{"id":34804,"date":"2018-12-26T13:23:13","date_gmt":"2018-12-26T13:23:13","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=34804"},"modified":"2020-11-27T17:01:13","modified_gmt":"2020-11-27T11:31:13","slug":"ncert-solutions-for-class-10-maths-chapter-14-ex-14-3","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-14-ex-14-3\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3"},"content":{"rendered":"<p>NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 14 <strong>Statistics\u00a0Class 10 NCERT Solutions Ex 14.3.<\/strong><\/p>\n<ul>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.1\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-14\/\" target=\"_blank\" rel=\"noopener\">Statistics Class 10 Ex 14.1<\/a><\/li>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.2\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-14-ex-14-2\/\" target=\"_blank\" rel=\"noopener\">Statistics Class 10 Ex 14.2<\/a><\/li>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.4\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-14-ex-14-4\/\" target=\"_blank\" rel=\"noopener\">Statistics Class 10 Ex 14.4<\/a><\/li>\n<\/ul>\n<table style=\"table-layout: fixed; width: 650px;\" border=\"1\">\n<tbody>\n<tr>\n<td><strong>Board<\/strong><\/td>\n<td>CBSE<\/td>\n<\/tr>\n<tr>\n<td><strong>Textbook<\/strong><\/td>\n<td>NCERT<\/td>\n<\/tr>\n<tr>\n<td><strong>Class<\/strong><\/td>\n<td>Class 10<\/td>\n<\/tr>\n<tr>\n<td><strong>Subject<\/strong><\/td>\n<td>Maths<\/td>\n<\/tr>\n<tr>\n<td><strong>Chapter<\/strong><\/td>\n<td>Chapter 14<\/td>\n<\/tr>\n<tr>\n<td><strong>Chapter Name<\/strong><\/td>\n<td>Statistics<\/td>\n<\/tr>\n<tr>\n<td><strong>Exercise<\/strong><\/td>\n<td>Ex 14.3<\/td>\n<\/tr>\n<tr>\n<td><strong>Number of Questions Solved<\/strong><\/td>\n<td>7<\/td>\n<\/tr>\n<tr>\n<td><strong>Category<\/strong><\/td>\n<td>NCERT Solutions<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3<\/h2>\n<p><a class=\"button-red\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths\/\">NCERT Solutions for Class 10 Maths<\/a><\/p>\n<p><strong>Question 1.<br \/>\n<\/strong>The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.<\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"256\"><strong>Monthly consumption (in units)<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"257\"><strong>Number of consumers<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"256\">65 &#8211; 85<\/td>\n<td style=\"text-align: center;\" width=\"257\">4<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"256\">85 &#8211; 105<\/td>\n<td style=\"text-align: center;\" width=\"257\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"256\">105 &#8211; 125<\/td>\n<td style=\"text-align: center;\" width=\"257\">13<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"256\">125 &#8211; 145<\/td>\n<td style=\"text-align: center;\" width=\"257\">20<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"256\">145 &#8211; 165<\/td>\n<td style=\"text-align: center;\" width=\"257\">14<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"256\">165 &#8211; 185<\/td>\n<td style=\"text-align: center;\" width=\"257\">8<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"256\">185 &#8211; 205<\/td>\n<td style=\"text-align: center;\" width=\"257\">4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Solution:<br \/>\n<\/strong>We may find class marks by using the relation<\/p>\n<div class=\"table-responsive\">\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-102134\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-1s.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 1s\" width=\"385\" height=\"50\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-1s.png 385w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-1s-300x39.png 300w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><br \/>\nTaking 135 as assumed mean (a) we may find d<sub>i<\/sub>, u<sub>i<\/sub>, f<sub>i<\/sub>u<sub>i<\/sub>, according to step deviation method as following<\/p>\n<table border=\"1\" width=\"593\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"176\"><strong>Monthly consumption\u00a0<\/strong><br \/>\n<strong>(in units)<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"101\"><strong>Number of consumers (<em>f\u00a0<sub>i<\/sub><\/em>)<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"82\"><strong><em>x<sub>i<\/sub><\/em><\/strong><strong>\u00a0class mark<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"93\"><strong><em>d<sub>i<\/sub>\u00a0<\/em><\/strong><strong>=\u00a0<em>x<sub>i<\/sub>\u00a0<\/em>&#8211; 135<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\"><strong><img loading=\"lazy\" class=\"alignnone size-full wp-image-102138\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-1s.1.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 1s.1\" width=\"43\" height=\"32\" \/> <\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\"><strong>f<sub>i<\/sub>u<sub>i<\/sub>\u00a0<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"176\">65 &#8211; 85<\/td>\n<td style=\"text-align: center;\" width=\"101\">4<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"82\">75<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"93\">&#8211; 60<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">&#8211; 3<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">&#8211; 12<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"176\">85 &#8211; 105<\/td>\n<td style=\"text-align: center;\" width=\"101\">5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"82\">95<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"93\">&#8211; 40<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">&#8211; 2<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">&#8211; 10<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"176\">105 &#8211; 125<\/td>\n<td style=\"text-align: center;\" width=\"101\">13<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"82\">115<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"93\">&#8211; 20<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">&#8211; 1<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">&#8211; 13<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"176\">125 &#8211; 145<\/td>\n<td style=\"text-align: center;\" width=\"101\">20<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"82\">135<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"93\">0<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">0<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"176\">145 &#8211; 165<\/td>\n<td style=\"text-align: center;\" width=\"101\">14<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"82\">155<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"93\">20<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">1<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">14<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"176\">165 &#8211; 185<\/td>\n<td style=\"text-align: center;\" width=\"101\">8<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"82\">175<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"93\">40<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">2<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">16<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"176\">185 &#8211; 205<\/td>\n<td style=\"text-align: center;\" width=\"101\">4<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"82\">195<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"93\">60<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">3<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">12<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"176\">Total<\/td>\n<td style=\"text-align: center;\" width=\"101\">68<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"82\"><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"93\"><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\"><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"70\">7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>From the table we may observe that<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-102140\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-1s.2.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 1s.2\" width=\"202\" height=\"230\" \/><\/p>\n<p>Now from table it is clear that maximum class frequency is 20 belonging to class interval 125 &#8211; 145.<br \/>\nModal class = 125 &#8211; 145<br \/>\nLower limit (l) of modal class = 125<br \/>\nClass size (h) = 20<br \/>\nFrequency (f<sub>1<\/sub>) of modal class = 20<br \/>\nFrequency (f<sub>0<\/sub>) of class preceding modal class = 13<br \/>\nFrequency (f<sub>2<\/sub>) of class succeeding the modal class = 14<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-102142\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-1s.3.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 1s.3\" width=\"287\" height=\"178\" \/><br \/>\nWe know that<br \/>\n3 median = mode + 2 mean<br \/>\n= 135.76 + 2 (137.058)<br \/>\n= 135.76 + 274.116<br \/>\n= 409.876<br \/>\nMedian = 136.625<br \/>\nSo median, mode, mean of given data is 136.625, 135.76, 137.05 respectively.<\/p>\n<p><strong>Question 2.<br \/>\n<\/strong>If the median of the distribution is given below is 28.5, find the values of x and y.<\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"256\"><strong>Class interval<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"257\"><strong>Frequency<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"256\">0 &#8211; 10<\/td>\n<td style=\"text-align: center;\" width=\"257\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"256\">10 &#8211; 20<\/td>\n<td style=\"text-align: center;\" width=\"257\"><em>x<\/em><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"256\">20 &#8211; 30<\/td>\n<td style=\"text-align: center;\" width=\"257\">20<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"256\">30 &#8211; 40<\/td>\n<td style=\"text-align: center;\" width=\"257\">15<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"256\">40 &#8211; 50<\/td>\n<td style=\"text-align: center;\" width=\"257\"><em>y<\/em><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"256\">50 &#8211; 60<\/td>\n<td style=\"text-align: center;\" width=\"257\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"256\">Total<\/td>\n<td style=\"text-align: center;\" width=\"257\">60<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Solution:<\/strong><br \/>\nWe may find cumulative frequency for the given data as following<\/p>\n<div class=\"table-responsive\">\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"175\"><strong>Class interval<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"184\"><strong>Frequency<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"154\"><strong>Cumulative frequency\u00a0<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"175\">0 &#8211; 10<\/td>\n<td style=\"text-align: center;\" width=\"184\">5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"154\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"175\">10 &#8211; 20<\/td>\n<td style=\"text-align: center;\" width=\"184\"><em>x<\/em><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"154\">5<em>\u00a0<\/em>+<em>\u00a0x<\/em><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"175\">20 &#8211; 30<\/td>\n<td style=\"text-align: center;\" width=\"184\">20<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"154\">25 +\u00a0<em>x<\/em><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"175\">30 &#8211; 40<\/td>\n<td style=\"text-align: center;\" width=\"184\">15<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"154\">40 +\u00a0<em>x<\/em><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"175\">40 &#8211; 5<\/td>\n<td style=\"text-align: center;\" width=\"184\"><em>y<\/em><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"154\">40<em>\u00a0<\/em>+<em>\u00a0x\u00a0<\/em>+<em>\u00a0y<\/em><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"175\">50 &#8211; 60<\/td>\n<td style=\"text-align: center;\" width=\"184\">5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"154\">45 +\u00a0<em>x<\/em>\u00a0+\u00a0<em>y<\/em><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"175\">Total (<em>n<\/em>)<\/td>\n<td style=\"text-align: center;\" width=\"184\">60<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"154\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>It is clear that n = 60<\/p>\n<p>45 + x + y = 60<\/p>\n<p>x + y = 15\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0(1)<br \/>\nMedian of data is given as 28.5 which lies in interval 20 &#8211; 30.<br \/>\nSo, median class = 20 &#8211; 30<br \/>\nLower limit (l) of median class = 20<br \/>\nCumulative frequency (cf) of class preceding the median class = 5 + x<br \/>\nFrequency (f) of median class = 20<br \/>\nClass size (h) = 10<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-102143\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-2s.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 2s\" width=\"420\" height=\"223\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-2s.png 420w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-2s-300x159.png 300w\" sizes=\"(max-width: 420px) 100vw, 420px\" \/><br \/>\nFrom equation (1)<br \/>\n8 + y = 15<br \/>\ny = 7<br \/>\nHence values of x and y are 8 and 7 respectively.<\/p>\n<p><strong>Question 3<\/strong><\/p>\n<p class=\"ques\">A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year.<\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"229\"><strong>Age (in years)<\/strong><\/td>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"259\"><strong>Number of policy holders<\/strong><\/td>\n<\/tr>\n<tr>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"229\">Below 20<\/td>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"259\">2<\/td>\n<\/tr>\n<tr>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"229\">Below 25<\/td>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"259\">6<\/td>\n<\/tr>\n<tr>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"229\">Below 30<\/td>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"259\">24<\/td>\n<\/tr>\n<tr>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"229\">Below 35<\/td>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"259\">45<\/td>\n<\/tr>\n<tr>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"229\">Below 40<\/td>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"259\">78<\/td>\n<\/tr>\n<tr>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"229\">Below 45<\/td>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"259\">89<\/td>\n<\/tr>\n<tr>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"229\">Below 50<\/td>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"259\">92<\/td>\n<\/tr>\n<tr>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"229\">Below 55<\/td>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"259\">98<\/td>\n<\/tr>\n<tr>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"229\">Below 60<\/td>\n<td class=\"mceSelected\" style=\"text-align: center;\" width=\"259\">100<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Solution:<br \/>\n<\/strong>Here class width is not same. There is no need to adjust the frequencies according to class intervals. Now given frequency table is of less than type represented with upper class limits. As policies were given only to persons having age 18 years onwards but less than 60 years, we can define class intervals with their respective cumulative frequency as below<\/p>\n<div class=\"table-responsive\">\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"160\"><strong>Age (in years)<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"192\"><strong>Number of policy holders (<em>f<sub>i<\/sub><\/em>)<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"161\"><strong>Cumulative frequency (<em>cf<\/em>)<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"160\">18 &#8211; 20<\/td>\n<td style=\"text-align: center;\" width=\"192\">2<\/td>\n<td style=\"text-align: center;\" width=\"161\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"160\">20 &#8211; 25<\/td>\n<td style=\"text-align: center;\" width=\"192\">6 &#8211; 2 = 4<\/td>\n<td style=\"text-align: center;\" width=\"161\">6<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"160\">25 &#8211; 30<\/td>\n<td style=\"text-align: center;\" width=\"192\">24 &#8211; 6 = 18<\/td>\n<td style=\"text-align: center;\" width=\"161\">24<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"160\">30 &#8211; 35<\/td>\n<td style=\"text-align: center;\" width=\"192\">45 &#8211; 24 = 21<\/td>\n<td style=\"text-align: center;\" width=\"161\">45<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"160\">35 &#8211; 40<\/td>\n<td style=\"text-align: center;\" width=\"192\">78 &#8211; 45 = 33<\/td>\n<td style=\"text-align: center;\" width=\"161\">78<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"160\">40 &#8211; 45<\/td>\n<td style=\"text-align: center;\" width=\"192\">89 &#8211; 78 = 11<\/td>\n<td style=\"text-align: center;\" width=\"161\">89<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"160\">45 &#8211; 50<\/td>\n<td style=\"text-align: center;\" width=\"192\">92 &#8211; 89 = 3<\/td>\n<td style=\"text-align: center;\" width=\"161\">92<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"160\">50 &#8211; 55<\/td>\n<td style=\"text-align: center;\" width=\"192\">98 &#8211; 92 = 6<\/td>\n<td style=\"text-align: center;\" width=\"161\">98<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"160\">55 &#8211; 60<\/td>\n<td style=\"text-align: center;\" width=\"192\">100 &#8211; 98 = 2<\/td>\n<td style=\"text-align: center;\" width=\"161\">100<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"160\">Total (<em>n<\/em>)<\/td>\n<td style=\"text-align: center;\" width=\"192\"><\/td>\n<td style=\"text-align: center;\" width=\"161\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Now from table we may observe that\u00a0<em>n<\/em>\u00a0= 100.<\/p>\n<p>Cumulative frequency (<em>cf<\/em>) just greater than <img loading=\"lazy\" class=\"alignnone size-full wp-image-102145\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-3s.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 3s\" width=\"147\" height=\"50\" \/>\u00a0is 78 belonging to interval 35 &#8211; 40<br \/>\nSo, median class = 35 &#8211; 40<br \/>\nLower limit (l) of median class = 35<br \/>\nClass size (h) = 5<br \/>\nFrequency (f) of median class = 33<br \/>\nCumulative frequency (cf) of class preceding median class = 45<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-102147\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-3s1.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 3s1\" width=\"226\" height=\"170\" \/><br \/>\nSo, median age is 35.76 years.<\/p>\n<p><strong>Question 4.<\/strong><\/p>\n<p class=\"ques\">The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:<\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\"><strong>Length (in mm)<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\"><strong>Number or leaves\u00a0<em>f<sub>i<\/sub><\/em><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">118 &#8211; 126<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\">3<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">127 &#8211; 135<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">136 &#8211; 144<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\">9<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">145 &#8211; 153<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\">12<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">154 &#8211; 162<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">163 &#8211; 171<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\">4<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">172 &#8211; 180<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\">2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Find the median length of the leaves.<br \/>\n(Hint: The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 &#8211; 126.5, 126.5 &#8211; 135.5 &#8211; 171.5 &#8211; 180.5)<br \/>\n<strong>Solution:<\/strong><\/p>\n<div class=\"table-responsive\">\n<p>The given data is not having continuous class intervals. We can observe that difference between two class intervals is 1. So, we have to add and subtract 1\/2=0.5\u00a0 to upper class limits and lower class limits.<br \/>\nNow continuous class intervals with respective cumulative frequencies can be represented as below<\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\"><strong>Length (in mm)<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\"><strong>Number or leaves\u00a0<em>f<sub>i<\/sub><\/em><\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\"><strong>Cumulative frequency<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">117.5 &#8211; 126.5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">3<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\">3<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">126.5 &#8211; 135.5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\">3 + 5 = 8<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">135.5 &#8211; 144.5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">9<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\">8 + 9 = 17<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">144.5 &#8211; 153.5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">12<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\">17 + 12 = 29<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">153.5 &#8211; 162.5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\">29 + 5 = 34<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">162.5 &#8211; 171.5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">4<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\">34 + 4 = 38<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">171.5 &#8211; 180.5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">2<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"184\">38 + 2 = 40<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>From the table we may observe that cumulative frequency just greater then <img loading=\"lazy\" class=\"alignnone size-full wp-image-102149\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-4s.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 4s\" width=\"137\" height=\"50\" \/>\u00a0 is 29, belonging to class interval 144.5 &#8211; 153.5.<br \/>\nMedian class = 144.5 &#8211; 153.5<br \/>\nLower limit (l) of median class = 144.5<br \/>\nClass size (h) = 9<br \/>\nFrequency (f) of median class = 12<br \/>\nCumulative frequency (cf) of class preceding median class = 17<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-102151\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-4s1.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 4s1\" width=\"239\" height=\"152\" \/><br \/>\nSo, median length of leaves is 146.75 mm.<\/p>\n<p><strong>Question 5.<br \/>\n<\/strong>Find the following tables gives the distribution of the life time of 400 neon lamps:<\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\"><strong>Life time (in hours)<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\"><strong>Number of lamps<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">1500 &#8211; 2000<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">14<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">2000 &#8211; 2500<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">56<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">2500 &#8211; 3000<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">60<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">3000 &#8211; 3500<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">86<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">3500 &#8211; 4000<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">74<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">4000 &#8211; 4500<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">62<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">4500 &#8211; 5000<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">48<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Find the median life time of a lamp.<br \/>\n<strong>Solution:<br \/>\n<\/strong>We can find cumulative frequencies with their respective class intervals as below &#8211;<\/p>\n<div class=\"table-responsive\">\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"112\"><strong>Life time<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"152\"><strong>Number of lamps (<em>f<sub>i<\/sub><\/em>)<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\"><strong>Cumulative frequency<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"112\">1500 &#8211; 2000<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"152\">14<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">14<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"112\">2000 &#8211; 2500<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"152\">56<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">14 + 56 = 70<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"112\">2500 &#8211; 3000<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"152\">60<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">70 + 60 = 130<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"112\">3000 &#8211; 3500<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"152\">86<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">130 + 86 = 216<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"112\">3500 &#8211; 4000<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"152\">74<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">216 + 74 = 290<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"112\">4000 &#8211; 4500<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"152\">62<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">290 + 62 = 352<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"112\">4500 &#8211; 5000<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"152\">48<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\">352 + 48 = 400<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"112\">Total (<em>n<\/em>)<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"152\">400<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"176\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Now we may observe that cumulative frequency just greater than <img loading=\"lazy\" class=\"alignnone size-full wp-image-102171\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-5s.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 5s\" width=\"157\" height=\"50\" \/>\u00a0is 216 belonging to class interval 3000 &#8211; 3500.<br \/>\nMedian class = 3000 &#8211; 3500<br \/>\nLower limit (l) of median class = 3000<br \/>\nFrequency (f) of median class = 86<br \/>\nCumulative frequency (cf) of class preceding median class = 130<br \/>\nClass size (h) = 500<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-102201\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-5s1.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 5s1\" width=\"285\" height=\"152\" \/><br \/>\nSo, median life time of lamps is 3406.98 hours.<\/p>\n<p><strong>Question 6.<br \/>\n<\/strong>100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:<\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"89\"><strong>Number of letters<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"69\">1 &#8211; 4<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"69\">4 &#8211; 7<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"69\">7 &#8211; 10<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"69\">10 &#8211; 13<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"69\">13 &#8211; 16<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"69\">16 &#8211; 19<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"89\"><strong>Number of surnames<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"69\">6<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"69\">30<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"69\">40<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"69\">6<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"69\">4<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"69\">4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.<br \/>\n<strong>Solution:<br \/>\n<\/strong>We can find cumulative frequencies with their respective class intervals as below<\/p>\n<div class=\"table-responsive\">\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"160\"><strong>Number of letters<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\"><strong>Frequency (<em>f<sub>i<\/sub><\/em>)<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"168\"><strong>Cumulative frequency<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"160\">1 &#8211; 4<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">6<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"168\">6<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"160\">4 &#8211; 7<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">30<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"168\">30 + 6 = 36<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"160\">7 &#8211; 10<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">40<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"168\">36 + 40 = 76<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"160\">10 &#8211; 13<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">16<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"168\">76 + 16 = 92<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"160\">13 &#8211; 16<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">4<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"168\">92 + 4 = 96<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"160\">16 &#8211; 19<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">4<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"168\">96 + 4 = 100<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"160\">Total (<em>n<\/em>)<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"144\">100<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"168\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Now we may observe that cumulative frequency just greater than\u00a0 is 76 belonging to class <img loading=\"lazy\" class=\"alignnone size-full wp-image-102207\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-6s1.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 6s1\" width=\"147\" height=\"50\" \/>\u00a0interval 7 &#8211; 10.<br \/>\nMedian class = 7 &#8211; 10<br \/>\nLower limit (l) of median class = 7<br \/>\nCumulative frequency (cf) of class preceding median class = 36<br \/>\nFrequency (f) of median class = 40<br \/>\nClass size (h) = 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-102208\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-6s2.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 6s2\" width=\"203\" height=\"170\" \/><br \/>\nNow we can find class marks of given class intervals by using relation<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-102290\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-6s3.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 6s3\" width=\"392\" height=\"50\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-6s3.png 392w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-6s3-300x38.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/p>\n<p>Taking 11.5 as assumed mean (a) we can find d<sub>i<\/sub>, u<sub>i<\/sub>\u00a0and f<sub>i<\/sub>u<sub>i<\/sub>\u00a0according to step deviation method as below.<\/p>\n<table border=\"1\" width=\"566\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"156\"><strong>Number of<\/strong><br \/>\n<strong>letters<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"103\"><strong>Number of<\/strong><br \/>\n<strong>surnames<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"50\"><strong><em>x<sub>i<\/sub><\/em><\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"64\"><strong><em>x<sub>i<\/sub>\u00a0<\/em><\/strong><strong>&#8211;\u00a0<em>a<\/em><\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\"><strong> <img loading=\"lazy\" class=\"alignnone size-full wp-image-102292\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-6s4.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 6s4\" width=\"60\" height=\"30\" \/><\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\"><strong><em>f<sub>i<\/sub>u<sub>i<\/sub><\/em><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"156\">1 &#8211; 4<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"103\">6<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"50\">2.5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"64\">-9<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\">-3<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\">-18<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"156\">4 &#8211; 7<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"103\">30<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"50\">5.5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"64\">-6<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\">-2<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\">-60<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"156\">7 &#8211; 10<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"103\">40<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"50\">8.5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"64\">-3<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\">-1<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\">-40<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"156\">10 &#8211; 13<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"103\">16<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"50\">11.5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"64\">0<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\">0<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"156\">13 &#8211; 16<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"103\">4<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"50\">14.5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"64\">3<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\">1<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\">4<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"156\">16 &#8211; 19<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"103\">4<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"50\">17.5<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"64\">6<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\">2<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\">8<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"156\">Total<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"103\">100<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"50\"><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"64\"><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\"><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"96\">-106<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-102295\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-6s5.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 6s5\" width=\"253\" height=\"189\" \/><\/p>\n<p>We know that<br \/>\n3 median = mode + 2 mean<br \/>\n3(8.05) = mode + 2(8.32)<br \/>\n24.15 &#8211; 16.64 = mode<br \/>\n7.51 = mode<br \/>\nSo, median number and mean number of letters in surnames is 8.05 and 8.32 respectively while modal size of surnames is 7.51.<\/p>\n<p><strong>Question 7<\/strong><\/p>\n<p class=\"ques\">The distribution below gives the weights of 30 students of a class. Find the median weight of the students.<\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"72\"><strong>Weight\u00a0<\/strong><br \/>\n<strong>(in kg)<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"64\">40 &#8211; 45<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"66\">45 &#8211; 50<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"63\">50 &#8211; 55<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"63\">55 &#8211; 60<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"63\">60 &#8211; 65<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"66\">65 &#8211; 70<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"72\">70 &#8211; 75<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" valign=\"top\" width=\"72\"><strong>Number of students<\/strong><\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"64\">2<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"66\">3<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"63\">8<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"63\">6<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"63\">6<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"66\">3<\/td>\n<td style=\"text-align: center;\" valign=\"top\" width=\"72\">2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Solution:<br \/>\n<\/strong>We may find cumulative frequencies with their respective class intervals as below<br \/>\nCumulative frequency just greater than <img loading=\"lazy\" class=\"alignnone size-full wp-image-102296\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-7s.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 7s\" width=\"135\" height=\"50\" \/>\u00a0is 19, belonging to class interval 55 &#8211; 60.<br \/>\nMedian class = 55 &#8211; 60<br \/>\nLower limit (l) of median class = 55<br \/>\nFrequency (f) of median class = 6<br \/>\nCumulative frequency (cf) of median class = 13<br \/>\nClass size (h) = 5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-102302\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-14-Statistics-ex-14.3-7s1.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.3 7s1\" width=\"217\" height=\"170\" \/><br \/>\nSo, median weight is 56.67 kg.<\/p>\n<div class=\"solnBox\">\n<div class=\"table-responsive\">\n<div class=\"table-responsive\">\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>We hope the NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 14 Statistics\u00a0Class 10 NCERT Solutions Ex 14.3. 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