCEAAAhCAAAS6IkCi0xVJ2oEABCAAAQhAoDgCJDrFhQSDIAABCEAAAhDoigCJTlckaQcCEIAABCAAgeIIkOgUFxIMggAEIAABCECgKwIkOl2RpB0IQAACEIAABIojQKJTXEgwCAIQgAAEIACBrgiQ6HRFknYgAAEIQAACECiOAIlOcSHBIAhAAAIQgAAEuiJAotMVSdqBAAQgAAEIQKA4AiQ6xYUEgyAAAQhAAAIQ6IoAiU5XJGkHAhCAAAQgAIHiCJDoFBcSDIIABCAAAQhAoCsC62Y0tCqjDlUgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEOiQwP8DJnVlMMvo8aYAAAAASUVORK5CYII=)
Answer:This is a grouped frequency distribution.
To find x and y, we’ll need to find mean of the following distribution by assumed mean method and equate it to the given mean of the following distribution, 332.
And class size, c = 50.
[∵ (150 – 100) = (200 – 150) = (250 – 200) = … = (550 – 500) = 50]
This given data is in exclusive type.
So, let’s construct a table finding midpoints and stating frequencies.
![](data:image/png;base64,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)
So now, we have
∑fiui = -130 – 3x
And ∑fi = 146 + x + y = 200
Mean is given by
![](data:image/png;base64,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)
⇒
[given, mean = 332 and using the values from the table]
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ 43 × 4 = 130 + 3x
⇒ 172 = 130 + 3x
⇒ 3x = 172 – 130
⇒ 3x = 42
⇒ ![](data:image/png;base64,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)
⇒ x = 14 …(i)
Since, there are 200 observations.
⇒ Sum of frequencies = 200 [Sum of frequencies depict total number of observation]
⇒ ∑fi = 200
⇒ 146 + x + y = 200
⇒ x + y = 200 – 146
⇒ x + y = 54 …(ii)
Putting the value of x from equation (i) into equation (ii), we get
x + y = 54
⇒ 14 + y = 54
⇒ y = 54 – 14
⇒ y = 40
Thus, the missing frequencies are x = 14 and y = 40.
Question 4.Find the mode of the following frequency distribution:
![](data:image/png;base64,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)
Answer:Observe that, from the given data:
The maximum class frequency, here, is 57 and the class corresponding to this frequency is 45 – 60.
So, this implies that,
Modal class = 45 – 60
Mode of such grouped frequency distribution is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the modal class = 45
f0 = frequency of the class preceding the modal class = 23
f1 = frequency of the modal class = 57
f2 = frequency of the class succeeding the modal class = 33
c = size of class interval (the class intervals are same) = 15
∴ Substituting the values l = 45, f0 = 23, f1 = 57, f2 = 33 and c = 15 in the formula of mode. We get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 45 + 8.793
⇒ Mode = 53.793
Thus, the mode of the data is 53.793.
Question 5.Find the mode of the following data:
![](data:image/png;base64,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)
Answer:Observe that, from the given data:
The maximum class frequency, here, is 28 and the class corresponding to this frequency is 50 – 60.
So, this implies that,
Modal class = 50 – 60
Mode of such grouped frequency distribution is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the modal class = 50
f0 = frequency of the class preceding the modal class = 17
f1 = frequency of the modal class = 28
f2 = frequency of the class succeeding the modal class = 23
c = size of class interval (the class intervals are same) = 10
∴ Substituting the values l = 50, f0 = 17, f1 = 28, f2 = 23 and c = 10 in the formula of mode. We get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 50 + 6.875
⇒ Mode = 56.875
Thus, the mode of the data is 56.875.
Question 6.The mode of the following frequency distribution of 165 observations is 34.5. Find the value of a and b.
![](data:image/png;base64,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)
Answer:Given that,
Total number of observations = 165
⇒ Sum of frequencies = 165
⇒ 5 + 11 + a + 53 + b + 16 + 10 = 165
⇒ 95 + a + b = 165
⇒ a + b = 165 – 95
⇒ a + b = 70 …(i)
Also, given that
Mode of the data = 34.5
Corresponding to the modal value, the class it lies between is 32 – 41. [∵ 34.5 lies between 32 – 41]
⇒ Modal class = 32 – 41
Now,
Mode of such grouped frequency distribution is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the modal class = 32
f0 = frequency of the class preceding the modal class = a
f1 = frequency of the modal class = 53
f2 = frequency of the class succeeding the modal class = b
c = size of class interval (the class intervals are same) = 9
∴ Substituting the values l = 32, f0 = a, f1 = 53, f2 = b and c = 9 in the formula of mode. We get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ 2.5 × (106 – a – b) = 477 – 9a
⇒ 265 – 2.5a – 2.5b = 477 – 9a
⇒ 9a – 2.5a – 2.5b = 477 – 265
⇒ 6.5a – 2.5b = 212
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ 65a – 25b = 2120
⇒ 13a – 5b = 424 …(ii)
Multiply 5 by equation (i),
a + b = 70 [× 5
⇒ 5a + 5b = 350 …(iii)
Solving equation (i) and (iii), we get
13a – 5b = 424
5a + 5b = 350
18a + 0 = 774
⇒ 18a = 774
⇒ ![](data:image/png;base64,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)
⇒ a = 43
Putting value a = 43 in equation (i),
a + b = 70
⇒ 43 + b = 70
⇒ b = 70 – 43
⇒ b = 27
Thus, a = 43 and b = 27.
Question 7.Find the mode of the following frequency distribution:
![](data:image/png;base64,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)
Answer:Observe that, from the given data:
The maximum class frequency, here, is 86 and the class corresponding to this frequency is 3000 – 3500.
So, this implies that,
Modal class = 3000 – 3500
Mode of such grouped frequency distribution is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the modal class = 3000
f0 = frequency of the class preceding the modal class = 60
f1 = frequency of the modal class = 86
f2 = frequency of the class succeeding the modal class = 74
c = size of class interval (the class intervals are same) = 500
∴ Substituting the values l = 3000, f0 = 60, f1 = 86, f2 = 74 and c = 500 in the formula of mode. We get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMEAAAAgCAMAAACchOyJAAAAAXNSR0IArs4c6QAAAKtQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGZmAGaQAGa2OgAAOgA6OgBmOjoAOjpmOjqQOmY6OmZmOmaQOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmY6ZmaQZpC2ZpDbZra2ZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNu2kNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29uQ29u22/+22////7Zm/9uQ/9u2//+2///btqyGqwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAC30lEQVRYR+1YbXPaMAy26UpHtm5rKWXrXlhauqYr0G3kxf//l02PZAdWZBJ23HG5wx8SXc6W9EiPZDvGHMcxAsY9DhCF+bntfe1kOOYXYyBwt/dm0XvoJAQz4xzQKN50HEE5nXQzBSEHmX3VcQTGPCff956E3Nr9K33hpcteL42prh9MsRXBPFIk1Sg4ObP2aiMEeQsEbnFu7Snrd1Nr3/+MSWqAySwbnifRblokmMONSjNAEPoUA0PvTQANYRGXst69KVMYcGl/WaYnT7oUALh0x7yucqMZoPTdMLr8bPy/CNANZ0hWDk2cNk1qi6D6RCGgUfr3WhhVtdX1jxG57tJveFFTHgciQPrA1CSpab/MEHl+VCNCpEltEbj0FBCq0dCvWOVAVUslhO95/w8jKJIJUQKeQHJ3CCik7X2inF4S+5FjWO4vNamugkYW8WoOhIwaga6WECDv2VXFCDKs4yUZ3GFKQHKpV5ihqnjUZwB0g0uaLAbw1KT2CKDi93iA6vQI3iXcKnS1hIC8K94+MQKBgadIwOKhcb3HxnNCaWuBYAN/HQ8RvH6XSnuR4W7BCwpYFIGZndx4l8VbBHwdASsHs+Ijp04WkjxQpR1yQOvXEfhE6AbCVkIAG3IQHFBYJFwl6L7QIlId0sZuyix6kfP1BvGPAd4Mmf2MQMII7gjxUQd1CegZcCnSxgUjLTUmtUYQKjnwKBM+01MzQI6TVQyhDdhQMowZNqqP4hN1pXns+uHAUFkSa0MSl7YI/OxVM8rYgHRqrc/5UwUaCiAsaAsfwp57tL3hrwQQsON/iRZyOQ1LTElbCLoSbUeK5CE0ddPys5gq/BtxJLV8WNmiVmfI8WubCPh7cot9v422A8zx9+RqNGl1jDyAh80m+Z6c87lKOVs2rz/8DEaAW34ZTi6H92k3D+RfBd10LrTz/W66DjO7/tvCm2sHh9yTudd3swzCPdmlnf3Z0kHa7Nflv4hifbK7H2IPAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 3000 + 342.10
⇒ Mode = 3342.10
Thus, the mode of the data is 3342.10.
Question 8.Find the median of the following frequency distribution:
![](data:image/png;base64,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)
Answer:Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
![](data:image/png;base64,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)
We have added up all the values of the frequency in the second column and have got,
Total = n = 100
Now, we just need to find the value of n/2. So,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, look up for a value in the cumulative frequency just greater than 50.
We have, 59.
Corresponding to this value of cumulative frequency, we can say that median class is 40 – 50.
That is,
Median class = 40 – 50
∴ we have almost everything we require to calculate median.
Median is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the median class = 40
n = Total number of observation (sum of frequencies) = 100
cf = cumulative frequency of the class preceding the median class = 35
f = frequency of the median class = 24
c = class size (class sizes are equal) = 10
Putting the values, l = 40, n/2 = 50, cf = 35, f = 24 and c = 10 in the given formula of median, we get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Median = 40 + 6.25
⇒ Median = 46.25
Thus, the median of the data is 46.25.
Question 9.The median of the following data is 525. Find the value of x and y, if the sum of frequency is 100.
![](data:image/png;base64,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)
Answer:Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
![](data:image/png;base64,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)
We have added up all the values of the frequency in the second column and have got,
Total = n = 76 + x + y …(i)
But given is, sum of frequencies, ∑f = n = 100 …(ii)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Comparing equations (i) and (ii), we get
76 + x + y = 100
⇒ x + y = 100 – 76
⇒ x + y = 24 …(iii)
Also, given that, median = 525
Corresponding to this value of median, we can say that median lies in the class is 500 – 600. [∵ 525 lies between 500 – 600]
⇒ Median class = 500 – 600
Median is given by,
![](data:image/png;base64,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)
Where,
l = lower limit of the median class = 500
n = Total number of observation (sum of frequencies) = 100
cf = cumulative frequency of the class preceding the median class = 36 + x
f = frequency of the median class = 20
c = class size (class sizes are equal) = 100
Putting the values, l = 500, n/2 = 50, cf = 36 + x, f = 20 and c = 100 in the given formula of median, we get
![](data:image/png;base64,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)
⇒
[∵ given that, median = 525]
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ (14 – x) × 5 = 25
⇒ 14 – x = 5
⇒ x = 14 – 5
⇒ x = 9
Substituting the value, x = 9 in equation (iii), we get
x + y = 24
⇒ 9 + y = 24
⇒ y = 24 – 9
⇒ y = 15
Thus, x = 9 and y = 15.
Question 10.Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
For some data, if Z = 25 and
= 25, then M =
A. 25
B. 75
C. 50
D. 0
Answer:Given: Z = 25 [Z denotes mode]
[
denotes mean]
We have to find M (that is, median).
By empirical relationship, we can say
Mode = 3 (Median) – 2 (Mean)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Putting in the given values, we can
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIIAAAArCAMAAACDzqDpAAAAAXNSR0IArs4c6QAAAI1QTFRFAAAAAAAAAAA6AABmADpmADqQAGZmAGa2OgAAOgA6OgBmOjoAOjpmOmaQOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmY6ZmaQZra2ZrbbZrb/kDoAkDo6kGY6kLbbkNu2kNv/tmYAttv/tv//25A625Bm27Zm27aQ29u22/+22////7Zm/9uQ/9u2//+2///b1us9EgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACKUlEQVRYR+1YaVODMBAlPSwebWm1HlhtLFothPz/n+duCCRpCwEazYzjfoGB3bcveyQsQfAv/SPwvulvq1t2wOG7JSEj9JuFBGRQS0FpniLZHufImpLHgEXDLVJ4OnjLY/2J0jxFoQnHElc6AYWEgC8rhUoTLPI7IA3C5DVowmmT2rQNBQEkNEF4PEIOeTTT8Wtw2lCgbRIhgIRmwWG8BwYYGSU1OC0oFCnIwpuwKMxSzFrAp1qygMPncrLX4etw7BR4PBfreobCjMuOoNgeQrQekZplHAgEwmB8AsfuXoRUi2YWCpjSidkjhibYmRTqcaw0qB5NI7uHiTA0RSL0MNTj2CgkCJPC2imuvykKlaZejlUqGnAsFLJLKECO7ikkncVlxRdu9EQoTfFKBEAFrQnHQkGWHVBgt1B707fajlCaoMLui+Vn8ho04dgS8bff5xGRm2lCiNZpv7lq4CBLxheDIF+sxMaWXiw9BQEovEbgm8cPePEi+WKDJ1c6/vJJAc9vOs8VhZOHz88FCKIAJ0d2tdUoHHmrzsMfuIHNc7EJkuFqDruox1qAUweawmsi4OyBbwGPUYjkOeeNQrVB442vYnDbbPzjWo5dbnE7oNHBi/Z128HQnaoal9xh9kGqJpk+xi5s2Nr4rnMB2Q0DO2tqzC7d7N1o70L9A9sNZleU1P8OY0w6Xfmfq19MtOXvhXPRetlznLlZMUP5EraG32Eznwx8rfw8v99t3zSNhzgOhgAAAABJRU5ErkJggg==)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ M = 25
Thus, option (a) is correct.
Question 11.Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
For some data Z — M = 2.5. If the mean of the data is 20, then Z =
A. 21.25
B. 22.75
C. 23.75
D. 22.25
Answer:We have been given that,
Z – M = 2.5
⇒ M = Z – 2.5 …(i)
And
…(ii)
Here, Z = Mode,
M = Median
& ![](data:image/png;base64,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)
So, by empirical relationship we have,
Mode = 3 (Median) – 2 (Mean)
⇒ ![](data:image/png;base64,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)
Putting equations (i) and (ii) in the above equation, we get
Z = 3(Z – 2.5) – 2×20
⇒ Z = 3Z – 7.5 – 40
⇒ 3Z – Z = 40 + 7.5
⇒ 2Z = 47.5
⇒ ![](data:image/png;base64,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)
⇒ Z = 23.75
Thus, option (c) is correct.
Question 12.Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
If
— Z = 3 and
+ Z = 45, then M =
A. 24
B. 22
C. 26
D. 23
Answer:Solving the given equations,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Put this value in
,
24 – Z = 3
⇒ Z = 24 – 3
⇒ Z = 21
By empirical relationship, we can write
Mode = 3 (Median) – 2 (Mean)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGIAAAAXCAMAAADHlGpOAAAAAXNSR0IArs4c6QAAAIdQTFRFAAAAAAAAAAA6AABmADpmADqQAGZmAGa2OgAAOgA6OgBmOjoAOmY6OmaQOma2OpDbZgAAZgA6ZgBmZjoAZjpmZmYAZmY6Zra2ZrbbZrb/kDoAkDo6kGY6kLbbkNu2kNv/tmYAttv/tv//25A627Zm27aQ2/+22////7Zm/9uQ/9u2//+2///b9rTOMwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABZUlEQVRIS+1Ui1KDMBC8UCvx0QJWq8YqsVglJP//fd4jxekMCR8gN8PAwN7t3t4FgCX+kwO+VhyrY6rr8HWn1FULQNBXRnVKVQl4OO0Yfa67/sFHAvcxdyrPFu8wmEI4MIPvKQaw6gWG+kKwf0D5vubU6bAl60b9vtkTE/TXuzTFiL6s1nFmLizp8s0H9RzMM7eeDjLFKmwZHRVrnSbqTAyHzScZ1LRE1a+/ZyhYkEXdwQgD8JsYSB5j7Iwmt+EZNC3rq2SAyXCaCgeDXURcnx7eucpJi1FtMKW7Pf5RTCjC2lLY6futFCC2vE/4lWUgBXSrfRXXMJGEKuKXccS8LDmjRFGkcBoNzBply6jYPz7JBHxNpLy7kyFt88GhLoB2OEfRkSc9Ld5bK7V58Lj3ydMd6NQNbKavY78ZCneD5YKt+BJ/nZ77gQwHhGyZIW45PaRWKs6/CkYV2EUaODv+BbA4MO3AL/49H2wj4MSBAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Putting in the given values, we can
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ M = 23
Thus, option (d) is correct.
Question 13.Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
If Z = 24,
= 18, then M=
A. 10
B. 20
C. 30
D. 40
Answer:Given that,
Z = 24
![](data:image/png;base64,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)
To find: M = ?
By empirical relationship, we can write
Mode = 3 (Median) – 2 (Mean)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Putting in the given values, we can
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIIAAAAqCAMAAABIknNMAAAAAXNSR0IArs4c6QAAAJNQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGZmAGa2OgAAOgA6OgBmOjoAOjqQOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmY6ZmZmZmaQZpDbZra2ZrbbZrb/kDoAkGY6kLbbkNu2kNv/tmYAttv/tv//25A627Zm27aQ29u22/+22////7Zm/9uQ/9u2//+2///bLs+r9AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACQElEQVRYR+2Y2VbDIBBAobXauFQT465xoY2pzcL/f50zDEnB1hTOSQ4PykPJwzBzGWaBMvY/3D0gi5Tz2YdekE/ar10NtuQeC8UNLf4853zy6I4g+DOrk+lKragiC0FmL4YiS3LXQJ1y0pJPngGDx84MYo6ruLLVJPd9CIYka24JutYzqxbLXCHIDOWYON44M6BgSQgiLnsQlEYtCYZmaK9JLreGbAQF4j6E4i8vNgcRSFJtFrbZJKYhQgBKPIieoNrHVUXohOb6gx1CIMmWYZ3OTW9rBFZEEI6/h/U+Aplh6KhfQMjJiODtMLSRZMfA7fPWCFUEQjq6HA9Cx0/ZmtxmgZ0RXaT1I6gTonNyHsLwZv9BmJJoZJ1adsgLOj66oHHgyFFNqR3ci2BJtuFo7LXNCMXlkZTVKQSOFBrBro72QViS2tFWSujFOb/a+JUmCgFCgHgwQ/lndTQk6wfafqVnJl8hD/gR1mUs0LM3hwP4GyJNwqnsQo569IxBnQMMKjZhdu9agxJAwb1TsVWepOEQ3hOwLbMnnIIMaDtYosrjr5AI2N1F3GwR9jaf8RwEXoAOVJ2tDIQda10/HOGD+n8+vYshJQLGAt1Hgx4ENCy4WQX0QqIvH8EQugKNH6GCYdhkk6oH+91KhyVgYvLG6szzZjwsg/nsGlaznzafS6mfZkfp+nWxdBQdRwwza+HxOBiHoojaJ+U4+l20luErjHovhhr0om3/XghCIbEq1V6P1cE5a3wuXQbPiMH3NbbCb8SdOXIf3Il9AAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ M = 20
Thus, option (b) is correct.
Question 14.Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
If M = 15,
= 10, then Z=
A. 15
B. 20
C. 25
D. 30
Answer:Given that,
M = 15
![](data:image/png;base64,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)
So, by empirical relationship we have,
Mode = 3 (Median) – 2 (Mean)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGIAAAAXCAMAAADHlGpOAAAAAXNSR0IArs4c6QAAAIdQTFRFAAAAAAAAAAA6AABmADpmADqQAGZmAGa2OgAAOgA6OgBmOjoAOmY6OmaQOma2OpDbZgAAZgA6ZgBmZjoAZjpmZmYAZmY6Zra2ZrbbZrb/kDoAkDo6kGY6kLbbkNu2kNv/tmYAttv/tv//25A627Zm27aQ2/+22////7Zm/9uQ/9u2//+2///b9rTOMwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABZUlEQVRIS+1Ui1KDMBC8UCvx0QJWq8YqsVglJP//fd4jxekMCR8gN8PAwN7t3t4FgCX+kwO+VhyrY6rr8HWn1FULQNBXRnVKVQl4OO0Yfa67/sFHAvcxdyrPFu8wmEI4MIPvKQaw6gWG+kKwf0D5vubU6bAl60b9vtkTE/TXuzTFiL6s1nFmLizp8s0H9RzMM7eeDjLFKmwZHRVrnSbqTAyHzScZ1LRE1a+/ZyhYkEXdwQgD8JsYSB5j7Iwmt+EZNC3rq2SAyXCaCgeDXURcnx7eucpJi1FtMKW7Pf5RTCjC2lLY6futFCC2vE/4lWUgBXSrfRXXMJGEKuKXccS8LDmjRFGkcBoNzBply6jYPz7JBHxNpLy7kyFt88GhLoB2OEfRkSc9Ld5bK7V58Lj3ydMd6NQNbKavY78ZCneD5YKt+BJ/nZ77gQwHhGyZIW45PaRWKs6/CkYV2EUaODv+BbA4MO3AL/49H2wj4MSBAAAAAElFTkSuQmCC)
Putting given values in the above equation, we get
Z = 3(15) – 2×10
⇒ Z = 45 – 20
⇒ Z = 25
Thus, option (c) is correct.
Question 15.Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
(6) If M = 22, Z = 16, then
=
A. 22
B. 25
C. 32
D. 66
Answer:Given that,
M = 22
Z = 16
So, by empirical relationship we have,
Mode = 3 (Median) – 2 (Mean)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Putting in the given values in the above equation, we get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Thus, option (b) is correct.
Question 16.Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
(7) If
= 21.44 and Z = 19.13, then M =
A. 21.10
B. 19.67
C. 20.10
D. 20.67
Answer:Given that,
Z = 19.13
![](data:image/png;base64,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)
To find: M = ?
By empirical relationship, we can write
Mode = 3 (Median) – 2 (Mean)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Putting in the given values, we can
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEYAAAAgCAMAAACYXf7xAAAAAXNSR0IArs4c6QAAAJZQTFRFAAAAAAAAAAA6AABmADo6ADqQAGZmAGaQAGa2OgAAOgA6OgBmOjoAOjo6OmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZmY6ZpDbZra2ZrbbZrb/kDoAkDo6kGY6kLbbkNu2kNv/tmYAtmY6tv//25A625Bm27Zm27aQ29u229vb2/+22////7Zm/9uQ/9u2//+2///bW3+YNQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABS0lEQVRIS9WUy1LDMAxFpYRAw6shTVogoQU3Dwpxav//zyHZmZQZ6NQTlwXa2AvdM7qSZYD/Ge1y3gHscsTEGNBrDB7NZTtzdqS3DwQBlW2gDd5YVs+6/ppuzX3ujqkPqUYMalGALlMLdK1Gl/PlHZtildGqjGDCANwxfZx87Eojam1rJmGMqI6onNpSpppKOs3VSKLIAmRYici2GLS46oiKWFjPiMb1r7HnQdtszieMyjF4tjJErg65WD6PU06PQmUr8xDkZe6HeV2QXpdPfEwOGoIIK5DRpy9GUtNEqg4YwW0zYR++Q1A1NMr+pvqG+SEbsUcu9jnW4SqlUXn2BvqYivc2ZXfMsxra+GFLPEyNy8AXD47DMP8mpbkdfmEvvH4Z/2MvDontT+Mb+zX/NL4h8OIcGID3eHhs0yviJez9MdDE5xj4dB8nlV+zOR7C3c5MLgAAAABJRU5ErkJggg==)
⇒ M = 20.67
Thus, option (d) is correct.
Question 17.Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
If M = 26,
=36, then Z =
A. 6
B. 5
C. 4
D. 3
Answer:Given that,
M = 15
![](data:image/png;base64,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)
So, by empirical relationship we have,
Mode = 3 (Median) – 2 (Mean)
⇒ ![](data:image/png;base64,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)
Putting given values in the above equation, we get
Z = 3(15) – 2×10
⇒ Z = 45 – 20
⇒ Z = 25
Thus, option (c) is correct.
Question 18.Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
(9) The modal class of the frequency distribution given below is
![](data:image/png;base64,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)
A. 10-20
B. 20-30
C. 30-40
D. 40-50
Answer:Observe that, from the given data:
The maximum class frequency, here, is 17 and the class corresponding to this frequency is 30 – 40.
So, this implies that,
Modal class = 30 – 40
[∵ modal class in a grouped frequency table can be calculated by corresponding maximum class frequency]
Thus, option (c) is correct.
Question 19.Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
The cumulative frequency of class 20-30 of the frequency distribution given in (9) is ….
A. 25
B. 35
C. 15
D. 40
Answer:We have
![](data:image/png;base64,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)
Cumulative frequency of a class is just the sum of frequencies of the particular class along with all the classes preceding the class.
So, Cumulative frequency of class 20 – 30 = Sum of frequency of the class 20 – 30 along with frequencies of all the classes preceding the class 20 – 30.
⇒ Cumulative frequency of class 20 – 30 = 7 + 15 + 13
⇒ Cumulative frequency of class 20 – 30 = 35
Thus, option (b) is correct.
Question 20.Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
The median class of the frequency distribution given in (9) is ….
A. 40-50
B. 30-40
C. 20-30
D. 10-20
Answer:We have
![](data:image/png;base64,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)
We need to show it into a proper table representing frequencies and cumulative frequencies.
So,
![](data:image/png;base64,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)
We have added up all the values of the frequency in the second column and have got,
Total = n = 62
Now, we just need to find the value of n/2. So,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADUAAAAqCAMAAAAkuOMMAAAAAXNSR0IArs4c6QAAAGlQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjpmOma2OpC2OpDbZgAAZjoAZrbbZrb/kDoAkLaQkLbbkNv/tmYAtmY6tv//25A625Bm27Zm27aQ29v/2////7Zm/9uQ/9u2//+2///bQs6WKgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABLUlEQVRIS+2U3U7DMAyFbQbL6Chb2cIKY8ma939I4iS0kzW7GRKCC3yRSs13Ev+0B+CvRXg1DyeAcHxGvN9XZudM80GoxQ2c28WhSubMJnN2GZcetwAOcftmsJH1Q0vwGI5U4M3jPh8gRMbGsClDb+JLb55ElV28xCY0sRsUCS+PoRVVocP1CY7l2NBlMIlVFTUdbFpDV2qsVPWpHLu8TFS5C3L56a6eFkc5phZp3fAmXvCeqFX8LoKNKm/iwIYWUW6ip+9oR/dhCpkU5/C/8VMdKDOJY7lTfvU8OAohjwmYRW+tpC7DW0/9Bb7OUDlVZ6icmgxVK/QqxZxS0HMqO8pcMKoY6oyKUV+GqqsYNRqqquLUaKiqilGToWoqRk2Gqok4VWeoddTc6L6z/wmzKxLSfXLd4AAAAABJRU5ErkJggg==)
⇒ ![](data:image/png;base64,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)
Now, look up for a value in the cumulative frequency just greater than 31.
We have, 35.
Corresponding to this value of cumulative frequency, we can say that median class is 20 – 30.
That is,
Median class = 20 – 30
Thus, option (c) is correct.
In a retail market, a fruit vendor was selling apples kept in packed boxes. These boxes contained varying number of apples. The following was the distribution of apples according to the number of boxes. Find the mean by the assumed mean number of apples kept in the box.
Answer:
We have grouped frequency distribution and we need to find mean by assumed-mean method.
Assumed-mean method is given such name because in this method, we actually assume a mean from xI (usually a centre value) and the formula of mean is also based on that particular assumed mean.
By using assumed-mean method, we can avoid the risk of miscalculation. Also, by using assumed mean method, we’ll be able to solve the question with ease and more accuracy.
So, let us assume mean from the midpoints. Let assumed mean, A = 57.5 (a value quite centrally placed).
So now, we have
∑fidi = -165 and ∑fi = 400.
And we have assumed mean as, A = 57.5
Mean is given by
⇒
⇒ Mean = 57.5 – 0.4125
⇒ Mean = 57.0875
Thus, mean number of apples in a box is 57.0875.
Question 2.
The daily expenditure of 50 hostel students are as follows:
Find the mean daily expenditure of the students of hostel using appropriate method.
Answer:
Let us solve by direct method since the frequencies have smaller values.
This is grouped frequency distribution.
We shall represent them by creating a table having columns of class intervals, midpoints, frequencies, and product of these midpoints and frequencies.
So now, we have
∑fi = 50 and ∑xifi = 7260
For grouped frequency distribution, mean is taken out from the formula:
⇒ [from the table]
⇒
⇒ Mean = 145.2
Thus, the mean daily expenditure of the students is Rs. 145.2.
Question 3.
The mean of the following frequency distribution of 200 observations is 332. Find the value of x and y.
Answer:
This is a grouped frequency distribution.
To find x and y, we’ll need to find mean of the following distribution by assumed mean method and equate it to the given mean of the following distribution, 332.
And class size, c = 50.
[∵ (150 – 100) = (200 – 150) = (250 – 200) = … = (550 – 500) = 50]
This given data is in exclusive type.
So, let’s construct a table finding midpoints and stating frequencies.
So now, we have
∑fiui = -130 – 3x
And ∑fi = 146 + x + y = 200
Mean is given by
⇒ [given, mean = 332 and using the values from the table]
⇒
⇒
⇒ 43 × 4 = 130 + 3x
⇒ 172 = 130 + 3x
⇒ 3x = 172 – 130
⇒ 3x = 42
⇒
⇒ x = 14 …(i)
Since, there are 200 observations.
⇒ Sum of frequencies = 200 [Sum of frequencies depict total number of observation]
⇒ ∑fi = 200
⇒ 146 + x + y = 200
⇒ x + y = 200 – 146
⇒ x + y = 54 …(ii)
Putting the value of x from equation (i) into equation (ii), we get
x + y = 54
⇒ 14 + y = 54
⇒ y = 54 – 14
⇒ y = 40
Thus, the missing frequencies are x = 14 and y = 40.
Question 4.
Find the mode of the following frequency distribution:
Answer:
Observe that, from the given data:
The maximum class frequency, here, is 57 and the class corresponding to this frequency is 45 – 60.
So, this implies that,
Modal class = 45 – 60
Mode of such grouped frequency distribution is given by,
Where,
l = lower limit of the modal class = 45
f0 = frequency of the class preceding the modal class = 23
f1 = frequency of the modal class = 57
f2 = frequency of the class succeeding the modal class = 33
c = size of class interval (the class intervals are same) = 15
∴ Substituting the values l = 45, f0 = 23, f1 = 57, f2 = 33 and c = 15 in the formula of mode. We get
⇒
⇒
⇒
⇒
⇒ Mode = 45 + 8.793
⇒ Mode = 53.793
Thus, the mode of the data is 53.793.
Question 5.
Find the mode of the following data:
Answer:
Observe that, from the given data:
The maximum class frequency, here, is 28 and the class corresponding to this frequency is 50 – 60.
So, this implies that,
Modal class = 50 – 60
Mode of such grouped frequency distribution is given by,
Where,
l = lower limit of the modal class = 50
f0 = frequency of the class preceding the modal class = 17
f1 = frequency of the modal class = 28
f2 = frequency of the class succeeding the modal class = 23
c = size of class interval (the class intervals are same) = 10
∴ Substituting the values l = 50, f0 = 17, f1 = 28, f2 = 23 and c = 10 in the formula of mode. We get
⇒
⇒
⇒
⇒ Mode = 50 + 6.875
⇒ Mode = 56.875
Thus, the mode of the data is 56.875.
Question 6.
The mode of the following frequency distribution of 165 observations is 34.5. Find the value of a and b.
Answer:
Given that,
Total number of observations = 165
⇒ Sum of frequencies = 165
⇒ 5 + 11 + a + 53 + b + 16 + 10 = 165
⇒ 95 + a + b = 165
⇒ a + b = 165 – 95
⇒ a + b = 70 …(i)
Also, given that
Mode of the data = 34.5
Corresponding to the modal value, the class it lies between is 32 – 41. [∵ 34.5 lies between 32 – 41]
⇒ Modal class = 32 – 41
Now,
Mode of such grouped frequency distribution is given by,
Where,
l = lower limit of the modal class = 32
f0 = frequency of the class preceding the modal class = a
f1 = frequency of the modal class = 53
f2 = frequency of the class succeeding the modal class = b
c = size of class interval (the class intervals are same) = 9
∴ Substituting the values l = 32, f0 = a, f1 = 53, f2 = b and c = 9 in the formula of mode. We get
⇒
⇒
⇒
⇒ 2.5 × (106 – a – b) = 477 – 9a
⇒ 265 – 2.5a – 2.5b = 477 – 9a
⇒ 9a – 2.5a – 2.5b = 477 – 265
⇒ 6.5a – 2.5b = 212
⇒
⇒
⇒ 65a – 25b = 2120
⇒ 13a – 5b = 424 …(ii)
Multiply 5 by equation (i),
a + b = 70 [× 5
⇒ 5a + 5b = 350 …(iii)
Solving equation (i) and (iii), we get
13a – 5b = 424
5a + 5b = 350
18a + 0 = 774
⇒ 18a = 774
⇒
⇒ a = 43
Putting value a = 43 in equation (i),
a + b = 70
⇒ 43 + b = 70
⇒ b = 70 – 43
⇒ b = 27
Thus, a = 43 and b = 27.
Question 7.
Find the mode of the following frequency distribution:
Answer:
Observe that, from the given data:
The maximum class frequency, here, is 86 and the class corresponding to this frequency is 3000 – 3500.
So, this implies that,
Modal class = 3000 – 3500
Mode of such grouped frequency distribution is given by,
Where,
l = lower limit of the modal class = 3000
f0 = frequency of the class preceding the modal class = 60
f1 = frequency of the modal class = 86
f2 = frequency of the class succeeding the modal class = 74
c = size of class interval (the class intervals are same) = 500
∴ Substituting the values l = 3000, f0 = 60, f1 = 86, f2 = 74 and c = 500 in the formula of mode. We get
⇒
⇒
⇒
⇒
⇒ Mode = 3000 + 342.10
⇒ Mode = 3342.10
Thus, the mode of the data is 3342.10.
Question 8.
Find the median of the following frequency distribution:
Answer:
Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
We have added up all the values of the frequency in the second column and have got,
Total = n = 100
Now, we just need to find the value of n/2. So,
⇒
Now, look up for a value in the cumulative frequency just greater than 50.
We have, 59.
Corresponding to this value of cumulative frequency, we can say that median class is 40 – 50.
That is,
Median class = 40 – 50
∴ we have almost everything we require to calculate median.
Median is given by,
Where,
l = lower limit of the median class = 40
n = Total number of observation (sum of frequencies) = 100
cf = cumulative frequency of the class preceding the median class = 35
f = frequency of the median class = 24
c = class size (class sizes are equal) = 10
Putting the values, l = 40, n/2 = 50, cf = 35, f = 24 and c = 10 in the given formula of median, we get
⇒
⇒
⇒ Median = 40 + 6.25
⇒ Median = 46.25
Thus, the median of the data is 46.25.
Question 9.
The median of the following data is 525. Find the value of x and y, if the sum of frequency is 100.
Answer:
Here, we have grouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.
So,
We have added up all the values of the frequency in the second column and have got,
Total = n = 76 + x + y …(i)
But given is, sum of frequencies, ∑f = n = 100 …(ii)
⇒
⇒
Comparing equations (i) and (ii), we get
76 + x + y = 100
⇒ x + y = 100 – 76
⇒ x + y = 24 …(iii)
Also, given that, median = 525
Corresponding to this value of median, we can say that median lies in the class is 500 – 600. [∵ 525 lies between 500 – 600]
⇒ Median class = 500 – 600
Median is given by,
Where,
l = lower limit of the median class = 500
n = Total number of observation (sum of frequencies) = 100
cf = cumulative frequency of the class preceding the median class = 36 + x
f = frequency of the median class = 20
c = class size (class sizes are equal) = 100
Putting the values, l = 500, n/2 = 50, cf = 36 + x, f = 20 and c = 100 in the given formula of median, we get
⇒ [∵ given that, median = 525]
⇒
⇒
⇒ (14 – x) × 5 = 25
⇒ 14 – x = 5
⇒ x = 14 – 5
⇒ x = 9
Substituting the value, x = 9 in equation (iii), we get
x + y = 24
⇒ 9 + y = 24
⇒ y = 24 – 9
⇒ y = 15
Thus, x = 9 and y = 15.
Question 10.
Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
For some data, if Z = 25 and = 25, then M =
A. 25
B. 75
C. 50
D. 0
Answer:
Given: Z = 25 [Z denotes mode]
[
denotes mean]
We have to find M (that is, median).
By empirical relationship, we can say
Mode = 3 (Median) – 2 (Mean)
⇒
⇒
⇒
Putting in the given values, we can
⇒
⇒
⇒ M = 25
Thus, option (a) is correct.
Question 11.
Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
For some data Z — M = 2.5. If the mean of the data is 20, then Z =
A. 21.25
B. 22.75
C. 23.75
D. 22.25
Answer:
We have been given that,
Z – M = 2.5
⇒ M = Z – 2.5 …(i)
And …(ii)
Here, Z = Mode,
M = Median
&
So, by empirical relationship we have,
Mode = 3 (Median) – 2 (Mean)
⇒
Putting equations (i) and (ii) in the above equation, we get
Z = 3(Z – 2.5) – 2×20
⇒ Z = 3Z – 7.5 – 40
⇒ 3Z – Z = 40 + 7.5
⇒ 2Z = 47.5
⇒
⇒ Z = 23.75
Thus, option (c) is correct.
Question 12.
Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
If — Z = 3 and
+ Z = 45, then M =
A. 24
B. 22
C. 26
D. 23
Answer:
Solving the given equations,
⇒
⇒
⇒
Put this value in ,
24 – Z = 3
⇒ Z = 24 – 3
⇒ Z = 21
By empirical relationship, we can write
Mode = 3 (Median) – 2 (Mean)
⇒
⇒
⇒
Putting in the given values, we can
⇒
⇒
⇒ M = 23
Thus, option (d) is correct.
Question 13.
Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
If Z = 24, = 18, then M=
A. 10
B. 20
C. 30
D. 40
Answer:
Given that,
Z = 24
To find: M = ?
By empirical relationship, we can write
Mode = 3 (Median) – 2 (Mean)
⇒
⇒
⇒
Putting in the given values, we can
⇒
⇒
⇒ M = 20
Thus, option (b) is correct.
Question 14.
Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
If M = 15, = 10, then Z=
A. 15
B. 20
C. 25
D. 30
Answer:
Given that,
M = 15
So, by empirical relationship we have,
Mode = 3 (Median) – 2 (Mean)
⇒
Putting given values in the above equation, we get
Z = 3(15) – 2×10
⇒ Z = 45 – 20
⇒ Z = 25
Thus, option (c) is correct.
Question 15.
Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
(6) If M = 22, Z = 16, then =
A. 22
B. 25
C. 32
D. 66
Answer:
Given that,
M = 22
Z = 16
So, by empirical relationship we have,
Mode = 3 (Median) – 2 (Mean)
⇒
⇒
⇒
Putting in the given values in the above equation, we get
⇒
⇒
⇒
Thus, option (b) is correct.
Question 16.
Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
(7) If = 21.44 and Z = 19.13, then M =
A. 21.10
B. 19.67
C. 20.10
D. 20.67
Answer:
Given that,
Z = 19.13
To find: M = ?
By empirical relationship, we can write
Mode = 3 (Median) – 2 (Mean)
⇒
⇒
⇒
Putting in the given values, we can
⇒
⇒
⇒ M = 20.67
Thus, option (d) is correct.
Question 17.
Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
If M = 26, =36, then Z =
A. 6
B. 5
C. 4
D. 3
Answer:
Given that,
M = 15
So, by empirical relationship we have,
Mode = 3 (Median) – 2 (Mean)
⇒
Putting given values in the above equation, we get
Z = 3(15) – 2×10
⇒ Z = 45 – 20
⇒ Z = 25
Thus, option (c) is correct.
Question 18.
Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
(9) The modal class of the frequency distribution given below is
A. 10-20
B. 20-30
C. 30-40
D. 40-50
Answer:
Observe that, from the given data:
The maximum class frequency, here, is 17 and the class corresponding to this frequency is 30 – 40.
So, this implies that,
Modal class = 30 – 40
[∵ modal class in a grouped frequency table can be calculated by corresponding maximum class frequency]
Thus, option (c) is correct.
Question 19.
Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
The cumulative frequency of class 20-30 of the frequency distribution given in (9) is ….
A. 25
B. 35
C. 15
D. 40
Answer:
We have
Cumulative frequency of a class is just the sum of frequencies of the particular class along with all the classes preceding the class.
So, Cumulative frequency of class 20 – 30 = Sum of frequency of the class 20 – 30 along with frequencies of all the classes preceding the class 20 – 30.
⇒ Cumulative frequency of class 20 – 30 = 7 + 15 + 13
⇒ Cumulative frequency of class 20 – 30 = 35
Thus, option (b) is correct.
Question 20.
Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:
The median class of the frequency distribution given in (9) is ….
A. 40-50
B. 30-40
C. 20-30
D. 10-20
Answer:
We have
We need to show it into a proper table representing frequencies and cumulative frequencies.
So,
We have added up all the values of the frequency in the second column and have got,
Total = n = 62
Now, we just need to find the value of n/2. So,
⇒
Now, look up for a value in the cumulative frequency just greater than 31.
We have, 35.
Corresponding to this value of cumulative frequency, we can say that median class is 20 – 30.
That is,
Median class = 20 – 30
Thus, option (c) is correct.