{"id":6106,"date":"2023-10-08T06:00:29","date_gmt":"2023-10-08T06:00:29","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=6106"},"modified":"2023-10-08T06:00:29","modified_gmt":"2023-10-08T06:00:29","slug":"ncert-solutions-class-10-maths-chapter-14-statistics-ex-14-3","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-14-statistics-ex-14-3\/","title":{"rendered":"NCERT Solutions Class 10 Maths Chapter 14 Statistics Ex 14.3"},"content":{"rendered":"<h2 style=\"text-align: center;\"><strong><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 10 Maths\u00a0<\/span><\/strong><br \/>\n<strong><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 14 (Statistics)\u00a0<\/span><\/strong><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 10 Mathematics <strong>Chapter &#8211; 14 Statistics <\/strong>Exercise 14.3 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-14-1\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 14.1<\/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-14-2\" 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-14-1\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 14.4<\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><strong><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 14.3<\/span><\/strong><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>1. The following frequency distribution gives the monthly consumption of an electricity of 68 consumers in a locality. Find the median, mean and mode of the data and compare them.<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Monthly consumption(in units)<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>No. of customers<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">65-85<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">85-105<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">105-125<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">13<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">125-145<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">20<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">145-165<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">14<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">165-185<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">8<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">185-205<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/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 cumulative frequency of the given data as follows:<\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Class Interval<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Frequency<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Cumulative frequency<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">65-85<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">85-105<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">9<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">105-125<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">13<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">22<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">125-145<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">20<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">42<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">145-165<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">14<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">56<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">165-185<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">8<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">64<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">185-205<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">68<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">N = 68<\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">From the table, it is observed that,<br \/>\nN = 68 and hence N\/2 = 34<br \/>\nHence, the median class is 125 &#8211; 145 with cumulative frequency = 42<br \/>\nWhere,\u00a0<em>l<\/em>\u00a0= 125,<br \/>\nN = 68,<br \/>\ncf = 22,<br \/>\nf = 20,<br \/>\nh = 20<br \/>\n<strong>Median is calculated as follows:<br \/>\n<\/strong>Median = <em><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?l&amp;plus;%5Cfrac%7B%5Cfrac%7BN%7D%7B2%7D%20&amp;plus;%20cf%7D%7Bf%7D%20%5Ctimes%20h\" \/><br \/>\n<\/em>= 125 + [(34 \u2212 22)\/20] \u00d7 20<br \/>\n= 125 + 12<br \/>\n= 137<br \/>\nTherefore, median = 137<br \/>\n<strong>To calculate the mode:<br \/>\n<\/strong>Modal class = 125-145,<br \/>\nf<sub>m<\/sub>\u00a0or f<sub>1\u00a0<\/sub>= 20,<br \/>\nf<sub>0\u00a0<\/sub>= 13,<br \/>\nf<sub>2\u00a0<\/sub>= 14<br \/>\nh = 20<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Mode formula :<br \/>\n<\/strong>Mode\u00a0= l+ [(f<sub>1\u00a0<\/sub>\u2013 f<sub>0<\/sub>)\/(2f<sub>1\u00a0<\/sub>\u2013 f<sub>0\u00a0<\/sub>\u2013 f<sub>2<\/sub>)] \u00d7 h<br \/>\nMode = 125 + [(20 \u2013 13)\/ (40 \u2013 13 \u2013 14)] \u00d7 20<br \/>\n= 125 + (140\/13)<br \/>\n= 125 + 10.77<br \/>\n= 135.77<br \/>\nTherefore, mode = 135.77<br \/>\n<strong>Calculate the Mean :<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Class Interval<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>f<sub>i<\/sub><\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>x<sub>i<\/sub><\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>d<sub>i<\/sub>=x<sub>i<\/sub>-a<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>u<sub>i<\/sub>=d<sub>i<\/sub>\/h<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>f<sub>i<\/sub>u<sub>i<\/sub><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">65-85<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">75<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">-60<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">-3<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">-12<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">85-105<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">95<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">-40<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">-2<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">-10<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">105-125<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">13<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">115<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">-20<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">-1<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">-13<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">125-145<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">20<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">135 = a<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">0<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">0<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">145-165<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">14<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">155<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">20<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">1<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">14<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">165-185<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">8<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">175<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">40<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">2<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">16<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">185-205<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">195<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">60<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">3<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">12<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum\u00a0f<sub>i\u00a0<\/sub>= 68<\/span><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">Sum\u00a0f<sub>i<\/sub>u<sub>i<\/sub>= 7<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">x\u0304 = a + h (\u2211f<sub>i<\/sub>u<sub>i<\/sub>\/\u2211f<sub>i<\/sub>)<br \/>\n= 135 + 20 (7\/68)<br \/>\nMean = 137.05<br \/>\nIn this case, mean, median and mode are more\/less equal in this distribution.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>2. If the median of a distribution given below is 28.5, find the value of x &amp; y.<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Class Interval<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Frequency<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">0-10<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">10-20<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">x<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">20-30<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">20<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">30-40<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">15<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">40-50<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">y<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">50-60<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">Total<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">60<\/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;<\/strong> \u00a0Given data,<br \/>\nn = 60<br \/>\nMedian of the given data = 28.5<\/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>CI<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">0-10<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">10-20<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">20-30<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">30-40<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">40-50<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">50-60<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Frequency<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">x<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">20<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">15<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">y<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Cumulative frequency<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5+x<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">25+x<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">40+x<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">40+x+y<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">45+x+y<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Where, N\/2 = 30<br \/>\nMedian class is 20 \u2013 30 with a cumulative frequency = 25 + x<br \/>\nLower limit of median class,\u00a0<em>l\u00a0<\/em>= 20,<br \/>\ncf = 5 + x,<br \/>\nf = 20 &amp; h = 10<br \/>\nMedian = <em><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?l&amp;plus;%5Cfrac%7B%5Cfrac%7BN%7D%7B2%7D%20&amp;plus;%20cf%7D%7Bf%7D%20%5Ctimes%20h\" \/><br \/>\n<\/em>28.5 = 20 + [(30 \u2212 5 \u2212 x)\/20] \u00d7 10<br \/>\n8.5 = (25 \u2013 x)\/2<br \/>\n17 = 25 \u2013 x<br \/>\nTherefore, x = 8.<br \/>\nNow, from cumulative frequency, we can identify the value of x + y as follows:<br \/>\nSince,<br \/>\n60 = 45 + x + y<br \/>\nNow, substitute the value of x, to find y<br \/>\n60 = 45 + 8 + y<br \/>\ny = 60 \u2013 53<br \/>\ny = 7<br \/>\nTherefore, the value of x = 8 and y = 7.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>3. The life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to the persons whose age is 18 years onwards but less than the 60 years.<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Age (in years)<\/strong><\/span><\/td>\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Number of policy holder<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Below 20<\/span><\/td>\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">2<\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">Below 25<\/span><\/td>\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">6<\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">Below 30<\/span><\/td>\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">24<\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">Below 35<\/span><\/td>\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">45<\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">Below 40<\/span><\/td>\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">78<\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">Below 45<\/span><\/td>\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">89<\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">Below 50<\/span><\/td>\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">92<\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">Below 55<\/span><\/td>\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">98<\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">Below 60<\/span><\/td>\n<td style=\"height: 24px;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\">100<\/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; <\/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>Class interval<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Frequency<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Cumulative frequency<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">15-20<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">2<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">2<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">20-25<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">6<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">25-30<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">18<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">24<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">30-35<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">21<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">45<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">35-40<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">33<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">78<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">40-45<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">11<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">89<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">45-50<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">3<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">92<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">50-55<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">6<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">98<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">55-60<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">2<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">100<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Given data : <\/strong><br \/>\nN = 100 and N\/2 = 50<br \/>\nMedian class = 35 &#8211; 40<br \/>\n<em>l<\/em>\u00a0= 35,<br \/>\ncf = 45,<br \/>\nf = 33<br \/>\nh = 5<br \/>\nMedian = <em><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?l&amp;plus;%5Cfrac%7B%5Cfrac%7BN%7D%7B2%7D%20&amp;plus;%20cf%7D%7Bf%7D%20%5Ctimes%20h\" \/><br \/>\n<\/em>Median = 35 + [(50 \u2013 45)\/33] \u00d7 5<br \/>\n= 35 + (25\/33)<br \/>\n= 35.76<br \/>\nTherefore, the median age = 35.76 years.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>4. The lengths of 40 leaves in a plant are measured correctly to the nearest millimeter, and the data obtained is represented as in the following table:<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Length (in mm)<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Number of leaves<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">118-126<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">3<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">127-135<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">136-144<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">9<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">145-153<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">12<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">154-162<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">163-171<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">172-180<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">2<\/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 median length of the leaves.<br \/>\n<\/strong><strong>(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 \u2013 126.5, 126.5 \u2013 135.5, . . ., 171.5 \u2013 180.5.)<br \/>\n<\/strong><strong>Solution &#8211;<\/strong> \u00a0Since the data are not continuous reduce 0.5 in the lower limit and add 0.5 in the upper limit.<\/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>Class Interval<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Frequency<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Cumulative frequency<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">117.5-126.5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">3<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">3<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">126.5-135.5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">8<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">135.5-144.5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">9<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">17<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">144.5-153.5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">12<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">29<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">153.5-162.5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">34<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">162.5-171.5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">38<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">171.5-180.5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">2<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">40<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">So, the data obtained are:<br \/>\nN = 40 and N\/2 = 20<br \/>\nMedian class = 144.5 &#8211; 153.5<br \/>\n<em>l<\/em>\u00a0= 144.5,<br \/>\ncf = 17,<br \/>\nf = 12<br \/>\nh = 9<br \/>\nMedian = <em><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?l&amp;plus;%5Cfrac%7B%5Cfrac%7BN%7D%7B2%7D%20&amp;plus;%20cf%7D%7Bf%7D%20%5Ctimes%20h\" \/><br \/>\n<\/em>Median = 144.5 + [(20 \u2013 17)\/ 12] \u00d7 9<br \/>\n= 144.5 + (9\/4)<br \/>\n= 146.75 mm<br \/>\nTherefore, the median length of the leaves = 146.75 mm.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>5. The following table gives the distribution of a lifetime of 400 neon lamps.<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Lifetime (in hours)<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Number of lamps<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">1500-2000<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">14<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">2000-2500<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">56<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">2500-3000<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">60<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">3000-3500<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">86<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">3500-4000<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">74<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4000-4500<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">62<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4500-5000<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">48<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Find the median lifetime of a lamp.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Solution &#8211; <\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Class Interval<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Frequency<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Cumulative<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">1500-2000<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">14<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">14<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">2000-2500<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">56<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">70<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">2500-3000<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">60<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">130<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">3000-3500<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">86<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">216<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">3500-4000<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">74<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">290<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4000-4500<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">62<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">352<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4500-5000<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">48<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">400<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">N = 400 &amp; N\/2 = 200<br \/>\nMedian class = 3000 \u2013 3500<br \/>\n<em>l<\/em> = 3000,<br \/>\ncf = 130,<br \/>\nf = 86<br \/>\nh = 500<br \/>\nMedian = <em><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?l&amp;plus;%5Cfrac%7B%5Cfrac%7BN%7D%7B2%7D%20&amp;plus;%20cf%7D%7Bf%7D%20%5Ctimes%20h\" \/><br \/>\n<\/em>Median = 3000 + [(200 \u2013 130)\/86] \u00d7 500<br \/>\n= 3000 + (35000\/86)<br \/>\n= 3000 + 406.98<br \/>\n= 3406.98<br \/>\nTherefore, the median lifetime of the lamps = 3406.98 hours<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>6. 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:<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Number of letters<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">1-4<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4-7<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">7-10<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">10-13<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">13-16<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">16-19<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Number of surnames<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">6<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">30<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">40<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">16<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>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.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Solution &#8211;\u00a0<\/strong>To calculate median:<\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Class Interval<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Frequency<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Cumulative Frequency<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">1-4<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">6<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">6<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4-7<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">30<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">36<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">7-10<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">40<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">76<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">10-13<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">16<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">92<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">13-16<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">96<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">16-19<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">100<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">N = 100 &amp; N\/2 = 50<br \/>\nMedian class = 7 &#8211; 10<br \/>\n<em>l<\/em>\u00a0= 7,<br \/>\ncf = 36,<br \/>\nf = 40<br \/>\nh = 3<br \/>\nMedian = <em><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?l&amp;plus;%5Cfrac%7B%5Cfrac%7BN%7D%7B2%7D%20&amp;plus;%20cf%7D%7Bf%7D%20%5Ctimes%20h\" \/><br \/>\n<\/em>Median = 7 + [(50 \u2013 36)\/40] \u00d7 3<br \/>\nMedian = 7 + (42\/40)<br \/>\nMedian = 8.05<br \/>\n<strong>Calculate the Mode:<br \/>\n<\/strong>Modal class = 7-10,<br \/>\n<em>l<\/em>\u00a0= 7,<br \/>\nf<sub>1<\/sub>\u00a0= 40,<br \/>\nf<sub>0<\/sub>\u00a0= 30,<br \/>\nf<sub>2<\/sub> = 16<br \/>\nh = 3<br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?Mode%20%3D%20l%20&amp;plus;%5Cleft%20%28%20%5Cfrac%7Bf_1-f_0%7D%7B2f_1-f_0-f_2%7D%20%5Cright%20%29%5Ctimes%20h\" \/><br \/>\nMode = 7 + [(40 \u2013 30)\/(2 \u00d7 40 \u2013 30 \u2013 16)] \u00d7 3<br \/>\n= 7 + (30\/34)<br \/>\n= 7.88<br \/>\nTherefore mode = 7.88<br \/>\n<strong>Calculate the Mean :<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Class Interval<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>f<sub>i<\/sub><\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>x<sub>i<\/sub><\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>f<sub>i<\/sub>x<sub>i<\/sub><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">1-4<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">6<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">2.5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">15<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4-7<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">30<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5.5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">165<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">7-10<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">40<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">8.5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">340<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">10-13<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">16<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">11.5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">184<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">13-16<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">14.5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">58<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">16-19<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">4<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">17.5<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">70<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">Sum f<sub>i<\/sub>\u00a0= 100<\/span><\/td>\n<td><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">Sum f<sub>i<\/sub>x<sub>i<\/sub>\u00a0= 832<\/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 = \u2211f<sub>i\u00a0<\/sub>x<sub>i<\/sub>\u00a0\/\u2211f<sub>i<br \/>\n<\/sub>Mean = 832\/100 = 8.32<br \/>\nTherefore, mean = 8.32<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>7. The distribution below gives the weights of 30 students of a class. Find the median weight of the students.<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Weight(in kg)<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>40-45<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>45-50<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>50-55<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>55-60<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>60-65<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>65-70<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>70-75<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Number of students<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>2<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>3<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>8<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>6<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>6<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>3<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><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; <\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Class Interval<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Frequency<\/strong><\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\"><strong>Cumulative frequency<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">40-45<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">2<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">2<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">45-50<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">3<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">5<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">50-55<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">8<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">13<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">55-60<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">6<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">19<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">60-65<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">6<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">25<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">65-70<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">3<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">28<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">70-75<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">2<\/span><\/td>\n<td><span style=\"font-family: Georgia, Palatino; color: #000000;\">30<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">N = 30 and N\/2= 15<br \/>\nMedian class = 55 &#8211; 60<br \/>\nl = 55,<br \/>\nC<sub>f<\/sub>\u00a0= 13,<br \/>\nf = 6<br \/>\nh = 5<br \/>\nMedian = <em><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?l&amp;plus;%5Cfrac%7B%5Cfrac%7BN%7D%7B2%7D%20&amp;plus;%20cf%7D%7Bf%7D%20%5Ctimes%20h\" \/><br \/>\n<\/em>Median = 55 + [(15 \u2013 13)\/6] \u00d7 5<br \/>\n= 55 + (10\/6)<br \/>\n= 55 + 1.666<br \/>\n= 56.67<br \/>\nTherefore, the median weight of the students = 56.67<\/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 14.3 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; 14.1 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":[1045,1115,1118,1044,1049,1048],"class_list":["post-6106","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-14-3-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 v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 10 Maths Chapter 14 Statistics Ex 14.3 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 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