{"id":4602,"date":"2023-02-25T05:33:41","date_gmt":"2023-02-25T05:33:41","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=4602"},"modified":"2023-02-25T05:35:12","modified_gmt":"2023-02-25T05:35:12","slug":"ncert-solutions-class-9-maths-chapter-14-statistics-ex-14-4","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-14-statistics-ex-14-4\/","title":{"rendered":"NCERT Solutions Class 9 Maths Chapter 14 Statistics Ex 14.4"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 9 Maths\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 14 (Statistics)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 9 Mathematics\u00a0<strong>Chapter &#8211; 14 Statistics <\/strong>Exercise 14.4 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><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-14-statistics-ex-14-1\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 14.1<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-14-statistics-ex-14-2\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 14.2<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-14-statistics-ex-14-3\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 14.3<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 14.4<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. The following number of goals were scored by a team in a series of 10 matches:<br \/>\n<\/strong><strong>2, 3, 4, 5, 0, 1, 3, 3, 4, 3<br \/>\n<\/strong><strong>Find the mean, median and mode of these scores.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;\u00a0<\/strong><br \/>\n<strong>Mean<\/strong> = Average = Sum of all the observations\/Total number of observations<br \/>\n= (2+3+4+5+0+1+3+3+4+3)\/10<br \/>\n= 28\/10<br \/>\n= 2.8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Median<br \/>\n<\/strong>To find the median, we first arrange the data in ascending order.<br \/>\n0, 1, 2, 3, 3, 3, 3, 4, 4, 5<br \/>\nThe number of observations is 10, which is an even number. Therefore, the median score will be the average of 10\/2 i.e., 5th and 10\/2 + 1 i.e., 6th observation while arranged in ascending or descending order.<\/span><br \/>\n<span style=\"color: #000000;\">Median score = (5<sup>th<\/sup>\u00a0observation + 6<sup>th<\/sup> observation)\/2 <\/span><br \/>\n<span style=\"color: #000000;\">= (3 + 3)\/2 <\/span><br \/>\n<span style=\"color: #000000;\">= 6\/2 <\/span><br \/>\n<span style=\"color: #000000;\">= 3<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Mode<br \/>\n<\/strong>To find the mode, we first arrange the data in ascending order.<br \/>\n0, 1, 2, 3, 3, 3, 3, 4, 4, 5<br \/>\nWe find that 3 occurs most frequently (4 times)<br \/>\n\u2234 Mode = 3<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. In a Mathematics test given to 15 students, the following marks (out of 100) are recorded.<br \/>\n<\/strong><strong>41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60<br \/>\nFind the mean, median and mode of this data.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong>Mean = Average = Sum of all the observations\/Total number of observations<br \/>\n= (41 + 39 + 48 + 52 + 46 + 62 + 54 + 40 + 96 + 52 + 98 + 40 + 42 + 52 + 60)\/15<br \/>\n= 822\/15<br \/>\n= 54.8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Median<br \/>\n<\/strong>To find the median, we first arrange the data in ascending order.<br \/>\n39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98<br \/>\nAs the number of observations is 15 which is odd, therefore, the median of data will be (15 + 1)\/2 = 8<sup>th<\/sup> observation <\/span><br \/>\n<span style=\"color: #000000;\">Therefore, the median of the data = 52<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Mode<br \/>\n<\/strong>To find the mode, we first arrange the data in ascending order.<br \/>\n39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98<br \/>\nHere,<br \/>\nWe find that 52 occurs most frequently (3 times)<br \/>\n\u2234 Mode = 52<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.<br \/>\n<\/strong><strong>29, 32, 48, 50, x, x+2, 72, 78, 84, 95<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong>Since the number of observations is even, the median can be calculated as<\/span><br \/>\n<span style=\"color: #000000;\">Therefore, the median of this data\u00a0will be the average of 10\/2 i.e., 5<sup>th<\/sup>\u00a0and 10\/2 + 1 i.e., 6<sup>th\u00a0<\/sup>observation.<\/span><br \/>\n<span style=\"color: #000000;\">Therefore, median of the data = (5<sup>th<\/sup>\u00a0observation + 6<sup>th<\/sup>\u00a0observation) \/ 2<\/span><br \/>\n<span style=\"color: #000000;\">\u21d2 63 = (x\u00a0+ x\u00a0+ 2) \/ 2<\/span><br \/>\n<span style=\"color: #000000;\">\u21d2 63 = (2x + 2) \/ 2<\/span><br \/>\n<span style=\"color: #000000;\">\u21d2 63 = x\u00a0+ 1<\/span><br \/>\n<span style=\"color: #000000;\">\u2234\u00a0x = 62<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\nMode<br \/>\n<\/strong>To find the mode, we first arrange the given data in ascending order.<br \/>\n14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28<br \/>\nHere,<br \/>\nWe find that 14 occurs most frequently (4 times)<br \/>\n\u2234 Mode = 14<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>5. Find the mean salary of 60 workers in a factory from the following table.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4925\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/02\/NCERT-Solutions-Class-9-Maths-Ex-14.4-Q5.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"551\" height=\"434\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/02\/NCERT-Solutions-Class-9-Maths-Ex-14.4-Q5.png 551w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/02\/NCERT-Solutions-Class-9-Maths-Ex-14.4-Q5-300x236.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/02\/NCERT-Solutions-Class-9-Maths-Ex-14.4-Q5-480x378.png 480w\" sizes=\"auto, (max-width: 551px) 100vw, 551px\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;\u00a0<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">The grouped mean for data with different proportions is given by the formula\u00a0\u2211f<sub>i<\/sub>x<sub>i\u00a0<\/sub>\/ \u2211f<sub>i<br \/>\n<\/sub>The value of \u2211f<sub>i<\/sub>x<sub>i\u00a0<\/sub>and \u2211f<sub>i\u00a0<\/sub>can be calculated as follows:<\/span><\/p>\n<div class=\"table-responsive\" style=\"text-align: justify;\">\n<table class=\"table table-bordered\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>Salary (x<sub>i<\/sub>)<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>Number of workers (f<sub>i<\/sub>)<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>f<sub>i<\/sub>x<sub>i<\/sub><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">3000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">16<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">48000<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">4000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">12<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">48000<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">5000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">10<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">50000<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">6000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">8<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">48000<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">7000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">6<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">42000<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">8000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">32000<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">9000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">27000<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">10000<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">10000<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">Total<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">\u03a3f<sub>i<\/sub>\u00a0= 60<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">\u03a3f<sub>i<\/sub>x<sub>i<\/sub>\u00a0= 305000<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><span style=\"color: #000000;\">Mean salary = 305000\/60 = 5083.33 <\/span><br \/>\n<span style=\"color: #000000;\">Therefore, the\u00a0mean\u00a0salary of 60 workers is \u20b9 5083.33.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>6. Give one example of a situation in which<br \/>\n<\/strong><strong>(i) <\/strong>the mean is an appropriate measure of central tendency.<strong><br \/>\n<\/strong><strong>(ii)<\/strong>\u00a0the mean is not an appropriate measure of central tendency, but the median is an appropriate measure of central tendency.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong><strong>(i) <\/strong>Consider the following example \u2212 The following data represent the heights of the members of a family:<\/span><br \/>\n<span style=\"color: #000000;\">154.9 cm, 162.8 cm, 170.6 cm, 158.8 cm, 163.3 cm, 166.8 cm, 160.2 cm<\/span><br \/>\n<span style=\"color: #000000;\">In this case, it can be observed that the observations in the given data are close to each other.<\/span><br \/>\n<span style=\"color: #000000;\">Therefore, the\u00a0mean\u00a0will be\u00a0an appropriate measure of central tendency.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii)<\/strong> Runs scored by Mahendra Singh Dhoni in 7 matches are<br \/>\n39, 51, 56, 102, 83, 48, 91<br \/>\nHere,<br \/>\n<strong>Mean<\/strong> = (39 + 51 + 56 + 102 + 83 + 48 + 91)\/7<br \/>\n= 470\/7<br \/>\n= 67.1.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Median<br \/>\n<\/strong>Arranging in ascending order, we get 39, 48, 51, 56, 83, 91, 102<br \/>\nn = 7<br \/>\nMedian = [(n+1)\/2]<sup>th<\/sup>\u00a0observation<br \/>\n= ( (7+1)\/2)<sup>th\u00a0<\/sup>observation<br \/>\n= (8\/2)<sup>th\u00a0<\/sup>observation<br \/>\n= 4<sup>th\u00a0<\/sup>observation<br \/>\n= 56<\/span><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 9 Maths\u00a0 Chapter &#8211; 14 (Statistics)\u00a0 The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter &#8211; 14 Statistics Exercise 14.4 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 14: Statistics NCERT Solution Class 9 Maths Ex &#8211; 14.1 NCERT Solution Class 9 Maths [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[698],"tags":[727,702,186,728,701,5],"class_list":["post-4602","post","type-post","status-publish","format-standard","hentry","category-class-9-maths","tag-class-9th-chapter-14-statistics-in-english","tag-ncert-solution-class-9","tag-ncert-solutions","tag-ncert-solutions-class-9-maths-chapter-14-in-english","tag-ncert-solutions-class-9-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - 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