{"id":108932,"date":"2023-05-24T16:34:00","date_gmt":"2023-05-24T11:04:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=108932"},"modified":"2025-07-12T11:44:22","modified_gmt":"2025-07-12T06:14:22","slug":"ncert-solutions-for-class-11-statistics-chapter-5","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/","title":{"rendered":"Class 11 Statistics NCERT Solutions for Chapter 5 2026: Download Free PDF"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-108948\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/07\/Statistics-chapter5.jpg\" alt=\"NCERT Solutions for Class 11 Statistics Chapter 5\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/07\/Statistics-chapter5.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/07\/Statistics-chapter5-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>NCERT Solutions for Class 11 Statistics Chapter 5:<\/strong> We offer students with an excellent understanding of statistics. They offer up-to-date and improved solutions, with content prepared by subject matter specialists with years of experience. With the help of <a href=\"https:\/\/www.kopykitab.com\/NCERT-Solution-For-Class-11-Statistics-Ebook-by-Panel-Of-Experts\"><strong>NCERT Solutions For Class 11 Statistics<\/strong><\/a> Chapter 5, students can obtain information as well as good grades.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69e791d940b1f\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69e791d940b1f\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#ncert-solutions-for-class-11-statistics-chapter-5-pdf\" title=\"NCERT Solutions for Class 11 Statistics Chapter 5 PDF\">NCERT Solutions for Class 11 Statistics Chapter 5 PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#download-the-free-pdf-for-ncert-solutions-for-class-11-statistics-chapter-5\" title=\"Download the Free PDF for NCERT Solutions for Class 11 Statistics Chapter 5\">Download the Free PDF for NCERT Solutions for Class 11 Statistics Chapter 5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#ncert-solutions-for-class-11-statistics-chapter-5-overview\" title=\"NCERT Solutions for Class 11 Statistics Chapter 5: Overview\">NCERT Solutions for Class 11 Statistics Chapter 5: Overview<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#measures-of-central-tendency\" title=\"Measures of Central Tendency\">Measures of Central Tendency<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#access-ncert-solutions-for-class-11-statistics-chapter-5\" title=\"Access NCERT Solutions For Class 11 Statistics Chapter 5\">Access NCERT Solutions For Class 11 Statistics Chapter 5<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#question-1\" title=\"Question 1:\">Question 1:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#answer\" title=\"ANSWER:\">ANSWER:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#question-2i\" title=\"Question 2(i):\">Question 2(i):<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#answer-2\" title=\"ANSWER:\">ANSWER:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#question-2ii\" title=\"Question 2(ii):\">Question 2(ii):<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#answer-3\" title=\"ANSWER:\">ANSWER:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#page-no-72\" title=\"Page No 72:\">Page No 72:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#question-2iii\" title=\"Question 2(iii):\">Question 2(iii):<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#answer-4\" title=\"ANSWER:\">ANSWER:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#page-no-72-2\" title=\"Page No 72:\">Page No 72:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#question-3\" title=\"Question 3:\">Question 3:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#answer-5\" title=\"ANSWER:\">ANSWER:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#page-no-72-3\" title=\"Page No 72:\">Page No 72:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#question-4\" title=\"Question 4:\">Question 4:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#answer-6\" title=\"ANSWER:\">ANSWER:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#page-no-72-4\" title=\"Page No 72:\">Page No 72:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#question-5\" title=\"Question 5:\">Question 5:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#answer-7\" title=\"ANSWER:\">ANSWER:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#page-no-72-5\" title=\"Page No 72:\">Page No 72:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#question-6\" title=\"Question 6:\">Question 6:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#answer-8\" title=\"ANSWER:\">ANSWER:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-27\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#page-no-73\" title=\"Page No 73:\">Page No 73:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-28\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#question-7\" title=\"Question 7:\">Question 7:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-29\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#answer-9\" title=\"ANSWER:\">ANSWER:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-30\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#page-no-73-2\" title=\"Page No 73:\">Page No 73:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-31\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#question-8\" title=\"Question 8:\">Question 8:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-32\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#answer-10\" title=\"ANSWER:\">ANSWER:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-33\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#page-no-73-3\" title=\"Page No 73:\">Page No 73:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-34\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#question-9\" title=\"Question 9:\">Question 9:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-35\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#answer-11\" title=\"ANSWER:\">ANSWER:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-36\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#access-other-chapters-of-ncert-solutions-for-class-11-statistics\" title=\"Access Other Chapters of NCERT Solutions For Class 11 Statistics \">Access Other Chapters of NCERT Solutions For Class 11 Statistics <\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-37\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#faq-on-ncert-solutions-for-class-11-statistics-chapter-5\" title=\"FAQ on NCERT Solutions For Class 11 Statistics Chapter 5\">FAQ on NCERT Solutions For Class 11 Statistics Chapter 5<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-38\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#find-the-mean-median-and-mode-for-the-following-list-of-values-13-18-13-14-13-16-14-21-13\" title=\"Find the mean, median, and mode for the following list of values: 13, 18, 13, 14, 13, 16, 14, 21, 13.\">Find the mean, median, and mode for the following list of values: 13, 18, 13, 14, 13, 16, 14, 21, 13.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-39\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#what-is-the-difference-between-mean-and-median\" title=\"What is the difference between Mean and Median?\">What is the difference between Mean and Median?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-40\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#what-are-the-purposes-of-average-in-the-statistical-method\" title=\"What are the purposes of average in the statistical method?\">What are the purposes of average in the statistical method?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-41\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#what-are-the-different-kinds-of-statistical-averages\" title=\"What are the different kinds of statistical averages?\">What are the different kinds of statistical averages?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-42\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#what-are-the-two-methods-that-can-calculate-the-simple-arithmetic-mean-in-case-of-an-individual-series\" title=\"What are the two methods that can calculate the simple arithmetic mean in case\u00a0 of an individual series.\">What are the two methods that can calculate the simple arithmetic mean in case\u00a0 of an individual series.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-43\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/#what-are-the-methods-of-calculating-the-simple-arithmetic-mean\" title=\"What are the methods of calculating the simple arithmetic mean?\">What are the methods of calculating the simple arithmetic mean?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"ncert-solutions-for-class-11-statistics-chapter-5-pdf\"><\/span><strong>NCERT Solutions for Class 11 Statistics Chapter 5 PDF<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/07\/NCERT-Solutions-for-Class-11-Economics-Statistics-Chapter-5.pdf\" target=\"_blank\" rel=\"noopener\">NCERT Solutions For Statistics Class 11 Ch 5<\/a><\/p>\n<div id=\"example1\" style=\"text-align: justify;\">&nbsp;<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/07\/NCERT-Solutions-for-Class-11-Economics-Statistics-Chapter-5.pdf\", \"#example1\");<\/script><\/p>\n<h2><span class=\"ez-toc-section\" id=\"download-the-free-pdf-for-ncert-solutions-for-class-11-statistics-chapter-5\"><\/span><strong>Download the Free PDF for NCERT Solutions for Class 11 Statistics Chapter 5<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"text-align: center;\"><a style=\"width: auto; padding: 18px; cursor: pointer; font-weight: bold; border-radius: 40px; color: #ffffff; background: #ff4500;\" href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/07\/NCERT-Solutions-for-Class-11-Economics-Statistics-Chapter-5.pdf\" target=\"_blank\" rel=\"noopener\">Click Here<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"ncert-solutions-for-class-11-statistics-chapter-5-overview\"><\/span><strong>NCERT Solutions for Class 11 Statistics Chapter 5: Overview<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Class 11 Statistics NCERT Solutions Chapter 5 is free to download in PDF format from our official website. Students should take advantage of this opportunity to learn more. It is up to the student whether to use a soft copy or a hard copy. If they are willing to study from a physical copy, they will be able to learn without having to worry about their internet connection. It also helps to prepare for competitive exams and other board exams.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"measures-of-central-tendency\"><\/span><strong>Measures of Central Tendency<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ol>\n<li><strong> Introduction&nbsp;<\/strong><\/li>\n<\/ol>\n<p>Class 11 Statistics NCERT Solutions As the students have learned how to gather data and portray data, Chapter 5 aims to introduce the measures available for the central tendency in Statistics. The following step is to analyze and interpret the data. We can use three different measures of central trends to assess the data: arithmetic means, median, and mode.<\/p>\n<ol start=\"2\">\n<li><strong> Arithmetic Mean<\/strong><\/li>\n<\/ol>\n<p>The arithmetic mean is a widely used metric for determining the average of a set of data. The mean for grouped data and the mean for ungrouped data are two different versions explained in NCERT Solutions for Class 11 Statistics Chapter.<\/p>\n<ol start=\"5\">\n<li>The arithmetic mean is the sum The NCERT Solutions Class 11 Statistics Chapter 5 clearly explains available on our official website with an illustration. Again the grouped data has two kinds of series namely-discrete series and continuous series.<\/li>\n<\/ol>\n<p>There are three methods for computing the mean for ungrouped and grouped data, according to the Measures of Central Tendency in Statistics Class 11 NCERT Solutions. The three possibilities are a direct methodology, an assumed method, and a step division method. Each strategy may alter depending on whether the data is grouped or ungrouped.<\/p>\n<ol start=\"3\">\n<li><strong> Median<\/strong><\/li>\n<\/ol>\n<p>The students are urged to master another measure of central tendency, the median, in this section. The median is a straightforward concept, according to the NCERT Class 11 Statistics Chapter 5 Measures of Central Tendency. It can be computed by taking the middle value, which is the value that divides both sides of the values. However, this is only conceivable if the series&#8217; length is odd. If students are asked to find the median for a set of even number values, we must first find the average of the two middle words.&nbsp;<\/p>\n<p>Another topic covered with the students is quartiles. The term quartile refers to the division of a full size into four equal pieces. It can be calculated separately for both series by themselves. Percentiles are a topic for which the whole size is divided into 99 Parts which reaches the cent.&nbsp;<\/p>\n<ol start=\"4\">\n<li><strong> Mode&nbsp;<\/strong><\/li>\n<\/ol>\n<p>Our NCERT solutions for Statistics Chapter 5 in Class 11 specify that students comprehend each measure of central tendency. Because it is impossible for kids to forget the meaning and formula if they grasp them. Despite the fact that the mode is the last measure of central tendency, it is quite important.<\/p>\n<p>The mode is a French word that refers to the most popular or common value in the set. In simple terms, the mean is the value with the greatest number of occurrences. We can calculate directly using the direct technique by looking at itself. There is a specific formula for determining the value of mode in the continuous approach.<\/p>\n<ol start=\"5\">\n<li><strong>The relative position of arithmetic mean, median, and mode<\/strong><\/li>\n<\/ol>\n<p>The placements of three measures of central tendency are also mentioned in the NCERT Solutions For Class 11 Statistics Chapter 5. The median should be in the middle of the magnitude of three measures can be stirred in any direction. The arithmetic means and mode will be at one of the two extremes.<\/p>\n<ol start=\"6\">\n<li><strong> Conclusion<\/strong><\/li>\n<\/ol>\n<p>Thus Chapter 5 of measures of central tendency has been explained very well by professional teachers to the students. The material is provided with different examples of all six concepts.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-ncert-solutions-for-class-11-statistics-chapter-5\"><\/span>Access NCERT Solutions For Class 11 Statistics Chapter 5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"ques Answ opnQuestion\">\n<h4 class=\"tenClassQues\"><span class=\"ez-toc-section\" id=\"question-1\"><\/span>Question 1:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Which average would be suitable in the following cases?<\/p>\n<p>(i) Average size of readymade garments.<\/p>\n<p>(ii) Average intelligence of students in a class.<\/p>\n<p>(iii) Average production in a factory per shift.<\/p>\n<p>(iv) Average wage in an industrial concern.<\/p>\n<p>(v) When the sum of absolute deviations from average is least.<\/p>\n<p>(vi) When quantities of the variable are in ratios.<\/p>\n<p>(vii) In case of open-ended frequency distribution.<\/p>\n<\/div>\n<div id=\"quesA1\" class=\"ques Answ opnAnswer\">\n<h4><span class=\"ez-toc-section\" id=\"answer\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>(i) The demand for the average size of any readymade garment is the maximum. As, the modal value represents the value with the highest frequency, so the number of the average size to be produced is given by the Modal value.<\/p>\n<p>(ii) Median will be the best measure for calculating the average intelligence of students in a class. It is the value that divides the series into two equal parts. So, number of students below and above the average intelligence can easily be estimated by median.<\/p>\n<p>(iii) It is advisable to use mean for calculating the average production in a factory per shift. The average production is best calculated by arithmetic mean.<\/p>\n<p>(iv) Mean will be the most suitable measure. It is calculated by dividing the sum of wages of all the labour by the total number of labours in the industry.<\/p>\n<p>(v) When the sum of absolute deviations from average is the least, then mean could be used to calculate the average. This is an important mathematical property of arithmetic mean. The algebraic sum of the deviations of a set of n values from A.M. is 0.<\/p>\n<p>(vi) Median will be the most suitable measure in case the variables are in ratios. It is least affected by the extreme values.<\/p>\n<p>(vii) In case of open ended frequency distribution, Median is the most suitable measure as it can be easily computed. Moreover, the median value can be estimated even in case of incomplete statistical series.<\/p>\n<div class=\"ques Answ opnQuestion\">\n<h4 class=\"tenClassQues\"><span class=\"ez-toc-section\" id=\"question-2i\"><\/span>Question 2(i):<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>The most suitable average for qualitative measurement is<\/p>\n<p>(a) arithmetic mean<\/p>\n<p>(b) median<\/p>\n<p>(c) mode<\/p>\n<p>(d) geometric mean<\/p>\n<p>(e) none of the above<\/p>\n<\/div>\n<div id=\"quesA2(i)\" class=\"ques Answ opnAnswer\">\n<h4><span class=\"ez-toc-section\" id=\"answer-2\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Median is the most suitable average for qualitative measurement. This is because Median divides a series in two equal parts.<\/p>\n<\/div>\n<\/div>\n<h4><span class=\"ez-toc-section\" id=\"question-2ii\"><\/span>Question 2(ii):<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Which average is affected most by the presence of extreme items?<\/p>\n<p>(a) median<\/p>\n<p>(b) mode<\/p>\n<p>(c) arithmetic mean<\/p>\n<p>(d) geometric mean<br><br>(e) harmonic mean<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-3\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Arithmetic mean is the most affected by the presence of extreme items. It is one of the prime demerits of the arithmetic mean. It is easily distorted by the extreme values, and also the value of arithmetic mean may not figure out at all in the series.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"page-no-72\"><\/span>Page No 72:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"question-2iii\"><\/span>Question 2(iii):<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>The algebraic sum of deviation of a set of n values from A.M. is<\/p>\n<p>(a) n<\/p>\n<p>(b) 0<\/p>\n<p>(c) 1<\/p>\n<p>(d) none of the above<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-4\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>The algebraic sum of deviation of a set of n values from A.M. is zero. This is one of the mathematical properties of arithmetic mean.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"page-no-72-2\"><\/span>Page No 72:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"question-3\"><\/span>Question 3:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Comment whether the following statements are true or false.<\/p>\n<p>(i) The sum of deviation of items from median is zero.<\/p>\n<p>(ii) An average alone is not enough to compare series.<\/p>\n<p>(iii) Arithmetic mean is a positional value.<\/p>\n<p>(iv) Upper quartile is the lowest value of top 25% of items.<\/p>\n<p>(v) Median is unduly affected by extreme observations.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-5\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>(i) The sum of deviation of items from median is zero.&nbsp;<b><strong>False<\/strong><\/b><\/p>\n<p>The statement is false. This mathematical property applies to the arithmetic mean that states that the sum of the deviation of all items from the mean is zero.<\/p>\n<p>(ii) An average alone is not enough to compare series.<b><strong>&nbsp;True<\/strong><\/b><\/p>\n<p>An average indicates only the behaviour of a particular series. Therefore, in order to measure the extent of divergence of different items from the central tendency is measured by dispersion. So, average is not enough to compare the series.<\/p>\n<p>(iii) Arithmetic mean is a positional value.&nbsp;<b><strong>False<\/strong><\/b><\/p>\n<p>This statement is false as mean is not a positional average, rather the statement holds true for median and mode. The calculation of median and modal values is based on the position of the items in the series, i.e. why these are also termed as positional averages.<\/p>\n<p>(iv) Upper quartile is the lowest value of top 25% of items.<b><strong>&nbsp;True<\/strong><\/b><\/p>\n<p>The value that divides a statistical series into four equal parts, the end value of each part is called quartile. The third quartile or the upper quartile has 75 % of the items below it and 25 % of items above it,<\/p>\n<p>(v) Median is unduly affected by extreme observations.<b><strong>&nbsp;False<\/strong><\/b><\/p>\n<p>This statement is true for Arithmetic mean. Arithmetic mean is most affected by the presence of extreme items. It is one of the prime demerits of the arithmetic mean. It is easily distorted by the extreme values, and also the value of arithmetic mean may not figure out at all in the series.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"page-no-72-3\"><\/span>Page No 72:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"question-4\"><\/span>Question 4:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>If the arithmetic mean of the data given below is 28, find (a) the missing frequency, and (b) the median of the series:<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"199\">\n<p><em>Profit per retail shop (in Rs)<\/em><\/p>\n<\/td>\n<td width=\"60\">\n<p>0 \u2013 10<\/p>\n<\/td>\n<td width=\"66\">\n<p>10 \u2013 20<\/p>\n<\/td>\n<td width=\"66\">\n<p>20 \u2013 30<\/p>\n<\/td>\n<td width=\"66\">\n<p>30 \u2013 40<\/p>\n<\/td>\n<td width=\"66\">\n<p>40 \u2013 50<\/p>\n<\/td>\n<td width=\"69\">\n<p>50 \u2013 60<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"199\">\n<p><em>Number of retail shops<\/em><\/p>\n<\/td>\n<td width=\"60\">\n<p>12<\/p>\n<\/td>\n<td width=\"66\">\n<p>18<\/p>\n<\/td>\n<td width=\"66\">\n<p>27<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u2013<\/p>\n<\/td>\n<td width=\"66\">\n<p>17<\/p>\n<\/td>\n<td width=\"69\">\n<p>6<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-6\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>(i) Let the missing frequency be&nbsp;<em>f<\/em><sub>1&nbsp;<\/sub><\/p>\n<p>Arithmetic Mean = 28<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"156\">\n<p><b><strong>Profit per Retail Shop (in Rs)<\/strong><\/b><\/p>\n<\/td>\n<td width=\"118\">\n<p><b><strong>No of Retail Shops<\/strong><\/b><\/p>\n<\/td>\n<td width=\"122\">\n<p><b><strong>Mid Value<\/strong><\/b><\/p>\n<\/td>\n<td width=\"174\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"156\">\n<p><b><strong>Class Interval<\/strong><\/b><\/p>\n<\/td>\n<td width=\"118\">\n<p><b><strong>(<em>f<\/em>)<\/strong><\/b><\/p>\n<\/td>\n<td width=\"122\">\n<p><b><strong>(<em>m<\/em>)<\/strong><\/b><\/p>\n<\/td>\n<td width=\"174\">\n<p><b><strong><em>fm<\/em><\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"156\">\n<p>0 \u2013 10<\/p>\n<\/td>\n<td width=\"118\">\n<p>12<\/p>\n<\/td>\n<td width=\"122\">\n<p>5<\/p>\n<\/td>\n<td width=\"174\">\n<p>60<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"156\">\n<p>10 \u2013 20<\/p>\n<\/td>\n<td width=\"118\">\n<p>18<\/p>\n<\/td>\n<td width=\"122\">\n<p>15<\/p>\n<\/td>\n<td width=\"174\">\n<p>270<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"156\">\n<p>20 \u2013 30<\/p>\n<\/td>\n<td width=\"118\">\n<p>27<\/p>\n<\/td>\n<td width=\"122\">\n<p>25<\/p>\n<\/td>\n<td width=\"174\">\n<p>675<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"156\">\n<p>30 \u2013 40<\/p>\n<\/td>\n<td width=\"118\">\n<p><em>f<\/em><sub>1<\/sub><\/p>\n<\/td>\n<td width=\"122\">\n<p>35<\/p>\n<\/td>\n<td width=\"174\">\n<p>35<em>f<\/em><sub>1<\/sub><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"156\">\n<p>40 \u2013 50<\/p>\n<\/td>\n<td width=\"118\">\n<p>17<\/p>\n<\/td>\n<td width=\"122\">\n<p>45<\/p>\n<\/td>\n<td width=\"174\">\n<p>765<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"156\">\n<p>50 \u2013 60<\/p>\n<\/td>\n<td width=\"118\">\n<p>6<\/p>\n<\/td>\n<td width=\"122\">\n<p>55<\/p>\n<\/td>\n<td width=\"174\">\n<p>330<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"156\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"118\">&nbsp;<\/td>\n<td width=\"122\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"174\">&nbsp;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>or, 2240 + 28<em>f<\/em><sub>1<\/sub>&nbsp;= 2100 + 35<em>f<\/em><sub>1<\/sub><\/p>\n<p>or, 2240 \u2013 2100 = 35<em>f<\/em><sub>1<\/sub>&nbsp;\u2013 28<em>f<\/em><sub>1<\/sub><\/p>\n<p>or, 140 = 7<em>f<\/em><sub>1<\/sub><\/p>\n<p><em>f<\/em><sub>1<\/sub>&nbsp;= 20<\/p>\n<p>&nbsp;<\/p>\n<p>(ii)<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"42\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"111\">\n<p><b><strong>Class Interval<\/strong><\/b><\/p>\n<\/td>\n<td width=\"101\">\n<p><b><strong>Frequency<\/strong><\/b><\/p>\n<p>&nbsp;<\/p>\n<p><b><strong><em>(f)<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"108\">\n<p><b><strong>Cumulative<\/strong><\/b><\/p>\n<p><b><strong>Frequency<\/strong><\/b><\/p>\n<p><b><strong><em>(CF)<\/em><\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"42\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"111\">\n<p>0 \u2013 10<\/p>\n<\/td>\n<td width=\"101\">\n<p>12<\/p>\n<\/td>\n<td width=\"108\">\n<p>12<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"42\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"111\">\n<p>10 \u2013 20<\/p>\n<\/td>\n<td width=\"101\">\n<p>18<\/p>\n<\/td>\n<td width=\"108\">\n<p>30<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"42\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"111\">\n<p>20 \u2013 30<\/p>\n<\/td>\n<td width=\"101\">\n<p>27<\/p>\n<\/td>\n<td width=\"108\">\n<p>57<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"42\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"111\">\n<p>30 \u2013 40<\/p>\n<\/td>\n<td width=\"101\">\n<p>20<\/p>\n<\/td>\n<td width=\"108\">\n<p>77<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"42\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"111\">\n<p>40 \u2013 50<\/p>\n<\/td>\n<td width=\"101\">\n<p>17<\/p>\n<\/td>\n<td width=\"108\">\n<p>94<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"42\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"111\">\n<p>50 \u2013 60<\/p>\n<\/td>\n<td width=\"101\">\n<p>6<\/p>\n<\/td>\n<td width=\"108\">\n<p>100<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"42\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"111\">\n<p>Total<\/p>\n<\/td>\n<td width=\"101\">&nbsp;<\/td>\n<td width=\"108\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>So, the Median class = Size of&nbsp;&nbsp;item<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 50<sup>th<\/sup>&nbsp;item<\/p>\n<p>50<sup>th<\/sup>&nbsp;item lies in the 57<sup>th<\/sup>&nbsp;cumulative frequency and the corresponding class interval is 20 \u2013 30.<\/p>\n<p>&nbsp;<\/p>\n<h4><span class=\"ez-toc-section\" id=\"page-no-72-4\"><\/span>Page No 72:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"question-5\"><\/span>Question 5:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>The following table gives the daily income of ten workers in a factory. Find the arithmetic mean.<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"144\">\n<p><em>Workers<\/em><\/p>\n<\/td>\n<td width=\"43\">\n<p>A<\/p>\n<\/td>\n<td width=\"42\">\n<p>B<\/p>\n<\/td>\n<td width=\"42\">\n<p>C<\/p>\n<\/td>\n<td width=\"42\">\n<p>D<\/p>\n<\/td>\n<td width=\"42\">\n<p>E<\/p>\n<\/td>\n<td width=\"42\">\n<p>F<\/p>\n<\/td>\n<td width=\"42\">\n<p>G<\/p>\n<\/td>\n<td width=\"42\">\n<p>H<\/p>\n<\/td>\n<td width=\"42\">\n<p>I<\/p>\n<\/td>\n<td width=\"42\">\n<p>J<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"144\">\n<p><em>Daily Income (in Rs)<\/em><\/p>\n<\/td>\n<td width=\"43\">\n<p>120<\/p>\n<\/td>\n<td width=\"42\">\n<p>150<\/p>\n<\/td>\n<td width=\"42\">\n<p>180<\/p>\n<\/td>\n<td width=\"42\">\n<p>200<\/p>\n<\/td>\n<td width=\"42\">\n<p>250<\/p>\n<\/td>\n<td width=\"42\">\n<p>300<\/p>\n<\/td>\n<td width=\"42\">\n<p>220<\/p>\n<\/td>\n<td width=\"42\">\n<p>350<\/p>\n<\/td>\n<td width=\"42\">\n<p>370<\/p>\n<\/td>\n<td width=\"42\">\n<p>260<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-7\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<table>\n<tbody>\n<tr>\n<td width=\"85\">\n<p><b><strong>Workers<\/strong><\/b><\/p>\n<\/td>\n<td width=\"242\">\n<p><b><strong>Daily Income (in Rs)<\/strong><\/b><\/p>\n<p><b><strong>(<em>X<\/em>)<\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"85\">\n<p>A<\/p>\n<\/td>\n<td width=\"242\">\n<p>120<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"85\">\n<p>B<\/p>\n<\/td>\n<td width=\"242\">\n<p>150<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"85\">\n<p>C<\/p>\n<\/td>\n<td width=\"242\">\n<p>180<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"85\">\n<p>D<\/p>\n<\/td>\n<td width=\"242\">\n<p>200<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"85\">\n<p>E<\/p>\n<\/td>\n<td width=\"242\">\n<p>250<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"85\">\n<p>F<\/p>\n<\/td>\n<td width=\"242\">\n<p>300<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"85\">\n<p>G<\/p>\n<\/td>\n<td width=\"242\">\n<p>220<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"85\">\n<p>H<\/p>\n<\/td>\n<td width=\"242\">\n<p>350<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"85\">\n<p>I<\/p>\n<\/td>\n<td width=\"242\">\n<p>370<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"85\">\n<p>J<\/p>\n<\/td>\n<td width=\"242\">\n<p>260<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"85\">\n<p>Total<\/p>\n<\/td>\n<td width=\"242\">&nbsp;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p><em>N<\/em>&nbsp;= 10<\/p>\n<p>Arithmetic mean = Rs 240<\/p>\n<h4><span class=\"ez-toc-section\" id=\"page-no-72-5\"><\/span>Page No 72:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"question-6\"><\/span>Question 6:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Following information pertains to the daily income of 150 families. Calculate the arithmetic mean.<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"118\">\n<p><em>Income (in Rs)<\/em><\/p>\n<\/td>\n<td width=\"148\">\n<p><em>Number of families<\/em><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"118\">\n<p>More than 75<\/p>\n<\/td>\n<td width=\"148\">\n<p>150<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"118\">\n<p>More than 85<\/p>\n<\/td>\n<td width=\"148\">\n<p>140<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"118\">\n<p>More than 95<\/p>\n<\/td>\n<td width=\"148\">\n<p>115<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"118\">\n<p>More than 105<\/p>\n<\/td>\n<td width=\"148\">\n<p>95<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"118\">\n<p>More than 115<\/p>\n<\/td>\n<td width=\"148\">\n<p>70<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"118\">\n<p>More than 125<\/p>\n<\/td>\n<td width=\"148\">\n<p>60<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"118\">\n<p>More than 135<\/p>\n<\/td>\n<td width=\"148\">\n<p>40<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"118\">\n<p>More than 145<\/p>\n<\/td>\n<td width=\"148\">\n<p>25<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-8\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<table>\n<tbody>\n<tr>\n<td width=\"139\">\n<p><b><strong>Income<\/strong><\/b><\/p>\n<\/td>\n<td width=\"145\">\n<p><b><strong>No. of families<\/strong><\/b><\/p>\n<\/td>\n<td width=\"132\">\n<p><b><strong>Frequency<\/strong><\/b><\/p>\n<\/td>\n<td width=\"132\">\n<p><b><strong>Mid Value<\/strong><\/b><\/p>\n<\/td>\n<td width=\"155\">\n<p><b><strong><em>fm<\/em><\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p><b><strong>Class Interval<\/strong><\/b><\/p>\n<\/td>\n<td width=\"145\">\n<p><b><strong>(<em>CF<\/em>)<\/strong><\/b><\/p>\n<\/td>\n<td width=\"132\">\n<p><b><strong>(<em>f<\/em>)<\/strong><\/b><\/p>\n<\/td>\n<td width=\"132\">\n<p><b><strong><em>(m)<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"155\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>75 \u2013 85<\/p>\n<\/td>\n<td width=\"145\">\n<p>150<\/p>\n<\/td>\n<td width=\"132\">\n<p>150 \u2013 140 = 10<\/p>\n<\/td>\n<td width=\"132\">\n<p>80<\/p>\n<\/td>\n<td width=\"155\">\n<p>800<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>85 \u2013 95<\/p>\n<\/td>\n<td width=\"145\">\n<p>140<\/p>\n<\/td>\n<td width=\"132\">\n<p>140 \u2013 115 = 25<\/p>\n<\/td>\n<td width=\"132\">\n<p>90<\/p>\n<\/td>\n<td width=\"155\">\n<p>2250<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>95 \u2013 105<\/p>\n<\/td>\n<td width=\"145\">\n<p>115<\/p>\n<\/td>\n<td width=\"132\">\n<p>115 \u2013 95 = 20<\/p>\n<\/td>\n<td width=\"132\">\n<p>100<\/p>\n<\/td>\n<td width=\"155\">\n<p>2000<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>105 \u2013 115<\/p>\n<\/td>\n<td width=\"145\">\n<p>95<\/p>\n<\/td>\n<td width=\"132\">\n<p>95 \u2013 70 = 25<\/p>\n<\/td>\n<td width=\"132\">\n<p>110<\/p>\n<\/td>\n<td width=\"155\">\n<p>2750<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>115 \u2013 125<\/p>\n<\/td>\n<td width=\"145\">\n<p>70<\/p>\n<\/td>\n<td width=\"132\">\n<p>70 \u2013 60 = 10<\/p>\n<\/td>\n<td width=\"132\">\n<p>120<\/p>\n<\/td>\n<td width=\"155\">\n<p>1200<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>125 \u2013 135<\/p>\n<\/td>\n<td width=\"145\">\n<p>60<\/p>\n<\/td>\n<td width=\"132\">\n<p>60 \u2013 40 = 20<\/p>\n<\/td>\n<td width=\"132\">\n<p>130<\/p>\n<\/td>\n<td width=\"155\">\n<p>2600<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>135 \u2013 145<\/p>\n<\/td>\n<td width=\"145\">\n<p>40<\/p>\n<\/td>\n<td width=\"132\">\n<p>40 \u2013 25 = 15<\/p>\n<\/td>\n<td width=\"132\">\n<p>140<\/p>\n<\/td>\n<td width=\"155\">\n<p>2100<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>145 \u2013 155<\/p>\n<\/td>\n<td width=\"145\">\n<p>25<\/p>\n<\/td>\n<td width=\"132\">\n<p>25<\/p>\n<\/td>\n<td width=\"132\">\n<p>150<\/p>\n<\/td>\n<td width=\"155\">\n<p>3750<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>Total<\/p>\n<\/td>\n<td width=\"145\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"132\">&nbsp;<\/td>\n<td width=\"132\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"155\">&nbsp;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>= Rs 116.33<\/p>\n<h3><strong><br style=\"font-weight: 400;\"><br style=\"font-weight: 400;\"><\/strong><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"page-no-73\"><\/span>Page No 73:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"question-7\"><\/span>Question 7:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>The size of land holdings of 380 families in a village is given below. Find the median size of land holdings.<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"215\">\n<p><em>Size of Land Holdings (in acres)<\/em><\/p>\n<\/td>\n<td width=\"109\">\n<p>Less than 100<\/p>\n<\/td>\n<td width=\"84\">\n<p>100 \u2013 200<\/p>\n<\/td>\n<td width=\"84\">\n<p>200 \u2013 300<\/p>\n<\/td>\n<td width=\"84\">\n<p>300 \u2013 400<\/p>\n<\/td>\n<td width=\"117\">\n<p>400 and above<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"215\">\n<p><em>Number of families<\/em><\/p>\n<\/td>\n<td width=\"109\">\n<p>40<\/p>\n<\/td>\n<td width=\"84\">\n<p>89<\/p>\n<\/td>\n<td width=\"84\">\n<p>148<\/p>\n<\/td>\n<td width=\"84\">\n<p>64<\/p>\n<\/td>\n<td width=\"117\">\n<p>39<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-9\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<table>\n<tbody>\n<tr>\n<td width=\"170\">\n<p><b><strong>Size of Land Holdings<\/strong><\/b><\/p>\n<p><b><strong>Class Interval<\/strong><\/b><\/p>\n<\/td>\n<td width=\"125\">\n<p><b><strong>No. of Families<\/strong><\/b><\/p>\n<p>&nbsp;<\/p>\n<p><b><strong>(<em>f<\/em>)<\/strong><\/b><\/p>\n<\/td>\n<td width=\"199\">\n<p><b><strong>Cumulative Frequency<\/strong><\/b><\/p>\n<p><b><strong>(<em>CF)<\/em><\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"170\">\n<p>0 \u2013 100<\/p>\n<\/td>\n<td width=\"125\">\n<p>40<\/p>\n<\/td>\n<td width=\"199\">\n<p>40<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"170\">\n<p>100 \u2013 200<\/p>\n<\/td>\n<td width=\"125\">\n<p>89<\/p>\n<\/td>\n<td width=\"199\">\n<p>129<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"170\">\n<p>200 \u2013 300<\/p>\n<\/td>\n<td width=\"125\">\n<p>148<\/p>\n<\/td>\n<td width=\"199\">\n<p>277<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"170\">\n<p>300 \u2013 400<\/p>\n<\/td>\n<td width=\"125\">\n<p>64<\/p>\n<\/td>\n<td width=\"199\">\n<p>341<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"170\">\n<p>400 \u2013 500<\/p>\n<\/td>\n<td width=\"125\">\n<p>39<\/p>\n<\/td>\n<td width=\"199\">\n<p>380<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"170\">\n<p>Total<\/p>\n<\/td>\n<td width=\"125\">&nbsp;<\/td>\n<td width=\"199\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>So, the Median class = Size of&nbsp;&nbsp;item = 190<sup>th<\/sup>&nbsp;item<\/p>\n<p>&nbsp;<\/p>\n<p>190<sup>th<\/sup>&nbsp;item lies in the 129<sup>th<\/sup>&nbsp;cumulative frequency and the corresponding class interval is 200 \u2013 300.<\/p>\n<p>The median size of land holdings = 241.22 acres<\/p>\n<h4><span class=\"ez-toc-section\" id=\"page-no-73-2\"><\/span>Page No 73:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"question-8\"><\/span>Question 8:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>The following series relates to the daily income of workers employed in a firm. Compute (a) highest income of lowest 50% workers (b) minimum income earned by the top 25% workers and (c) maximum income earned by lowest 25% workers.<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"151\">\n<p><em>Daily Income (in Rs)<\/em><\/p>\n<\/td>\n<td width=\"66\">\n<p>10 \u2013 14<\/p>\n<\/td>\n<td width=\"66\">\n<p>15 \u2013 19<\/p>\n<\/td>\n<td width=\"66\">\n<p>20 \u2013 24<\/p>\n<\/td>\n<td width=\"66\">\n<p>25 \u2013 29<\/p>\n<\/td>\n<td width=\"66\">\n<p>30 \u2013 34<\/p>\n<\/td>\n<td width=\"69\">\n<p>35 \u2013 39<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"151\">\n<p><em>Number of workers<\/em><\/p>\n<\/td>\n<td width=\"66\">\n<p>5<\/p>\n<\/td>\n<td width=\"66\">\n<p>10<\/p>\n<\/td>\n<td width=\"66\">\n<p>15<\/p>\n<\/td>\n<td width=\"66\">\n<p>20<\/p>\n<\/td>\n<td width=\"66\">\n<p>10<\/p>\n<\/td>\n<td width=\"69\">\n<p>5<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>(Hint: Compute median, lower quartile and upper quartile)<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-10\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<table>\n<tbody>\n<tr>\n<td width=\"152\">\n<p><b><strong>Daily Income<\/strong><\/b><\/p>\n<p><b><strong>(in Rs)<\/strong><\/b><\/p>\n<p><b><strong>Class Interval<\/strong><\/b><\/p>\n<\/td>\n<td width=\"120\">\n<p><b><strong>No. of Workers<\/strong><\/b><\/p>\n<p><b><strong>(<em>f<\/em>)<\/strong><\/b><\/p>\n<\/td>\n<td width=\"224\">\n<p><b><strong>Cumulative frequency<\/strong><\/b><\/p>\n<p><b><strong><em>(CF)<\/em><\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"152\">\n<p>9.5 \u2013 14.5<\/p>\n<\/td>\n<td width=\"120\">\n<p>5<\/p>\n<\/td>\n<td width=\"224\">\n<p>5<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"152\">\n<p>14.5 \u2013 19.5<\/p>\n<\/td>\n<td width=\"120\">\n<p>10<\/p>\n<\/td>\n<td width=\"224\">\n<p>15<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"152\">\n<p>19.5 \u2013 24.5<\/p>\n<\/td>\n<td width=\"120\">\n<p>15<\/p>\n<\/td>\n<td width=\"224\">\n<p>30<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"152\">\n<p>24.5 \u2013 29.5<\/p>\n<\/td>\n<td width=\"120\">\n<p>20<\/p>\n<\/td>\n<td width=\"224\">\n<p>50<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"152\">\n<p>29.5 \u2013 34.5<\/p>\n<\/td>\n<td width=\"120\">\n<p>10<\/p>\n<\/td>\n<td width=\"224\">\n<p>60<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"152\">\n<p>34.5 \u2013 39.5<\/p>\n<\/td>\n<td width=\"120\">\n<p>5<\/p>\n<\/td>\n<td width=\"224\">\n<p>65<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"152\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"120\">&nbsp;<\/td>\n<td width=\"224\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>(a) Highest income of lowest 50% workers<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>32.5<sup>th<\/sup>&nbsp;item lies in the 50<sup>th<\/sup>&nbsp;cumulative frequency and the corresponding class interval is 24.5 \u2013 29.5.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>(b) Minimum income earned by top 25% workers<br>In order to calculate the minimum income earned by top 25% workers, we need to ascertain&nbsp;<em>Q<\/em><sub>3<\/sub>.<\/p>\n<p>48.75<sup>th<\/sup>&nbsp;item lies in 50<sup>th<\/sup>&nbsp;item and the corresponding class interval is 24.5 \u2013 29.5.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"font-weight: 400;\">(c) Maximum&nbsp; income earned by lowest 25% workers<br>In order to calculate the maximum income earned by lowest 25% workers, we need to ascertain&nbsp;<em>Q<\/em><sub>1<\/sub>.<\/p>\n<p>&nbsp;&nbsp;<\/p>\n<p>16.25<sup>th<\/sup>&nbsp;item lies in the 30<sup>th<\/sup>&nbsp;cumulative frequency and the corresponding class interval is 19.5 \u2013 24.5<\/p>\n<h4><span class=\"ez-toc-section\" id=\"page-no-73-3\"><\/span>Page No 73:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"question-9\"><\/span>Question 9:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>The following table gives production yield in kg. per hectare of wheat of 150 farms in a village. Calculate the mean, median and mode values.<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"127\">\n<p><em>Production yield (kg. per hectare)<\/em><\/p>\n<\/td>\n<td width=\"66\">\n<p>50 \u2013 53<\/p>\n<\/td>\n<td width=\"66\">\n<p>53 \u2013 56<\/p>\n<\/td>\n<td width=\"66\">\n<p>56 \u2013 59<\/p>\n<\/td>\n<td width=\"66\">\n<p>59 \u2013 62<\/p>\n<\/td>\n<td width=\"66\">\n<p>62 \u2013 65<\/p>\n<\/td>\n<td width=\"66\">\n<p>65 \u2013 68<\/p>\n<\/td>\n<td width=\"66\">\n<p>68 \u2013 71<\/p>\n<\/td>\n<td width=\"66\">\n<p>71 \u2013 74<\/p>\n<\/td>\n<td width=\"69\">\n<p>74 \u2013 77<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"127\">\n<p><em>Number of farms<\/em><\/p>\n<\/td>\n<td width=\"66\">\n<p>3<\/p>\n<\/td>\n<td width=\"66\">\n<p>8<\/p>\n<\/td>\n<td width=\"66\">\n<p>14<\/p>\n<\/td>\n<td width=\"66\">\n<p>30<\/p>\n<\/td>\n<td width=\"66\">\n<p>36<\/p>\n<\/td>\n<td width=\"66\">\n<p>28<\/p>\n<\/td>\n<td width=\"66\">\n<p>16<\/p>\n<\/td>\n<td width=\"66\">\n<p>10<\/p>\n<\/td>\n<td width=\"69\">\n<p>5<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-11\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>(i) Mean<\/p>\n<table width=\"602\">\n<tbody>\n<tr>\n<td width=\"117\">\n<p><b><strong>Production Yield<\/strong><\/b><\/p>\n<\/td>\n<td width=\"121\">\n<p><b><strong>No. of farms<\/strong><\/b><\/p>\n<\/td>\n<td width=\"75\">\n<p><b><strong>Mid value<\/strong><\/b><\/p>\n<\/td>\n<td width=\"73\">\n<p><b><strong><em>A<\/em>&nbsp;= 63.5<\/strong><\/b><\/p>\n<\/td>\n<td width=\"107\">&nbsp;<\/td>\n<td width=\"109\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td width=\"117\">\n<p>50 \u2013 53<\/p>\n<\/td>\n<td width=\"121\">\n<p>3<\/p>\n<\/td>\n<td width=\"75\">\n<p>51.5<\/p>\n<\/td>\n<td width=\"73\">\n<p>\u201312<\/p>\n<\/td>\n<td width=\"107\">\n<p>\u20134<\/p>\n<\/td>\n<td width=\"109\">\n<p>\u201312<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"117\">\n<p>53 \u2013 56<\/p>\n<\/td>\n<td width=\"121\">\n<p>8<\/p>\n<\/td>\n<td width=\"75\">\n<p>54.5<\/p>\n<\/td>\n<td width=\"73\">\n<p>\u20139<\/p>\n<\/td>\n<td width=\"107\">\n<p>\u20133<\/p>\n<\/td>\n<td width=\"109\">\n<p>\u201324<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"117\">\n<p>56 \u2013 59<\/p>\n<\/td>\n<td width=\"121\">\n<p>14<\/p>\n<\/td>\n<td width=\"75\">\n<p>57.5<\/p>\n<\/td>\n<td width=\"73\">\n<p>\u20136<\/p>\n<\/td>\n<td width=\"107\">\n<p>\u20132<\/p>\n<\/td>\n<td width=\"109\">\n<p>\u201328<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"117\">\n<p>59 \u2013 62<\/p>\n<\/td>\n<td width=\"121\">\n<p>30<\/p>\n<\/td>\n<td width=\"75\">\n<p>60.5<\/p>\n<\/td>\n<td width=\"73\">\n<p>\u20133<\/p>\n<\/td>\n<td width=\"107\">\n<p>\u20131<\/p>\n<\/td>\n<td width=\"109\">\n<p>\u201330<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"117\">\n<p>62 \u2013 65<\/p>\n<\/td>\n<td width=\"121\">\n<p>36<\/p>\n<\/td>\n<td width=\"75\">\n<p>63.5<\/p>\n<\/td>\n<td width=\"73\">\n<p>0<\/p>\n<\/td>\n<td width=\"107\">\n<p>0<\/p>\n<\/td>\n<td width=\"109\">\n<p>0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"117\">\n<p>65 \u2013 68<\/p>\n<\/td>\n<td width=\"121\">\n<p>28<\/p>\n<\/td>\n<td width=\"75\">\n<p>66.5<\/p>\n<\/td>\n<td width=\"73\">\n<p>+3<\/p>\n<\/td>\n<td width=\"107\">\n<p>+1<\/p>\n<\/td>\n<td width=\"109\">\n<p>28<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"117\">\n<p>68 \u2013 71<\/p>\n<\/td>\n<td width=\"121\">\n<p>16<\/p>\n<\/td>\n<td width=\"75\">\n<p>69.5<\/p>\n<\/td>\n<td width=\"73\">\n<p>+6<\/p>\n<\/td>\n<td width=\"107\">\n<p>+2<\/p>\n<\/td>\n<td width=\"109\">\n<p>32<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"117\">\n<p>71 \u2013 74<\/p>\n<\/td>\n<td width=\"121\">\n<p>10<\/p>\n<\/td>\n<td width=\"75\">\n<p>72.5<\/p>\n<\/td>\n<td width=\"73\">\n<p>+9<\/p>\n<\/td>\n<td width=\"107\">\n<p>+3<\/p>\n<\/td>\n<td width=\"109\">\n<p>30<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"117\">\n<p>74 \u2013 77<\/p>\n<\/td>\n<td width=\"121\">\n<p>5<\/p>\n<\/td>\n<td width=\"75\">\n<p>75.5<\/p>\n<\/td>\n<td width=\"73\">\n<p>+12<\/p>\n<\/td>\n<td width=\"107\">\n<p>+4<\/p>\n<\/td>\n<td width=\"109\">\n<p>20<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"117\">\n<p>Total<\/p>\n<\/td>\n<td width=\"121\">&nbsp;<\/td>\n<td width=\"75\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"73\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"107\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"109\">&nbsp;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>= 63.5 + 0.32<\/p>\n<p>= 63.82 kg per hectare<\/p>\n<p>&nbsp;<\/p>\n<p>(ii) Median<\/p>\n<p>&nbsp;<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"122\">\n<p><b><strong>Class Interval<\/strong><\/b><\/p>\n<\/td>\n<td width=\"108\">\n<p><b><strong>Frequency<\/strong><\/b><\/p>\n<p><b><strong>(<em>f<\/em>)<\/strong><\/b><\/p>\n<\/td>\n<td width=\"97\">\n<p><b><strong><em>CF<\/em><\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"122\">\n<p>50 \u2013 53<\/p>\n<\/td>\n<td width=\"108\">\n<p>3<\/p>\n<\/td>\n<td width=\"97\">\n<p>3<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"122\">\n<p>53 \u2013 56<\/p>\n<\/td>\n<td width=\"108\">\n<p>8<\/p>\n<\/td>\n<td width=\"97\">\n<p>11<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"122\">\n<p>56 \u2013 59<\/p>\n<\/td>\n<td width=\"108\">\n<p>14<\/p>\n<\/td>\n<td width=\"97\">\n<p>25<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"122\">\n<p>59 \u2013 62<\/p>\n<\/td>\n<td width=\"108\">\n<p>30<\/p>\n<\/td>\n<td width=\"97\">\n<p>55<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"122\">\n<p>62 \u2013 65<\/p>\n<\/td>\n<td width=\"108\">\n<p>36<\/p>\n<\/td>\n<td width=\"97\">\n<p>91<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"122\">\n<p>65 \u2013 68<\/p>\n<\/td>\n<td width=\"108\">\n<p>28<\/p>\n<\/td>\n<td width=\"97\">\n<p>119<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"122\">\n<p>68 \u2013 71<\/p>\n<\/td>\n<td width=\"108\">\n<p>16<\/p>\n<\/td>\n<td width=\"97\">\n<p>135<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"122\">\n<p>71 \u2013 74<\/p>\n<\/td>\n<td width=\"108\">\n<p>10<\/p>\n<\/td>\n<td width=\"97\">\n<p>145<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"122\">\n<p>74 \u2013 77<\/p>\n<\/td>\n<td width=\"108\">\n<p>5<\/p>\n<\/td>\n<td width=\"97\">\n<p>150<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"122\">\n<p>Total<\/p>\n<\/td>\n<td width=\"108\">&nbsp;<\/td>\n<td width=\"97\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>75<sup>th<\/sup>&nbsp;item lies in the 91<sup>st<\/sup>&nbsp;cumulative frequency and the corresponding class interval is 62 \u2013 65.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;(iii) Mode<\/p>\n<p>&nbsp;<\/p>\n<table>\n<tbody>\n<tr>\n<td colspan=\"7\" width=\"530\">\n<p><b><strong>Grouping Table<\/strong><\/b><\/p>\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"1\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"0\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"116\">\n<p><b><strong>Class Interval<\/strong><\/b><\/p>\n<\/td>\n<td width=\"72\">\n<p><b><strong>I<\/strong><\/b><\/p>\n<\/td>\n<td width=\"78\">\n<p><b><strong>II<\/strong><\/b><\/p>\n<\/td>\n<td width=\"60\">\n<p><b><strong>III<\/strong><\/b><\/p>\n<\/td>\n<td width=\"66\">\n<p><b><strong>IV<\/strong><\/b><\/p>\n<\/td>\n<td width=\"72\">\n<p><b><strong>V<\/strong><\/b><\/p>\n<\/td>\n<td colspan=\"2\" width=\"67\">\n<p><b><strong>VI<\/strong><\/b><\/p>\n<\/td>\n<td width=\"0\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"116\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"72\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"78\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"60\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"72\">\n<p>&nbsp;<\/p>\n<\/td>\n<td colspan=\"2\" width=\"67\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"0\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"2\" width=\"116\">\n<p>50 \u2013 53<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"72\">\n<p>3<\/p>\n<\/td>\n<td width=\"78\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"60\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"72\">\n<p>&nbsp;<\/p>\n<\/td>\n<td colspan=\"2\" width=\"67\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"2\" width=\"78\">\n<p>11<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"60\">\n<p>22<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"66\">\n<p>25<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"72\">\n<p>52<\/p>\n<\/td>\n<td colspan=\"2\" rowspan=\"2\" width=\"67\">&nbsp;<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"2\" width=\"116\">\n<p>53 \u2013 56<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"72\">\n<p>8<\/p>\n<\/td>\n<td>&nbsp;<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td width=\"78\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"60\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"72\">\n<p>&nbsp;<\/p>\n<\/td>\n<td colspan=\"2\" width=\"67\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"2\" width=\"116\">\n<p>56 \u2013 59<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"72\">\n<p>14<\/p>\n<\/td>\n<td width=\"78\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"60\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"72\">\n<p>&nbsp;<\/p>\n<\/td>\n<td colspan=\"2\" width=\"67\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"2\" width=\"78\">\n<p>44<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"60\">&nbsp;<\/td>\n<td rowspan=\"2\" width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"72\">&nbsp;<\/td>\n<td colspan=\"2\" rowspan=\"2\" width=\"67\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"2\" width=\"116\">\n<p>59 \u2013 62<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"72\">\n<p>30<\/p>\n<\/td>\n<td>&nbsp;<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td width=\"78\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"60\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"72\">\n<p>&nbsp;<\/p>\n<\/td>\n<td colspan=\"2\" width=\"67\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"2\" width=\"116\">\n<p>62 \u2013 65<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"72\">&nbsp;<\/td>\n<td width=\"78\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"60\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"72\">\n<p>&nbsp;<\/p>\n<\/td>\n<td colspan=\"2\" width=\"67\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"2\" width=\"78\">&nbsp;<\/td>\n<td rowspan=\"2\" width=\"60\">\n<p>44<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"72\">&nbsp;<\/td>\n<td colspan=\"2\" rowspan=\"2\" width=\"67\">\n<p>54<\/p>\n<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"2\" width=\"116\">\n<p>65 \u2013 68<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"72\">\n<p>28<\/p>\n<\/td>\n<td>&nbsp;<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td width=\"78\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"60\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"72\">\n<p>&nbsp;<\/p>\n<\/td>\n<td colspan=\"2\" width=\"67\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"2\" width=\"116\">\n<p>68 \u2013 71<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"72\">\n<p>16<\/p>\n<\/td>\n<td width=\"78\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"60\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"72\">\n<p>&nbsp;<\/p>\n<\/td>\n<td colspan=\"2\" width=\"67\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"2\" width=\"78\">\n<p>26<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"60\">\n<p>15<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"66\">\n<p>31<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"72\">\n<p>&nbsp;<\/p>\n<\/td>\n<td colspan=\"2\" rowspan=\"2\" width=\"67\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"2\" width=\"116\">\n<p>71 \u2013 74<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"72\">\n<p>10<\/p>\n<\/td>\n<td>&nbsp;<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td width=\"78\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"60\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"72\">\n<p>&nbsp;<\/p>\n<\/td>\n<td colspan=\"2\" width=\"67\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"0\">&nbsp;<\/td>\n<\/tr>\n<tr>\n<td width=\"116\">\n<p>74 \u2013 77<\/p>\n<\/td>\n<td width=\"72\">\n<p>5<\/p>\n<\/td>\n<td width=\"78\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"60\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"72\">\n<p>&nbsp;<\/p>\n<\/td>\n<td colspan=\"2\" width=\"67\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"0\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"116\">&nbsp;<\/td>\n<td width=\"72\">&nbsp;<\/td>\n<td width=\"78\">&nbsp;<\/td>\n<td width=\"60\">&nbsp;<\/td>\n<td width=\"66\">&nbsp;<\/td>\n<td width=\"72\">&nbsp;<\/td>\n<td width=\"66\">&nbsp;<\/td>\n<td width=\"1\">&nbsp;<\/td>\n<td width=\"0\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;&nbsp;<\/p>\n<p><b><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Analysis Table<\/strong><\/b><\/p>\n<p>&nbsp;<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"70\">\n<p><b><strong>Column<\/strong><\/b><\/p>\n<\/td>\n<td width=\"69\">\n<p><b><strong>50 \u2013 53<\/strong><\/b><\/p>\n<\/td>\n<td width=\"66\">\n<p><b><strong>53 \u2013 56<\/strong><\/b><\/p>\n<\/td>\n<td width=\"66\">\n<p><b><strong>56 \u2013 59<\/strong><\/b><\/p>\n<\/td>\n<td width=\"66\">\n<p><b><strong>59 \u2013 62<\/strong><\/b><\/p>\n<\/td>\n<td width=\"66\">\n<p><b><strong>62 \u2013 65<\/strong><\/b><\/p>\n<\/td>\n<td width=\"66\">\n<p><b><strong>65 \u2013 68<\/strong><\/b><\/p>\n<\/td>\n<td width=\"66\">\n<p><b><strong>68 \u2013 71<\/strong><\/b><\/p>\n<\/td>\n<td width=\"66\">\n<p><b><strong>71 \u2013 74<\/strong><\/b><\/p>\n<\/td>\n<td width=\"69\">\n<p><b><strong>74 \u2013 77<\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"70\">\n<p><b><strong>I<\/strong><\/b><\/p>\n<\/td>\n<td width=\"69\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u221a<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"69\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"70\">\n<p><b><strong>II<\/strong><\/b><\/p>\n<\/td>\n<td width=\"69\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u221a<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u221a<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"69\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"70\">\n<p><b><strong>III<\/strong><\/b><\/p>\n<\/td>\n<td width=\"69\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u221a<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u221a<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"69\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"70\">\n<p><b><strong>IV<\/strong><\/b><\/p>\n<\/td>\n<td width=\"69\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u221a<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u221a<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u221a<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"69\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"70\">\n<p><b><strong>V<\/strong><\/b><\/p>\n<\/td>\n<td width=\"69\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u221a<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u221a<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u221a<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"69\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"70\">\n<p><b><strong>VI<\/strong><\/b><\/p>\n<\/td>\n<td width=\"69\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u221a<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u221a<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u221a<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"66\">\n<p>&nbsp;<\/p>\n<\/td>\n<td width=\"69\">\n<p>&nbsp;<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"70\">\n<p><b><strong>Total<\/strong><\/b><\/p>\n<\/td>\n<td width=\"69\">\n<p>\u2013<\/p>\n<\/td>\n<td width=\"66\">\n<p>\u2013<\/p>\n<\/td>\n<td width=\"66\">\n<p>1<\/p>\n<\/td>\n<td width=\"66\">\n<p>3<\/p>\n<\/td>\n<td width=\"66\">\n<p>6<\/p>\n<\/td>\n<td width=\"66\">\n<p>3<\/p>\n<\/td>\n<td width=\"66\">\n<p>1<\/p>\n<\/td>\n<td width=\"66\">\n<p><b><strong>\u2013<\/strong><\/b><\/p>\n<\/td>\n<td width=\"69\">\n<p><b><strong>\u2013<\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>Modal class = 62 \u2013 65<\/p>\n<p>&nbsp;<\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-other-chapters-of-ncert-solutions-for-class-11-statistics\"><\/span><strong>Access Other Chapters of <\/strong><strong style=\"background-color: initial;\">NCERT <\/strong><strong style=\"background-color: initial;\">Solutions For Class 11 Statistics <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>You can download the PDF of NCERT Solutions For Class 11 Statistics Other Chapters:<\/p>\n<ul>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-1\/\"><strong>Chapter-1 Introduction<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-2\/\"><strong>Chapter-2 Collection Of Data<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-3\/\"><b>Chapter-3 organization Of Data<\/b><\/a><\/li>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-4\/\"><strong>Chapter-4 Presentation of Data<\/strong><\/a><\/li>\n<li><strong>Chapter-6 Measures of Dispersion<\/strong><\/li>\n<li><strong>Chapter-7 Correlation<\/strong><\/li>\n<li><strong>Chapter-8 Index Numbers<\/strong><\/li>\n<li><strong>Chapter-9 Use of Statistical Tool<\/strong><\/li>\n<\/ul>\n<p><strong>We have provided all the important above in the article regarding the <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\">CBSE <\/a>NCERT Solutions For Class 11 Statistics Chapter 5. If you have any queries, you can mention them in the comment section.<\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"faq-on-ncert-solutions-for-class-11-statistics-chapter-5\"><\/span><strong>FAQ on<\/strong> <b>NCERT Solutions For Class 11 Statistics Chapter 5<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1627376429633\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"find-the-mean-median-and-mode-for-the-following-list-of-values-13-18-13-14-13-16-14-21-13\"><\/span><strong>Find the mean, median, and mode for the following list of values:<\/strong> 13, 18, 13, 14, 13, 16, 14, 21, 13.<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The mean is the usual average is,\u00a0<br \/>(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) \u00f7 9 = 15<br \/>The median is the middle value, so first, we have to rewrite the list in numerical order:<br \/>13, 13, 13, 13, 14, 14, 16, 18, 21<br \/>There are nine numbers in the list, so the size is an odd number.\u00a0<br \/>13, 13, 13, 13, 14, 14, 16, 18, 21<br \/>Hence, the median is 14.<br \/>A mode is a number that is repeated more times.<br \/>Hence, 13 is the mode.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1627376501472\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-is-the-difference-between-mean-and-median\"><\/span><strong>What is the difference between Mean and Median?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Mean is the average of all the values given in the set. On the contrary, the median is the exact middle number when a list of values will be written in order. So both are completely different and they have unique advantages in the field of Statistics.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1627376697449\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-purposes-of-average-in-the-statistical-method\"><\/span>What are the purposes of average in the statistical method?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The purposes of average are the statistical method are:<br \/>Brief description<br \/>Comparison<br \/>Formulation of policies<br \/>Statistical analysis<br \/>One value of all<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1627376714471\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-different-kinds-of-statistical-averages\"><\/span><strong>What are the different kinds of statistical averages?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The different kinds of statistical averages are:<br \/>Mathematical average<br \/>Positional average<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1627376738453\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-two-methods-that-can-calculate-the-simple-arithmetic-mean-in-case-of-an-individual-series\"><\/span><strong>What are the two methods that can calculate the simple arithmetic mean in case\u00a0<\/strong><br><strong>of an individual series.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The two methods that can calculate the simple arithmetic mean in the case of an individual series are:<br \/>\u00a0Direct method<br \/>\u00a0Shortcut method<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1627376761027\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-methods-of-calculating-the-simple-arithmetic-mean\"><\/span><strong>What are the methods of calculating the simple arithmetic mean?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The methods of calculating the simple arithmetic mean are:<br \/>\u00a0Individual series<br \/>\u00a0Discrete series<br \/>\u00a0Frequency distribution<br \/>\u00a0<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 11 Statistics Chapter 5: We offer students with an excellent understanding of statistics. They offer up-to-date and improved solutions, with content prepared by subject matter specialists with years of experience. With the help of NCERT Solutions For Class 11 Statistics Chapter 5, students can obtain information as well as good grades. &#8230; <a title=\"Class 11 Statistics NCERT Solutions for Chapter 5 2026: Download Free PDF\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/\" aria-label=\"More on Class 11 Statistics NCERT Solutions for Chapter 5 2026: Download Free PDF\">Read more<\/a><\/p>\n","protected":false},"author":250,"featured_media":108948,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2934,73694],"tags":[3570,76237,76483],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/108932"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/250"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=108932"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/108932\/revisions"}],"predecessor-version":[{"id":574300,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/108932\/revisions\/574300"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/108948"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=108932"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=108932"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=108932"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}