{"id":6104,"date":"2023-10-08T05:58:47","date_gmt":"2023-10-08T05:58:47","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=6104"},"modified":"2023-10-08T05:58:47","modified_gmt":"2023-10-08T05:58:47","slug":"ncert-solutions-class-10-maths-chapter-14-statistics-ex-14-1","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-14-statistics-ex-14-1\/","title":{"rendered":"NCERT Solutions Class 10 Maths Chapter 14 Statistics Ex 14.1"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"font-family: Georgia, Palatino;\"><strong><span style=\"color: #000000;\">NCERT Solutions Class 10 Maths\u00a0<\/span><\/strong><\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\"><strong><span style=\"color: #000000;\">Chapter &#8211; 14 (Statistics)\u00a0<\/span><\/strong><\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">The NCERT Solutions in English Language for Class 10 Mathematics <strong>Chapter &#8211; 14 Statistics <\/strong>Exercise 14.1 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Chapter : 14 Statistics<\/strong> <\/span><\/p>\n<ul>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-14-statistics-ex-14-2\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 14.2<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-14-statistics-ex-14-3\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 14.3<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-14-statistics-ex-14-1\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 14.4<\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"font-family: Georgia, Palatino;\"><strong><span style=\"color: #000000;\">Exercise &#8211; 14.1<\/span><\/strong><\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>1. A survey was conducted by a group of students as a part of their environment awareness program, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of Plants<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>0-2<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>2-4<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4-6<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>6-8<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>8-10<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>10-12<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>12-14<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of Houses<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>1<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>2<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>1<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>5<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>6<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>2<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>3<\/strong><\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Which method did you use for finding the mean, and why?<br \/>\n<\/strong><strong>Solution &#8211;\u00a0<\/strong>To find the mean value, we will use the direct method because the numerical value of f<sub>i<\/sub>\u00a0and x<sub>i<\/sub> are small.<br \/>\nFind the midpoint of the given interval using the formula.<br \/>\nMidpoint (x<sub>i<\/sub>) = (upper limit + lower limit)\/2<\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">No. of plants<br \/>\n(Class interval)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">No. of houses<br \/>\nFrequency (f<sub>i<\/sub><span style=\"font-size: inherit;\">)<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Mid-point (x<sub>i<\/sub>)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">f<sub>i<\/sub>x<sub>i<\/sub><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0-2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2-4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4-6<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">5<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6-8<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">7<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">35<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">8-10<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">9<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">54<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">10-12<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">11<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">22<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">12-14<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">13<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">39<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i\u00a0<\/sub>= 20<\/span><\/td>\n<td><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>x<sub>i<\/sub>\u00a0= 162<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">The formula to find the mean is:<br \/>\nMean = x\u0304 = \u2211f<sub>i\u00a0<\/sub>x<sub>i<\/sub>\u00a0\/\u2211f<sub>i<br \/>\n<\/sub>= 162\/20<br \/>\n= 8.1<br \/>\nTherefore, the mean number of plants per house is 8.1.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>2. Consider the following distribution of daily wages of 50 workers of a factory.<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Daily wages (in Rs.)<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>500-520<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>520-540<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>540-560<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>560-580<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>580-600<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of workers<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>12<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>14<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>8<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>6<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>10<\/strong><\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Find the mean daily wages of the workers of the factory by using an appropriate method<\/strong>.<br \/>\n<strong>Solution &#8211;<br \/>\n<\/strong>Find the midpoint of the given interval using the formula.<br \/>\nMidpoint (x<sub>i<\/sub>) = (upper limit + lower limit)\/2<br \/>\nIn this case, the value of mid-point (x<sub>i<\/sub>) is very large, so let us assume the mean value, a = 550.<br \/>\nClass interval (h) = 20<br \/>\nSo, u<sub>i\u00a0<\/sub>= (x<sub>i<\/sub>\u00a0\u2013 a)\/h<br \/>\nu<sub>i\u00a0<\/sub>= (x<sub>i<\/sub> \u2013 550)\/20<br \/>\nSubstitute and find the values as follows:<\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Daily wages<br \/>\n(Class interval)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Number of workers<br \/>\nfrequency (f<sub>i<\/sub><span style=\"font-size: inherit;\">)<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Mid-point (x<sub>i<\/sub>)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">u<sub>i\u00a0<\/sub>= (x<sub>i<\/sub>\u00a0\u2013 550)\/20<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">f<sub>i<\/sub>u<sub>i<\/sub><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">500-520<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">12<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">510<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-24<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">520-540<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">14<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">530<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-14<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">540-560<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">8<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">550 = a<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">560-580<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">570<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">580-600<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">10<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">590<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">20<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Total<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i\u00a0<\/sub>= 50<\/span><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>u<sub>i<\/sub>\u00a0= -12<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">So, the formula to find out the mean is:<br \/>\nMean = x\u0304 = a + h(\u2211f<sub>i<\/sub>u<sub>i<\/sub>\u00a0\/\u2211f<sub>i\u00a0<\/sub>)<br \/>\n= 550 + [20 \u00d7 (-12\/50)]<br \/>\n= 550 \u2013 4.8<br \/>\n= 545.20<br \/>\nThus, mean daily wage of the workers = Rs. 545.20<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>3. The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency f.<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Daily Pocket Allowance(in c)<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>11-13<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>13-15<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>15-17<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>17-19<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>19-21<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>21-23<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>23-35<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of children<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>7<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>6<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>9<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>13<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>f<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>5<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4<\/strong><\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Solution &#8211;\u00a0 <\/strong>To find out the missing frequency, use the mean formula.<br \/>\nGiven, mean x\u0304 = 18<\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Class interval<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Number of children (f<sub>i<\/sub>)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Mid-point (x<sub>i<\/sub>)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">f<sub>i<\/sub>x<sub>i<\/sub><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">11-13<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">7<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">12<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">84<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">13-15<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">14<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">84<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">15-17<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">9<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">16<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">144<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">17-19<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">13<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">18<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">234<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">19-21<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">f<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">20<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">20f<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">21-23<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">22<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">110<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">23-25<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">24<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">96<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Total<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">f<sub>i<\/sub>\u00a0= 44+f<\/span><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>x<sub>i<\/sub>\u00a0= 752+20f<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">The mean formula is Mean = x\u0304 = \u2211f<sub>i<\/sub>x<sub>i<\/sub>\u00a0\/\u2211f<sub>i<br \/>\n<\/sub>= (752 + 20f)\/ (44 + f)<br \/>\nNow substitute the values and equate to find the missing frequency (f)<br \/>\n\u21d2 18 = (752 + 20f)\/ (44 + f)<br \/>\n\u21d2 18(44 + f) = (752 + 20f)<br \/>\n\u21d2 792 + 18f = 752 + 20f<br \/>\n\u21d2 792 + 18f = 752 + 20f<br \/>\n\u21d2 792 \u2013 752 = 20f \u2013 18f<br \/>\n\u21d2 40 = 2f<br \/>\n\u21d2 f = 20<br \/>\nSo, the missing frequency, f = 20.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4. Thirty women were examined in a hospital by a doctor, and the number of heartbeats per minute were recorded and summarised as follows. Find the mean heartbeats per minute for these women, choosing a suitable method.<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of heart beats per minute<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>65-68<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>68-71<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>71-74<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>74-77<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>77-80<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>80-83<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>83-86<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of women<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>2<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>3<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>8<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>7<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>2<\/strong><\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Solution &#8211;\u00a0 <\/strong>From the given data, let us assume the mean as a = 75.5<br \/>\nx<sub>i\u00a0<\/sub>= (Upper limit + Lower limit)\/2<br \/>\nClass size (h) = 3<br \/>\nNow, find the u<sub>i\u00a0<\/sub>and f<sub>i<\/sub>u<sub>i<\/sub>\u00a0as follows:<\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Class Interval<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of women (f<sub>i<\/sub>)<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Mid-point (x<sub>i<\/sub>)<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>u<sub>i<\/sub>\u00a0= (x<sub>i<\/sub>\u00a0\u2013 75.5)\/h<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>f<sub>i<\/sub>u<sub>i<\/sub><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">65-68<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">66.5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-6<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">68-71<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">69.5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-8<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">71-74<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">72.5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-3<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">74-77<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">8<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">75.5 = a<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">77-80<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">7<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">78.5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">7<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">80-83<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">81.5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">8<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">83-86<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">84.5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>= 30<\/span><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>u<sub>i\u00a0<\/sub>= 4<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Mean = x\u0304 = a + h(\u2211f<sub>i<\/sub>u<sub>i<\/sub>\u00a0\/\u2211f<sub>i\u00a0<\/sub>)<br \/>\n= 75.5 + 3 \u00d7 (4\/30)<br \/>\n= 75.5 + (4\/10)<br \/>\n= 75.5 + 0.4<br \/>\n= 75.9<br \/>\nTherefore, the mean heart beats per minute for these women is 75.9<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>5. In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of mangoes<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>50-52<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>53-55<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>56-58<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>59-61<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>62-64<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of boxes<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>15<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>110<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>135<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>115<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>25<\/strong><\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?<br \/>\n<\/strong><strong>Solution &#8211;\u00a0 <\/strong>The given data is not continuous, so we add 0.5 to the upper limit and subtract 0.5 from the lower limit as the gap between two intervals is 1.<br \/>\nHere, assumed mean (a) = 57<br \/>\nClass size (h) = 3<br \/>\nHere, the step deviation is used because the frequency values are big.<\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Class Interval<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Number of boxes (f<sub>i<\/sub>)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Mid-point (x<sub>i<\/sub>)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">u<sub>i<\/sub>\u00a0= (x<sub>i<\/sub>\u00a0\u2013 57)\/h<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">f<sub>i<\/sub>u<sub>i<\/sub><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">49.5-52.5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">15<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">51<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-30<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">52.5-55.5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">110<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">54<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-110<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">55.5-58.5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">135<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">57 = a<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">58.5-61.5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">115<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">60<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">115<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">61.5-64.5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">25<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">63<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">50<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>\u00a0= 400<\/span><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>u<sub>i<\/sub>\u00a0= 25<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">The formula to find out the Mean is:<br \/>\nMean = x\u0304 = a + h(\u2211f<sub>i<\/sub>u<sub>i<\/sub>\u00a0\/\u2211f<sub>i\u00a0<\/sub>)<br \/>\n= 57 + 3(25\/400)<br \/>\n= 57 + 0.1875<br \/>\n= 57.19<br \/>\nTherefore, the mean number of mangoes kept in a packing box is 57.19<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>6. The table below shows the daily expenditure on food of 25 households in a locality.<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Daily expenditure(in c)<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>100-150<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>150-200<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>200-250<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>250-300<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>300-350<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of households<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>5<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>12<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>2<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>2<\/strong><\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Find the mean daily expenditure on food by a suitable method.<br \/>\n<\/strong><strong>Solution &#8211;\u00a0 <\/strong>Find the midpoint of the given interval using the formula.<br \/>\nMidpoint (x<sub>i<\/sub>) = (upper limit + lower limit)\/2<br \/>\nLet us assume the mean (a) = 225<br \/>\nClass size (h) = 50<\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Class Interval<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Number of households (f<sub>i<\/sub>)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Mid-point (x<sub>i<\/sub>)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">d<sub>i<\/sub>\u00a0= x<sub>i<\/sub>\u00a0\u2013 A<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">u<sub>i\u00a0<\/sub>= d<sub>i<\/sub>\/50<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">f<sub>i<\/sub>u<sub>i<\/sub><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">100-150<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">125<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-100<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-8<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">150-200<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">175<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-50<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-5<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">200-250<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">12<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">225 = a<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">250-300<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">275<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">50<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">300-350<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">325<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">100<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>\u00a0= 25<\/span><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>u<sub>i<\/sub>\u00a0= -7<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Mean = x\u0304 = a + h(\u2211f<sub>i<\/sub>u<sub>i<\/sub>\u00a0\/\u2211f<sub>i\u00a0<\/sub>)<br \/>\n= 225 + 50(-7\/25)<br \/>\n= 225 \u2013 14<br \/>\n= 211<br \/>\nTherefore, the mean daily expenditure on food is 211.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>7. To find out the concentration of SO<sub>2<\/sub>\u00a0in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Concentration of SO<sub>2<\/sub>\u00a0( in ppm)<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Frequency<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>0.00 \u2013 0.04<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>0.04 \u2013 0.08<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>9<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>0.08 \u2013 0.12<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>9<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>0.12 \u2013 0.16<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>2<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>0.16 \u2013 0.20<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>0.20 \u2013 0.24<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>2<\/strong><\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Find the mean concentration of SO<sub>2<\/sub> in the air.<br \/>\n<\/strong><strong>Solution &#8211;\u00a0<\/strong>To find out the mean, first find the midpoint of the given frequencies as follows:<\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Concentration of SO<sub>2\u00a0<\/sub>(in ppm)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Frequency (f<sub>i<\/sub>)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Mid-point (x<sub>i<\/sub>)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">f<sub>i<\/sub>x<sub>i<\/sub><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.00-0.04<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.02<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.08<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.04-0.08<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">9<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.06<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.54<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.08-0.12<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">9<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.10<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.90<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.12-0.16<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.14<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.28<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.16-0.20<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.18<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.72<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.20-0.24<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.22<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0.44<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Total<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>\u00a0= 30<\/span><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum (f<sub>i<\/sub>x<sub>i<\/sub>) = 2.96<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">The formula to find out the mean is Mean = x\u0304 = \u2211f<sub>i<\/sub>x<sub>i<\/sub>\u00a0\/\u2211f<sub>i<br \/>\n<\/sub>= 2.96\/30<br \/>\n= 0.099 ppm<br \/>\nTherefore, the mean concentration of SO<sub>2<\/sub>\u00a0in the air is 0.099 ppm.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>8. A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of days<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>0-6<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>6-10<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>10-14<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>14-20<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>20-28<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>28-38<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>38-40<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of students<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>11<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>10<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>7<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>3<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>1<\/strong><\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Solution &#8211;\u00a0 <\/strong>Find the midpoint of the given interval using the formula.<br \/>\nMidpoint (x<sub>i<\/sub>) = (upper limit + lower limit)\/2<\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Class interval<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Frequency (f<sub>i<\/sub>)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Mid-point (x<sub>i<\/sub>)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">f<sub>i<\/sub>x<sub>i<\/sub><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0-6<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">11<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">33<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6-10<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">10<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">8<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">80<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">10-14<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">7<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">12<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">84<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">14-20<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">17<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">68<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">20-28<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">24<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">96<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">28-38<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">33<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">99<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">38-40<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">39<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">39<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>\u00a0= 40<\/span><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>x<sub>i<\/sub>\u00a0= 499<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">The mean formula is,<br \/>\nMean = x\u0304 = \u2211f<sub>i<\/sub>x<sub>i<\/sub>\u00a0\/\u2211f<sub>i<br \/>\n<\/sub>= 499\/40<br \/>\n= 12.48 days<br \/>\nTherefore, the mean number of days a student was absent = 12.48.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>9. The following table gives the literacy rate (in percentage) of 35 cities. Find the mean <\/strong><strong>literacy rate.<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Literacy rate (in %)<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>45-55<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>55-65<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>65-75<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>75-85<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>85-98<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of cities<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>3<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>10<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>11<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>8<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>3<\/strong><\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Solution &#8211;\u00a0 <\/strong>Find the midpoint of the given interval using the formula.<br \/>\nMidpoint (x<sub>i<\/sub>) = (upper limit + lower limit)\/2<br \/>\nIn this case, the value of mid-point (x<sub>i<\/sub>) is very large, so let us assume the mean value, a = 70.<br \/>\nClass interval (h) = 10<br \/>\nSo, u<sub>i\u00a0<\/sub>= (x<sub>i\u00a0<\/sub>\u2013 a)\/h<br \/>\nu<sub>i\u00a0<\/sub>= (x<sub>i\u00a0<\/sub>\u2013 70)\/10<br \/>\nSubstitute and find the values as follows:<\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Class Interval<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Frequency (f<sub>i<\/sub>)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">(x<sub>i<\/sub>)<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">u<sub>i\u00a0<\/sub>= (x<sub>i\u00a0<\/sub>\u2013 70)\/10<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">f<sub>i<\/sub>u<sub>i<\/sub><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">45-55<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">50<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-6<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">55-65<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">10<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">60<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">-10<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">65-75<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">11<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">70 = a<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">75-85<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">8<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">80<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">8<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">85-95<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">90<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>\u00a0= 35<\/span><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>u<sub>i<\/sub>\u00a0= -2<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">So, Mean = x\u0304 = a + (\u2211f<sub>i<\/sub>u<sub>i<\/sub>\u00a0\/\u2211f<sub>i<\/sub>) \u00d7 h<br \/>\n= 70 + (-2\/35) \u00d7 10<br \/>\n= 69.43<br \/>\nTherefore, the mean literacy part = 69.43%<\/span><\/p>\n<p><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths\/\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: Georgia, Palatino;\"><b><i>Go Back To Chapters<\/i><\/b><\/span><\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 10 Maths\u00a0 Chapter &#8211; 14 (Statistics)\u00a0 The NCERT Solutions in English Language for Class 10 Mathematics Chapter &#8211; 14 Statistics Exercise 14.1 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter : 14 Statistics NCERT Class 10 Maths Solution Ex &#8211; 14.2 NCERT Class 10 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1043],"tags":[1045,1115,1116,1044,1049,1048],"class_list":["post-6104","post","type-post","status-publish","format-standard","hentry","category-class-10-maths","tag-class-10-ncert-mathematics-solutions","tag-ncert-class-10-mathematics-chapter-14-statistics-solutions","tag-ncert-class-10-mathematics-exercise-14-1-solutions","tag-ncert-class-10-mathematics-solutions-class-10-ncert-solutions","tag-ncert-solutions-class-10-mathematics","tag-ncert-solutions-class-10-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.5) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 10 Maths Chapter 14 Statistics Ex 14.1 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 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