{"id":6105,"date":"2023-10-08T06:00:19","date_gmt":"2023-10-08T06:00:19","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=6105"},"modified":"2023-10-08T06:00:19","modified_gmt":"2023-10-08T06:00:19","slug":"ncert-solutions-class-10-maths-chapter-14-statistics-ex-14-2","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-14-statistics-ex-14-2\/","title":{"rendered":"NCERT Solutions Class 10 Maths Chapter 14 Statistics Ex 14.2"},"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 14.2 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-14-3\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 14.3<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-14-statistics-ex-14-1\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 14.4<\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><strong><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 14.2<\/span><\/strong><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>1. The following table shows the ages of the patients admitted to a hospital during a year:<\/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>Age (in years)<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>5-15<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>15-25<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>25-35<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>35-45<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>45-55<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>55-65<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of patients<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>6<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>11<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>21<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>23<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>14<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>5<\/strong><\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>Find the mode and the mean of the data given above. Compare and interpret the two <\/strong><\/span><span style=\"font-family: Georgia, Palatino;\"><strong>measures of central tendency.<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">Solution &#8211;\u00a0<\/span><\/strong><span style=\"font-family: Georgia, Palatino;\">To find out the modal class, let us the consider the class interval with high frequency.<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Here, the greatest frequency = 23, so the modal class = 35 \u2013 45,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Lower limit of modal class = l = 35,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">class width (h) = 10,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">f<sub>m<\/sub> = 23,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">f<sub>1<\/sub>\u00a0= 21 and f<sub>2<\/sub>\u00a0= 14<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">The formula to find the mode is<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mode\u00a0= l + [(f<sub>m\u00a0<\/sub>\u2013 f<sub>1<\/sub>)\/(2f<sub>m\u00a0<\/sub>\u2013 f<sub>1\u00a0<\/sub>\u2013 f<sub>2<\/sub>)] \u00d7 h<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mode = 35 + [(23 &#8211; 21)\/(46 &#8211; 21 &#8211; 14)]\u00d710<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 35 + (20\/11)<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 35 + 1.8<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 36.8 years<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">So the mode of the given data = 36.8 years<br \/>\n<\/span><strong><span style=\"font-family: Georgia, Palatino;\">Calculation of Mean : <\/span><\/strong><span style=\"font-family: Georgia, Palatino;\">First find the midpoint using the formula,<br \/>\nx<sub>i\u00a0<\/sub>= (upper limit + lower limit)\/2<\/span><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">Class Interval<\/span><\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">Frequency (f<sub>i<\/sub>)<\/span><\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">Mid-point (x<sub>i<\/sub>)<\/span><\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">f<sub>i<\/sub>x<sub>i<\/sub><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">5-15<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">10<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">60<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">15-25<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">11<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">20<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">220<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">25-35<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">21<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">30<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">630<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">35-45<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">23<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">40<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">920<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">45-55<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">14<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">50<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">700<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">55-65<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">60<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">300<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>\u00a0= 80<\/span><\/td>\n<td><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>x<sub>i<\/sub>\u00a0= 2830<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\">The mean formula is<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mean = x\u0304 = \u2211f<sub>i<\/sub>x<sub>i<\/sub> \/ \u2211f<sub>i<br \/>\n<\/sub><\/span><span style=\"font-family: Georgia, Palatino;\">= 2830\/80<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 35.375 years<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Therefore, the mean of the given data = 35.375 years<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>2. The following data gives the information on the observed lifetimes (in hours) of 225 <\/strong><\/span><span style=\"font-family: Georgia, Palatino;\"><strong>electrical components:<\/strong><\/span><\/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>Lifetime (in hours)<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>0-20<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>20-40<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>40-60<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>60-80<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>80-100<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>100-120<\/strong><\/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=\"color: #000000; font-family: Georgia, Palatino;\"><strong>10<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>35<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>52<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>61<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>38<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>29<\/strong><\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>Determine the modal lifetimes of the components.<br \/>\n<\/strong><\/span><span style=\"font-family: Georgia, Palatino;\"><strong>Solution &#8211;\u00a0<\/strong><\/span><span style=\"font-family: Georgia, Palatino;\">From the given data the modal class is 60\u201380.<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Lower limit of modal class = l = 60,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">The frequencies are:<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">f<sub>m<\/sub>\u00a0= 61,<br \/>\nf<sub>1<\/sub>\u00a0= 52,<br \/>\nf<sub>2<\/sub> = 38<br \/>\nh = 20<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">The formula to find the mode is<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mode\u00a0= l+ [(f<sub>m\u00a0<\/sub>\u2013 f<sub>1<\/sub>)\/(2f<sub>m\u00a0<\/sub>\u2013 f<sub>1\u00a0<\/sub>\u2013 f<sub>2<\/sub>)] \u00d7 h<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mode = 60 + [(61 \u2013 52)\/ (122 \u2013 52 \u2013 38)] \u00d7 20<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mode = 60 + [(9 \u00d7 20)\/32]<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mode = 60 + (45\/8) = 60 + 5.625<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Therefore, modal lifetime of the components = 65.625 hours.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>3. The following data gives the distribution of total monthly household expenditure of 200 <\/strong><\/span><span style=\"font-family: Georgia, Palatino;\"><strong>families of a village. Find the modal monthly expenditure of the families. Also, find the <\/strong><\/span><span style=\"font-family: Georgia, Palatino;\"><strong>mean monthly expenditure:<\/strong><\/span><\/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>Expenditure (in Rs.)<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of families<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>1000-1500<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>24<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>1500-2000<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>40<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>2000-2500<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>33<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>2500-3000<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>28<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>3000-3500<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>30<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>3500-4000<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>22<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4000-4500<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>16<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4500-5000<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>7<\/strong><\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>Solution &#8211;<\/strong> \u00a0<\/span><span style=\"font-family: Georgia, Palatino;\">Given data:<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Modal class = 1500 &#8211; 2000,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\"><em>l<\/em> = 1500,<br \/>\n<\/span><strong><span style=\"font-family: Georgia, Palatino;\">Frequencies:<br \/>\n<\/span><\/strong><span style=\"font-family: Georgia, Palatino;\">f<sub>m<\/sub> = 40,<br \/>\nf<sub>1<\/sub>\u00a0= 24,<br \/>\nf<sub>2<\/sub> = 33,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">h = 500<br \/>\n<\/span><strong><span style=\"font-family: Georgia, Palatino;\">Mode formula :<br \/>\n<\/span><\/strong><span style=\"font-family: Georgia, Palatino;\">Mode\u00a0= l + [(f<sub>m\u00a0<\/sub>\u2013 f<sub>1<\/sub>)\/ (2f<sub>m\u00a0<\/sub>\u2013 f<sub>1\u00a0<\/sub>\u2013 f<sub>2<\/sub>)] \u00d7 h<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mode = 1500 + [(40 \u2013 24)\/ (80 \u2013 24 \u2013 33)] \u00d7 500<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mode = 1500 + [(16 \u00d7 500)\/23]<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mode = 1500 + (8000\/23) = 1500 + 347.83<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Therefore, modal monthly expenditure of the families = Rupees 1847.83<br \/>\n<\/span><strong><span style=\"font-family: Georgia, Palatino;\">Calculation for mean : <\/span><\/strong><span style=\"font-family: Georgia, Palatino;\">First find the midpoint using the formula,<br \/>\nx<sub>i\u00a0<\/sub>=(upper limit + lower limit)\/2<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Let us assume a mean, (a) be 2750.<\/span><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">Class Interval<\/span><\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">f<sub>i<\/sub><\/span><\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">x<sub>i<\/sub><\/span><\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">d<sub>i<\/sub>\u00a0= x<sub>i<\/sub>\u00a0\u2013 a<\/span><\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">u<sub>i<\/sub>\u00a0= d<sub>i<\/sub>\/h<\/span><\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">f<sub>i<\/sub>u<sub>i<\/sub><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">1000-1500<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">24<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">1250<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">-1500<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">-3<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">-72<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">1500-2000<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">40<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">1750<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">-1000<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">-2<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">-80<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">2000-2500<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">33<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">2250<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">-500<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">-1<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">-33<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">2500-3000<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">28<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">2750 = a<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">3000-3500<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">30<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">3250<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">500<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">30<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">3500-4000<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">22<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">3750<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">1000<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">44<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">4000-4500<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">16<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">4250<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">1500<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">48<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">4500-5000<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">7<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">4750<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">2000<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">28<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">f<sub>i<\/sub>\u00a0= 200<\/span><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">f<sub>i<\/sub>u<sub>i<\/sub>\u00a0= -35<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\">The formula to calculate the mean,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mean = x\u0304 = a +(\u2211f<sub>i<\/sub>u<sub>i<\/sub>\u00a0\/\u2211f<sub>i<\/sub>) \u00d7 h<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 2750 + (-35\/200) \u00d7 500<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 2750 \u2013 87.50<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 2662.50<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">So, the mean monthly expenditure of the families = Rs. 2662.50<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4. The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures<\/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>No of students per teacher<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of states \/ U.T<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\">1<\/span><span style=\"font-family: Georgia, Palatino;\">5-20<\/span><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">20-25<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">8<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">25-30<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">9<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">30-35<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">10<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">35-40<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">40-45<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">45-50<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">50-55<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">Solution &#8211;\u00a0 <\/span><\/strong><span style=\"font-family: Georgia, Palatino;\">Given data:<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Modal class = 30 \u2013 35,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\"><em>l<\/em> = 30,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Class width (h) = 5,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">f<sub>m<\/sub>\u00a0= 10,<br \/>\nf<sub>1<\/sub> = 9<br \/>\nf<sub>2<\/sub> = 3<br \/>\n<\/span><strong><span style=\"font-family: Georgia, Palatino;\">Mode Formula:<br \/>\n<\/span><\/strong><span style=\"font-family: Georgia, Palatino;\">Mode\u00a0= l + [(f<sub>m\u00a0<\/sub>\u2013 f<sub>1<\/sub>)\/ (2f<sub>m\u00a0<\/sub>\u2013 f<sub>1\u00a0<\/sub>\u2013 f<sub>2<\/sub>)] \u00d7 h<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mode = 30 + [(10 \u2013 9)\/ (20 \u2013 9 \u2013 3)] \u00d7 5<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 30 + (5\/8)<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 30 + 0.625<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 30.625<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Therefore, the mode of the given data = 30.625<br \/>\n<\/span><strong><span style=\"font-family: Georgia, Palatino;\">Calculation of mean : <\/span><\/strong><span style=\"font-family: Georgia, Palatino;\">Find the midpoint using the formula,<br \/>\nx<sub>i\u00a0<\/sub>=(upper limit + lower limit)\/2<\/span><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">Class Interval<\/span><\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">Frequency (f<sub>i<\/sub>)<\/span><\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">Mid-point (x<sub>i<\/sub>)<\/span><\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">f<sub>i<\/sub>x<sub>i<\/sub><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">15-20<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">17.5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">52.5<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">20-25<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">8<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">22.5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">180.0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">25-30<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">9<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">27.5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">247.5<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">30-35<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">10<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">32.5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">325.0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">35-40<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">37.5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">112.5<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">40-45<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">42.5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">45-50<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">47.5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">50-55<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">52.5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">105.0<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>\u00a0= 35<\/span><\/td>\n<td><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">Sum f<sub>i<\/sub>x<sub>i<\/sub>\u00a0= 1022.5<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\">Mean = x\u0304 = \u2211f<sub>i<\/sub>x<sub>i<\/sub>\u00a0\/\u2211f<sub>i<br \/>\n<\/sub><\/span><span style=\"font-family: Georgia, Palatino;\">= 1022.5\/35<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 29.2 (approx)<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Therefore, mean = 29.2<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>5. The given distribution shows the number of runs scored by some top batsmen of the world in one- day international cricket matches.<\/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>Run Scored<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of Batsman<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\">3<\/span><span style=\"font-family: Georgia, Palatino;\">000-4000<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">4000-5000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">18<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">5000-6000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">9<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">6000-7000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">7<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">7000-8000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">8000-9000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">9000-10000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">10000-11000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/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 mode of the data.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: Georgia, Palatino;\">Solution &#8211;\u00a0 <\/span><\/strong><span style=\"font-family: Georgia, Palatino;\">Given data :<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Modal class = 4000 \u2013 5000,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">l = 4000,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">class width (h) = 1000,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">f<sub>m<\/sub>\u00a0= 18,<br \/>\nf<sub>1<\/sub> = 4<br \/>\nf<sub>2<\/sub> = 9<br \/>\n<\/span><strong><span style=\"font-family: Georgia, Palatino;\">Mode Formula:<br \/>\n<\/span><\/strong><span style=\"font-family: Georgia, Palatino;\">Mode\u00a0= l + [(f<sub>m\u00a0<\/sub>\u2013 f<sub>1<\/sub>)\/ (2f<sub>m\u00a0<\/sub>\u2013 f<sub>1\u00a0<\/sub>\u2013 f<sub>2<\/sub>)] \u00d7 h<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mode = 4000 + [(18 \u2013 4)\/ (36 \u2013 4 \u2013 9)] \u00d7 1000<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 4000 + (14000\/23)<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 4000 + 608.695<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 4608.695<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 4608.7 (approximately)<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Thus, the mode of the given data is 4608.7 runs.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>6. A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarized it in the table given below. Find the mode of the data:<\/strong><\/span><\/p>\n<table class=\"table table-bordered\" border=\"1\">\n<thead>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Number of cars<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Frequency<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">0-10<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">7<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">10-20<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">14<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">20-30<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">13<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">30-40<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">12<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">40-50<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">20<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">50-60<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">11<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">60-70<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">15<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">70-80<\/span><\/td>\n<td><span style=\"color: #000000; font-family: Georgia, Palatino;\">8<\/span><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>Solution &#8211;<\/strong> \u00a0<\/span><span style=\"font-family: Georgia, Palatino;\">Given Data :<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Modal class = 40 \u2013 50,<br \/>\nl = 40,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Class width (h) = 10,<br \/>\nf<sub>m<\/sub>\u00a0= 20,<br \/>\nf<sub>1<\/sub> = 12<br \/>\nf<sub>2<\/sub> = 11<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mode\u00a0= l + [(f<sub>m\u00a0<\/sub>\u2013 f<sub>1<\/sub>)\/(2f<sub>m\u00a0<\/sub>\u2013 f<sub>1\u00a0<\/sub>\u2013 f<sub>2<\/sub>)] \u00d7 h<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Mode = 40 + [(20 \u2013 12)\/ (40 \u2013 12 \u2013 11)] \u00d7 10<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 40 + (80\/17)<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 40 + 4.7<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">= 44.7<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Thus, the mode of the given data is 44.7 cars.<\/span><\/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 14.2 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":[1045,1115,1117,1044,1049,1048],"class_list":["post-6105","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-14-2-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) - 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