{"id":107096,"date":"2021-08-07T18:25:00","date_gmt":"2021-08-07T12:55:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=107096"},"modified":"2021-08-07T18:25:25","modified_gmt":"2021-08-07T12:55:25","slug":"ncert-solutions-for-class-11-statistics-chapter-6","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/","title":{"rendered":"Class 11 Statistics NCERT Solutions for Chapter 6 2021: Download PDF"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-109430\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/07\/Statistics-chapter6-1.jpg\" alt=\"NCERT Solutions for Class 11 Statistics Chapter 6\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/07\/Statistics-chapter6-1.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/07\/Statistics-chapter6-1-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>NCERT Solutions for Class 11 Statistics Chapter 6<\/strong>: We are always concerned with the students&#8217; development. <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 6 enable students to comprehend each topic in depth, resulting in good knowledge and the development of expertise in that topic, chapter, or subject. The resources were created by a group of subject experts.\u00a0<\/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-69e791d816a13\" 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\" 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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-6\/#download-free-pdf-for-ncert-solutions-for-class-11-statistics-chapter-6\" title=\"Download Free PDF For NCERT Solutions For class 11 Statistics Chapter 6\u00a0\">Download Free PDF For NCERT Solutions For class 11 Statistics Chapter 6\u00a0<\/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-6\/#ncert-solutions-for-class-11-statistics-chapter-6-overview\" title=\"NCERT Solutions for Class 11 Statistics Chapter 6: Overview\">NCERT Solutions for Class 11 Statistics Chapter 6: 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-6\/#access-ncert-solutions-for-class-11-statistics-chapter-6\" title=\"Access NCERT Solutions For Class 11 Statistics Chapter 6\">Access NCERT Solutions For Class 11 Statistics Chapter 6<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-6\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-7\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#question-2\" title=\"Question 2:\">Question 2:<\/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-6\/#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-9\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-10\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-11\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-12\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-13\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-14\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-15\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-16\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-17\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-18\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-19\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-20\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-21\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-22\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#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-23\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#question-10\" title=\"Question 10:\">Question 10:<\/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-6\/#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-25\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#page-no-90\" title=\"Page No 90:\">Page No 90:<\/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-6\/#question-11\" title=\"Question 11:\">Question 11:<\/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-6\/#answer-11\" title=\"ANSWER:\">ANSWER:<\/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-6\/#question-12\" title=\"Question 12:\">Question 12:<\/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-6\/#answer-12\" 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-30\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#access-other-ncert-chapters-solutions-of-class-11-statistics\" title=\"Access Other NCERT Chapters Solutions of Class 11 Statistics \">Access Other NCERT Chapters Solutions of 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-31\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#faq-frequently-asked-questions-ncert-solutions-for-class-11-statistics-chapter-6\" title=\"FAQ (Frequently Asked Questions): NCERT Solutions for Class 11 Statistics Chapter 6\">FAQ (Frequently Asked Questions): NCERT Solutions for Class 11 Statistics Chapter 6<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-32\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#what-are-the-steps-involved-in-the-construction-of-the-lorenz-curve\" title=\"What are the steps involved in the construction of the Lorenz Curve?\">What are the steps involved in the construction of the Lorenz Curve?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-33\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#what-are-the-measures-used-for-the-dispersion-of-values\" title=\"What are the measures used for the Dispersion of Values?\">What are the measures used for the Dispersion of Values?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-34\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#define-mean-deviation\" title=\"Define mean deviation.\">Define mean deviation.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-35\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/#what-is-the-standard-deviation\" title=\"What is the standard deviation?\">What is the standard deviation?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"ncert-solutions-for-class-11-statistics-chapter-6-pdf\"><\/span><strong style=\"background-color: initial;\">NCERT Solutions for Class 11 Statistics Chapter 6 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-6.pdf\" target=\"_blank\" rel=\"noopener\">NCERT Solutions For Statistics Class 11 Ch 6<\/a><\/p>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/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-6.pdf\", \"#example1\");<\/script><\/p>\n<h2><span class=\"ez-toc-section\" id=\"download-free-pdf-for-ncert-solutions-for-class-11-statistics-chapter-6\"><\/span><strong>Download Free PDF For NCERT Solutions For class 11 Statistics Chapter 6\u00a0<\/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-6.pdf\" target=\"_blank\" rel=\"noopener\">Click Here<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"ncert-solutions-for-class-11-statistics-chapter-6-overview\"><\/span><strong style=\"background-color: initial;\">NCERT Solutions for Class 11 Statistics Chapter 6: Overview<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Measures of Dispersion<\/strong><\/p>\n<p>\u00a0<strong>Introduction<\/strong><\/p>\n<p>The NCERT Solutions for class 11th chapter 6 teach a new topic of dispersion to the students in this section. The students have already learned several statistical topics such as data collecting, data summarization, tools, and so on. The kids will study about dispersion in this lesson. Our NCERT Solutions explain it with illustrations.<\/p>\n<p><strong>\u00a0Measures Based upon the Spread of Values<\/strong><\/p>\n<p>Students will learn how to use a variety of measures to calculate dispersion based on values in this section. They are the set&#8217;s range, defined as the difference between the set&#8217;s largest and lowest values. The quartile dispersion is the following one. It is the technique of partitioning the entire set into four equal sections in order to eliminate the maximum and minimum values that cause dispersion.<\/p>\n<p><strong>Measures of Dispersion from Average<\/strong><\/p>\n<p>The measures of dispersion in the Statistics Class 11 NCERT Solutions describe the remaining two measures in this part with enough examples. We&#8217;d utilise range and quartile dispersion if we had a set of data.<\/p>\n<p>If the average needs to be calculated, standard deviation and mean deviation should be used instead. The mean deviation can be calculated in a variety of ways, including determining the median using both grouped and ungrouped data. Each concept is also supported by two or more instances.<\/p>\n<p><strong>Absolute and Relative Dispersion of Measures<\/strong><\/p>\n<p>Class 11 Statistics NCERT Solutions Chapter 6 explains another topic. The meaning and explanation of the Coefficient of Mean Deviation were discussed by NCERT Solutions. It also defines the significance of each term in the formula and explains the derived formula.<\/p>\n<p><strong>Lorenz Curve\u00a0<\/strong><\/p>\n<p>NCERT Class 11 Statistics Chapter 6 Measures of Dispersion introduces students to a new concept known as the Lawrence curve. The students have learnt how to measure dispersion using sets, averages, deviations, and other methods. The Lorenz curve is the graph paper curve that represents all of these measurements. The Lorenz Curve must be thoroughly studied by students.<\/p>\n<p>The building of the Lorenz curve was also covered in NCERT Solutions for Class 11 Statistics Chapter 6. Students can understand it as a step-by-step approach involving numerous things to study because it plays such an important function in the field of statistics. These Solutions also include a detailed graphic of these steps of the Lorenz curve to aid understanding.<\/p>\n<p><strong>Conclusion<\/strong><\/p>\n<p>This is the ending part of the chapter. Here the NCERT Solutions Class 11 Statistics Chapter 6 explains the importance of dispersion and the measures, different cases of dispersion like deviations, average, etc with proper examples and exercises also.<\/p>\n<p>An exercise with the 12 Long answer type questions<\/p>\n<p>NCERT Solutions provide a free download for PDF. A group of language experts are available to clarify the doubts of students through live chat.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-ncert-solutions-for-class-11-statistics-chapter-6\"><\/span>Access NCERT Solutions For Class 11 Statistics Chapter 6<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"question-1\"><\/span>Question 1:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>A measure of dispersion is a good supplement to the central value in understanding a frequency distribution. Comment. \u00a0<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>The study of the averages is only one sided distribution story. In order to understand the frequency distribution fully, it is essential to study the variability of the observations. The average measures center of the data whereas the quantum of the variation is measured by the measures of dispersion like range, quartile deviation, mean deviation and Standard Deviation.<\/p>\n<p>For example, if a country has very high income group people and very low income group people, then we can say that the country has large income disparity.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"question-2\"><\/span>Question 2:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Which measure of dispersion is the best and how?<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-2\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Standard Deviation is the best measure of dispersion as it satisfies the most essentials of the good measure of dispersion. The following points make Standard Deviation the best measure of dispersion:<\/p>\n<ol>\n<li>Most of the statistical theory is based on Standard Deviation. It helps to make comparison between variability of two or more sets of data. Also, Standard Deviation helps in testing the significance of random samples and in regression and correlation analysis.<\/li>\n<li>It is based on the values of all the observations. In other words, Standard Deviation makes use of every item in a particular distribution.<\/li>\n<li>Standard Deviation has a precise value and is a well-defined and definite measure of dispersion. That is, it is rigidly defined.<\/li>\n<li>It is independent of the origin.<\/li>\n<li>It is widely used measure of dispersion as all data distribution is nearer to the normal distribution.<\/li>\n<li>It enables algebraic treatment. It has correct mathematical processes in comparison to range, quartile deviation and mean deviation.<\/li>\n<\/ol>\n<h4><span class=\"ez-toc-section\" id=\"question-3\"><\/span>Question 3:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Some measures of dispersion depend upon the spread of values whereas some calculate the\u00a0variation of values from a central value. Do you agree?<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-3\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Yes, it is true that some measures of dispersion depend upon the spread of values, whereas some calculate the variation of values from the central value. The spread of values is determined by the absolute measures of dispersion like Range, Quartile Mean Deviation, and Standard Deviation.<\/p>\n<p>These measures express dispersion in terms of original unit of the series and it cannot be used for the comparison of statistical data having different units. On the other hand, the relative measures of the dispersion calculate the variability of the values from a central value. The relative measure includes coefficient of Range, Mean Deviation and Variation. It is used when the comparison has to be made between two statistical sets. These measures are free from any units.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"question-4\"><\/span>Question 4:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>In a town, 25% of the persons earned more than Rs 45,000 whereas 75% earned more than 18,000. Calculate the absolute and relative values of dispersion.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-4\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><b><strong>Absolute Value of Dispersion<\/strong><\/b><\/p>\n<p><b><strong>Relative Value of Dispersion<\/strong><\/b><\/p>\n<h4><span class=\"ez-toc-section\" id=\"question-5\"><\/span>Question 5:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>The yield of wheat and rice per acre for 10 districts of a state is as under:<\/p>\n<table>\n<tbody>\n<tr>\n<td>District<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>10<\/td>\n<\/tr>\n<tr>\n<td>Wheat<\/td>\n<td>12<\/td>\n<td>10<\/td>\n<td>15<\/td>\n<td>19<\/td>\n<td>21<\/td>\n<td>16<\/td>\n<td>18<\/td>\n<td>9<\/td>\n<td>25<\/td>\n<td>10<\/td>\n<\/tr>\n<tr>\n<td>Rice<\/td>\n<td>22<\/td>\n<td>29<\/td>\n<td>12<\/td>\n<td>23<\/td>\n<td>18<\/td>\n<td>15<\/td>\n<td>12<\/td>\n<td>34<\/td>\n<td>18<\/td>\n<td>12<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"font-weight: 400;\"><br \/>Calculate for each crop,<br \/>(i) Range<br \/>(ii) Q.D.<br \/>(iii) Mean Deviation about Mean<br \/>(iv) Mean Deviation about Median<br \/>(v) Standard Deviation<br \/>(vi) Which crop has greater variation?<br \/>(vii) Compare the value of different measures for each crop.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-5\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><b><strong>(i)<\/strong><\/b>\u00a0<b><strong>Range<\/strong><\/b><\/p>\n<ol>\n<li><b><\/b>Wheat<\/li>\n<\/ol>\n<p>Highest value of distribution (<em>H<\/em>) = 25<\/p>\n<p>Lowest value of distribution (<em>L<\/em>) = 9<\/p>\n<p><em>Range<\/em>\u00a0=\u00a0<em>H<\/em>\u00a0\u2013\u00a0<em>L<\/em><\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = 25 \u2013 9<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =16<\/p>\n<ol>\n<li><b><\/b>Rice<\/li>\n<\/ol>\n<p>Highest value of distribution (<em>H<\/em>) = 34<\/p>\n<p>Lowest value of distribution (<em>L<\/em>) = 12<\/p>\n<p><em>Range<\/em>\u00a0=\u00a0<em>H<\/em>\u00a0\u2013\u00a0<em>L<\/em><\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =34 \u2013 12<\/p>\n<p>= 22<\/p>\n<p><b><strong>(ii) Quartile Deviation<\/strong><\/b><\/p>\n<ol>\n<li><b><strong><em> Wheat<\/em><\/strong><\/b><\/li>\n<\/ol>\n<p>Arranging the production of wheat in increasing order<\/p>\n<p>9, 10, 10, 12, 15, 16, 18, 19, 21, 25<\/p>\n<p>= 2.75<sup>th<\/sup>\u00a0item<\/p>\n<p>=Size of 2th item + 0.75 (size of 3<sup>rd<\/sup>\u00a0item \u2013 size of 2<sup>nd<\/sup>\u00a0item)<\/p>\n<p>= 10 + 0.75 (10 \u2013 10)<\/p>\n<p>= 10 + 0.75 \u00d7 0<\/p>\n<p>=10<\/p>\n<p>= 8.25th<\/p>\n<p>=Size of 8<sup>th<\/sup>\u00a0item + 0.25 (size of 9<sup>th<\/sup>\u00a0item \u2013 size of 8<sup>th<\/sup>\u00a0item)<\/p>\n<p>= 19 + 0.25 (21 \u2013 19)<\/p>\n<p>= 19 + 0.25 \u00d7 2<\/p>\n<p>= 19 + 0.50 = 19.50<\/p>\n<p>= 4.75<\/p>\n<ol>\n<li><b><strong><em> Rice<\/em><\/strong><\/b><\/li>\n<\/ol>\n<p>Arranging the data of production of rice<\/p>\n<p>12, 12, 12, 15, 18, 18, 22, 23, 29, 34<\/p>\n<p>= 2.75th item<\/p>\n<p>= size of 2<sup>nd<\/sup>\u00a0item + 0.75 (size of 3<sup>rd<\/sup>\u00a0item \u2013 size of 2<sup>nd<\/sup>\u00a0item)<\/p>\n<p>= 12 + 0 .75 (12 \u2013 12)<\/p>\n<p>= 12 + 0.75 \u00d7 0<\/p>\n<p>= 12<\/p>\n<p>= 8.25th item<\/p>\n<p>= Size of 8<sup>th<\/sup>\u00a0item + 0.25 (size of 9th item \u2013 size of 8<sup>th<\/sup>\u00a0item)<\/p>\n<p>= 23 + 0.25 (29 \u2013 23)<\/p>\n<p>= 23 + 0.25 \u00d7 6<\/p>\n<p>= 23 + 1.5<\/p>\n<p>= 24.5<\/p>\n<p>= 6.25<\/p>\n<p>\u00a0<\/p>\n<p><b><strong>(iii) Mean Deviation about Mean<\/strong><\/b><\/p>\n<p>\u00a0<\/p>\n<ol>\n<li><b><strong><em> Wheat<\/em><\/strong><\/b><\/li>\n<\/ol>\n<table>\n<tbody>\n<tr>\n<td width=\"139\">\n<p><b><strong>Wheat Production<\/strong><\/b><\/p>\n<p><b><strong><em>x<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"192\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>9<\/p>\n<\/td>\n<td width=\"192\">\n<p>6<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>10<\/p>\n<\/td>\n<td width=\"192\">\n<p>5<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>10<\/p>\n<\/td>\n<td width=\"192\">\n<p>5<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>12<\/p>\n<\/td>\n<td width=\"192\">\n<p>3<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>15<\/p>\n<\/td>\n<td width=\"192\">\n<p>0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>16<\/p>\n<\/td>\n<td width=\"192\">\n<p>1<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>18<\/p>\n<\/td>\n<td width=\"192\">\n<p>3<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>19<\/p>\n<\/td>\n<td width=\"192\">\n<p>4<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>21<\/p>\n<\/td>\n<td width=\"192\">\n<p>6<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\n<p>25<\/p>\n<\/td>\n<td width=\"192\">\n<p>10<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"139\">\u00a0<\/td>\n<td width=\"192\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<ol>\n<li><b><strong><em> Rice<\/em><\/strong><\/b><\/li>\n<\/ol>\n<table>\n<tbody>\n<tr>\n<td width=\"127\">\n<p><b><strong>Rice Production<\/strong><\/b><\/p>\n<p><b><strong>\u00a0<em>x<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"194\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td width=\"127\">\n<p>12<\/p>\n<\/td>\n<td width=\"194\">\n<p>6<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"127\">\n<p>12<\/p>\n<\/td>\n<td width=\"194\">\n<p>6<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"127\">\n<p>12<\/p>\n<\/td>\n<td width=\"194\">\n<p>6<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"127\">\n<p>15<\/p>\n<\/td>\n<td width=\"194\">\n<p>3<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"127\">\n<p>18<\/p>\n<\/td>\n<td width=\"194\">\n<p>0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"127\">\n<p>18<\/p>\n<\/td>\n<td width=\"194\">\n<p>0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"127\">\n<p>22<\/p>\n<\/td>\n<td width=\"194\">\n<p>4<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"127\">\n<p>23<\/p>\n<\/td>\n<td width=\"194\">\n<p>5<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"127\">\n<p>29<\/p>\n<\/td>\n<td width=\"194\">\n<p>11<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"127\">\n<p>34<\/p>\n<\/td>\n<td width=\"194\">\n<p>16<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"127\">\u00a0<\/td>\n<td width=\"194\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<p><b><strong>(iv) Mean Deviation about Median<\/strong><\/b><\/p>\n<p>\u00a0<\/p>\n<ol>\n<li><b><strong><em> Wheat<\/em><\/strong><\/b><\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"103\">\n<p><b><strong>Production of Wheat<\/strong><\/b><\/p>\n<p><b><strong><em>x<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"125\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td width=\"103\">\n<p>09<\/p>\n<\/td>\n<td width=\"125\">\n<p>6<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"103\">\n<p>10<\/p>\n<\/td>\n<td width=\"125\">\n<p>5<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"103\">\n<p>10<\/p>\n<\/td>\n<td width=\"125\">\n<p>5<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"103\">\n<p>12<\/p>\n<\/td>\n<td width=\"125\">\n<p>3<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"103\">\n<p>15<\/p>\n<\/td>\n<td width=\"125\">\n<p>0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"103\">\n<p>16<\/p>\n<\/td>\n<td width=\"125\">\n<p>1<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"103\">\n<p>18<\/p>\n<\/td>\n<td width=\"125\">\n<p>3<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"103\">\n<p>19<\/p>\n<\/td>\n<td width=\"125\">\n<p>4<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"103\">\n<p>21<\/p>\n<\/td>\n<td width=\"125\">\n<p>6<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"103\">\n<p>25<\/p>\n<\/td>\n<td width=\"125\">\n<p>10<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"103\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"125\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<ol>\n<li><b><strong><em> Rice<\/em><\/strong><\/b><\/li>\n<\/ol>\n<table>\n<tbody>\n<tr>\n<td width=\"138\">\n<p>Production of rice<\/p>\n<\/td>\n<td width=\"110\">\n<p><em>d<\/em>\u00a0=\u00a0<em>X<\/em>\u201318<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"138\">\n<p>12<\/p>\n<\/td>\n<td width=\"110\">\n<p>6<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"138\">\n<p>12<\/p>\n<\/td>\n<td width=\"110\">\n<p>6<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"138\">\n<p>12<\/p>\n<\/td>\n<td width=\"110\">\n<p>6<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"138\">\n<p>15<\/p>\n<\/td>\n<td width=\"110\">\n<p>3<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"138\">\u00a0<\/td>\n<td width=\"110\">\n<p>0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"138\">\n<p>18<\/p>\n<\/td>\n<td width=\"110\">\n<p>0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"138\">\n<p>22<\/p>\n<\/td>\n<td width=\"110\">\n<p>4<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"138\">\n<p>23<\/p>\n<\/td>\n<td width=\"110\">\n<p>5<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"138\">\n<p>29<\/p>\n<\/td>\n<td width=\"110\">\n<p>11<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"138\">\n<p>34<\/p>\n<\/td>\n<td width=\"110\">\n<p>16<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"138\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"110\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Since\u00a0<em>n<\/em>\u00a0is even<\/p>\n<p><b><strong>(v) Standard Deviation<\/strong><\/b><\/p>\n<p>\u00a0<\/p>\n<ol>\n<li><b><strong><em> Wheat<\/em><\/strong><\/b><\/li>\n<\/ol>\n<table>\n<tbody>\n<tr>\n<td width=\"165\">\n<p><b><strong>Reduction of Wheat<\/strong><\/b><\/p>\n<p><b><strong><em>x<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"96\">\n<p><b><strong><em>Ax<\/em>\u00a0= 15<\/strong><\/b><\/p>\n<p><b><strong><em>d<\/em>=\u00a0<em>x<\/em>\u00a0\u2013\u00a0<em>Ax<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"103\">\n<p><b><strong><em>d<\/em><sup>2<\/sup><\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"165\">\n<p>9<\/p>\n<\/td>\n<td width=\"96\">\n<p>\u20136<\/p>\n<\/td>\n<td width=\"103\">\n<p>36<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"165\">\n<p>10<\/p>\n<\/td>\n<td width=\"96\">\n<p>\u20135<\/p>\n<\/td>\n<td width=\"103\">\n<p>25<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"165\">\n<p>10<\/p>\n<\/td>\n<td width=\"96\">\n<p>\u20135<\/p>\n<\/td>\n<td width=\"103\">\n<p>25<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"165\">\n<p>12<\/p>\n<\/td>\n<td width=\"96\">\n<p>\u20133<\/p>\n<\/td>\n<td width=\"103\">\n<p>9<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"165\">\n<p>15<\/p>\n<\/td>\n<td width=\"96\">\n<p>0<\/p>\n<\/td>\n<td width=\"103\">\n<p>0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"165\">\n<p>16<\/p>\n<\/td>\n<td width=\"96\">\n<p>1<\/p>\n<\/td>\n<td width=\"103\">\n<p>1<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"165\">\n<p>18<\/p>\n<\/td>\n<td width=\"96\">\n<p>3<\/p>\n<\/td>\n<td width=\"103\">\n<p>9<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"165\">\n<p>19<\/p>\n<\/td>\n<td width=\"96\">\n<p>4<\/p>\n<\/td>\n<td width=\"103\">\n<p>16<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"165\">\n<p>21<\/p>\n<\/td>\n<td width=\"96\">\n<p>6<\/p>\n<\/td>\n<td width=\"103\">\n<p>36<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"165\">\n<p>25<\/p>\n<\/td>\n<td width=\"96\">\n<p>10<\/p>\n<\/td>\n<td width=\"103\">\n<p>100<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"165\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"96\">\u00a0<\/td>\n<td width=\"103\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<ol>\n<li><b><strong><em> Rice<\/em><\/strong><\/b><\/li>\n<\/ol>\n<table>\n<tbody>\n<tr>\n<td width=\"147\">\n<p><b><strong>Production of rice<\/strong><\/b><\/p>\n<p><b><strong>\u00a0<em>x<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"90\">\n<p><b><strong><em>Ax<\/em>\u00a0= 18<\/strong><\/b><\/p>\n<p><b><strong><em>d<\/em>\u00a0=\u00a0<em>x<\/em>\u00a0\u2013\u00a0<em>A<\/em>\u00a0<em>x<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"127\">\n<p><b><strong><em>d<\/em><sup>2<\/sup><\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"147\">\n<p>12<\/p>\n<\/td>\n<td width=\"90\">\n<p>\u20136<\/p>\n<\/td>\n<td width=\"127\">\n<p>36<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"147\">\n<p>12<\/p>\n<\/td>\n<td width=\"90\">\n<p>\u20136<\/p>\n<\/td>\n<td width=\"127\">\n<p>36<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"147\">\n<p>12<\/p>\n<\/td>\n<td width=\"90\">\n<p>\u20136<\/p>\n<\/td>\n<td width=\"127\">\n<p>36<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"147\">\n<p>15<\/p>\n<\/td>\n<td width=\"90\">\n<p>\u20133<\/p>\n<\/td>\n<td width=\"127\">\n<p>9<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"147\">\n<p>18<\/p>\n<\/td>\n<td width=\"90\">\n<p>0<\/p>\n<\/td>\n<td width=\"127\">\n<p>0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"147\">\n<p>22<\/p>\n<\/td>\n<td width=\"90\">\n<p>4<\/p>\n<\/td>\n<td width=\"127\">\n<p>16<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"147\">\n<p>23<\/p>\n<\/td>\n<td width=\"90\">\n<p>5<\/p>\n<\/td>\n<td width=\"127\">\n<p>25<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"147\">\n<p>29<\/p>\n<\/td>\n<td width=\"90\">\n<p>11<\/p>\n<\/td>\n<td width=\"127\">\n<p>121<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"147\">\n<p>34<\/p>\n<\/td>\n<td width=\"90\">\n<p>16<\/p>\n<\/td>\n<td width=\"127\">\n<p>256<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"147\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"90\">\u00a0<\/td>\n<td width=\"127\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<p><b><strong>(vi) Coefficient of Variation<\/strong><\/b><\/p>\n<ol>\n<li><b><strong><em> Wheat<\/em><\/strong><\/b><\/li>\n<li><b><strong><em> Rice<\/em><\/strong><\/b><\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<p><b><strong>(vi)<\/strong><\/b>\u00a0Rice crop has greater variation as the coefficient of variation is higher for rice as compared to that of wheat.<\/p>\n<p><b><strong>(vii)<\/strong><\/b>\u00a0Rice crop has higher Range, Quartile Deviation, Mean Deviation about mean, Mean Deviation about median, Standard Deviation and Coefficient of Variation.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"question-6\"><\/span>Question 6:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>In the previous question, calculate the relative measures of variation and indicate the value which, in your opinion, is more reliable.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-6\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><b><strong>(i) Coefficient of Range<\/strong><\/b><\/p>\n<ol>\n<li><b><strong><em>a) Wheat<\/em><\/strong><\/b><\/li>\n<li><b><strong><em>b) Rice<\/em><\/strong><\/b><\/li>\n<\/ol>\n<p><b><strong>(ii)<\/strong><\/b>\u00a0<b><strong>Coefficient of Quartile Deviation<\/strong><\/b><\/p>\n<ol>\n<li><b><strong><em>a) Wheat<\/em><\/strong><\/b><\/li>\n<li><b><strong><em>b) Rice<\/em><\/strong><\/b><\/li>\n<\/ol>\n<p><em>Q<\/em><sub>1<\/sub>\u00a0= 12,\u00a0<em>Q<\/em><sub>3<\/sub> = 24.5<\/p>\n<p><b><strong>(iii) Coefficient of Mean Deviation from mean<\/strong><\/b><\/p>\n<ol>\n<li><b><strong><em>a) Wheat<\/em><\/strong><\/b><\/li>\n<li><b><strong><em>b) Rice<\/em><\/strong><\/b><\/li>\n<\/ol>\n<p><b><strong>(iv) Coefficient of Variation<\/strong><\/b><\/p>\n<ol>\n<li><b><strong><em>a) Wheat<\/em><\/strong><\/b><\/li>\n<li><b><strong><em>b) Rice<\/em><\/strong><\/b><\/li>\n<\/ol>\n<p>The coefficient of variation is more reliable than all other measures.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"question-7\"><\/span>Question 7:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>A batsman is to be selected for a cricket team. The choice is between X and Y on the basis of their scores in five previous tests which are:<br \/>\u00a0<\/p>\n<table>\n<tbody>\n<tr>\n<td>\n<p>X<\/p>\n<\/td>\n<td>\n<p>25<\/p>\n<\/td>\n<td>\n<p>85<\/p>\n<\/td>\n<td>\n<p>40<\/p>\n<\/td>\n<td>\n<p>80<\/p>\n<\/td>\n<td>\n<p>120<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>Y<\/p>\n<\/td>\n<td>\n<p>50<\/p>\n<\/td>\n<td>\n<p>70<\/p>\n<\/td>\n<td>\n<p>65<\/p>\n<\/td>\n<td>\n<p>45<\/p>\n<\/td>\n<td>\n<p>80<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"font-weight: 400;\"><br \/>Which batsman should be selected if we want,<br \/>(i) a higher run getter, or<br \/>(ii) a more reliable batsman in the team?<\/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 colspan=\"3\" width=\"333\">\n<p><b><strong>Batsman X<\/strong><\/b><\/p>\n<\/td>\n<td width=\"1\">\n<p>\u00a0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"112\">\n<p><em>X<\/em><\/p>\n<\/td>\n<td width=\"90\">\n<p><em>X \u2013\u00a0\u00a0= x<\/em><\/p>\n<p><em>X \u2013 70<\/em><\/p>\n<\/td>\n<td colspan=\"2\" width=\"132\">\n<p><em>x<\/em><sup>2<\/sup><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"112\">\n<p>25<\/p>\n<\/td>\n<td width=\"90\">\n<p>\u2013 45<\/p>\n<\/td>\n<td colspan=\"2\" width=\"132\">\n<p>2025<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"112\">\n<p>85<\/p>\n<\/td>\n<td width=\"90\">\n<p>+ 15<\/p>\n<\/td>\n<td colspan=\"2\" width=\"132\">\n<p>225<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"112\">\u00a0<\/td>\n<td width=\"90\">\n<p>\u2013 30<\/p>\n<\/td>\n<td colspan=\"2\" width=\"132\">\n<p>900<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"112\">\n<p>80<\/p>\n<\/td>\n<td width=\"90\">\n<p>10<\/p>\n<\/td>\n<td colspan=\"2\" width=\"132\">\n<p>100<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"112\">\n<p>120<\/p>\n<\/td>\n<td width=\"90\">\n<p>50<\/p>\n<\/td>\n<td colspan=\"2\" width=\"132\">\n<p>2500<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"112\">\u00a0<\/td>\n<td width=\"90\">\n<p>\u00a0<\/p>\n<\/td>\n<td colspan=\"2\" width=\"132\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td width=\"112\">\u00a0<\/td>\n<td width=\"90\">\u00a0<\/td>\n<td width=\"132\">\u00a0<\/td>\n<td width=\"1\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<table>\n<tbody>\n<tr>\n<td colspan=\"3\" width=\"287\">\n<p><b><strong>Batsman Y<\/strong><\/b><\/p>\n<\/td>\n<td width=\"1\">\n<p>\u00a0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"93\">\n<p><b><strong><em>Y<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"92\">\u00a0<\/td>\n<td colspan=\"2\" width=\"103\">\n<p><b><strong><em>y<\/em><sup>2<\/sup><\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"93\">\n<p>50<\/p>\n<\/td>\n<td width=\"92\">\n<p>\u2013 12<\/p>\n<\/td>\n<td colspan=\"2\" width=\"103\">\n<p>144<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"93\">\n<p>70<\/p>\n<\/td>\n<td width=\"92\">\n<p>8<\/p>\n<\/td>\n<td colspan=\"2\" width=\"103\">\n<p>64<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"93\">\n<p>65<\/p>\n<\/td>\n<td width=\"92\">\n<p>3<\/p>\n<\/td>\n<td colspan=\"2\" width=\"103\">\n<p>9<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"93\">\n<p>45<\/p>\n<\/td>\n<td width=\"92\">\n<p>\u2013 17<\/p>\n<\/td>\n<td colspan=\"2\" width=\"103\">\n<p>289<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"93\">\n<p>80<\/p>\n<\/td>\n<td width=\"92\">\n<p>18<\/p>\n<\/td>\n<td colspan=\"2\" width=\"103\">\n<p>324<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"93\">\u00a0<\/td>\n<td width=\"92\">\n<p>\u00a0<\/p>\n<\/td>\n<td colspan=\"2\" width=\"103\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td width=\"93\">\u00a0<\/td>\n<td width=\"95\">\u00a0<\/td>\n<td width=\"102\">\u00a0<\/td>\n<td width=\"1\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<p>(i) Average of Batsman\u00a0<em>X<\/em>\u00a0is higher than that of Batsman\u00a0<em>Y<\/em>, so he should be selected if we want to score\u00a0 higher run.<\/p>\n<p>(ii) The Batsman\u00a0<em>X\u00a0<\/em>is more reliable than Batsman\u00a0<em>Y<\/em>. This is because the coefficient of variation of Batsman\u00a0<em>X<\/em>\u00a0is higher than that of Batsman\u00a0<em>Y<\/em>.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"question-8\"><\/span>Question 8:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>To check the quality of two brands of light bulbs, their life in burning hours was estimated as under for 100 bulbs of each brand.<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"90\">\n<p><b><strong><em>Life\u00a0<\/em><\/strong><\/b><\/p>\n<\/td>\n<td rowspan=\"2\" width=\"59\">\n<p>\u00a0<\/p>\n<\/td>\n<td colspan=\"2\" width=\"161\">\n<p><b><strong><em>No. of bulbs<\/em><\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"90\">\n<p><b><strong><em>(in hrs)<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"72\">\n<p><b><strong><em>Brand A<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"89\">\n<p><b><strong><em>Brand B<\/em><\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"90\">\n<p>0 \u2013 50<\/p>\n<\/td>\n<td width=\"59\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"72\">\n<p>15<\/p>\n<\/td>\n<td width=\"89\">\n<p>2<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"90\">\n<p>50 \u2013 100<\/p>\n<\/td>\n<td width=\"59\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"72\">\n<p>20<\/p>\n<\/td>\n<td width=\"89\">\n<p>8<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"90\">\n<p>100 \u2013 150<\/p>\n<\/td>\n<td width=\"59\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"72\">\n<p>18<\/p>\n<\/td>\n<td width=\"89\">\n<p>60<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"90\">\n<p>150 \u2013 200<\/p>\n<\/td>\n<td width=\"59\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"72\">\n<p>25<\/p>\n<\/td>\n<td width=\"89\">\n<p>25<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"90\">\n<p>200 \u2013 250<\/p>\n<\/td>\n<td width=\"59\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"72\">\n<p>22<\/p>\n<\/td>\n<td width=\"89\">\n<p>5<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"90\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"59\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"72\">\n<p>100<\/p>\n<\/td>\n<td width=\"89\">\n<p>100<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>(i) Which brand gives higher life?<\/p>\n<p>(ii) Which brand is more dependable?<\/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 colspan=\"8\" width=\"696\">\n<p><b><strong>For Brand A<\/strong><\/b><\/p>\n<\/td>\n<td width=\"1\">\n<p>\u00a0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"107\">\n<p><b><strong>Life<\/strong><\/b><\/p>\n<p><b><strong>(in hours)<\/strong><\/b><\/p>\n<\/td>\n<td width=\"101\">\n<p><b><strong>No. of bulbs<\/strong><\/b><\/p>\n<\/td>\n<td width=\"39\">\n<p><b><strong><em>M<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"83\">\n<p><b><strong>A = 125<\/strong><\/b><\/p>\n<\/td>\n<td width=\"102\">\u00a0<\/td>\n<td width=\"36\">\n<p><b><strong><em>d<\/em>&#8216;<sup>2<\/sup><\/strong><\/b><\/p>\n<\/td>\n<td width=\"104\">\n<p><b><strong><em>fd<\/em>&#8216;<\/strong><\/b><\/p>\n<\/td>\n<td colspan=\"2\" width=\"125\">\n<p><b><strong><em>fd<\/em>&#8216;<sup>2<\/sup><\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"107\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"101\">\n<p><b><strong><em>f<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"39\">\n<p><b><strong><em>x<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"83\">\n<p><b><strong><em>X \u2013 A<\/em>\u00a0=\u00a0<em>d<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"102\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"36\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"104\">\n<p>\u00a0<\/p>\n<\/td>\n<td colspan=\"2\" width=\"125\">\n<p>\u00a0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"107\">\n<p>0 \u2013 50<\/p>\n<\/td>\n<td width=\"101\">\n<p>15<\/p>\n<\/td>\n<td width=\"39\">\n<p>25<\/p>\n<\/td>\n<td width=\"83\">\n<p>\u2013 100<\/p>\n<\/td>\n<td width=\"102\">\n<p>\u2013 2<\/p>\n<\/td>\n<td width=\"36\">\n<p>4<\/p>\n<\/td>\n<td width=\"104\">\n<p>\u2013 30<\/p>\n<\/td>\n<td colspan=\"2\" width=\"125\">\n<p>60<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"107\">\n<p>50 \u2013 100<\/p>\n<\/td>\n<td width=\"101\">\n<p>20<\/p>\n<\/td>\n<td width=\"39\">\n<p>75<\/p>\n<\/td>\n<td width=\"83\">\n<p>\u2013 50<\/p>\n<\/td>\n<td width=\"102\">\n<p>\u2013 1<\/p>\n<\/td>\n<td width=\"36\">\n<p>1<\/p>\n<\/td>\n<td width=\"104\">\n<p>\u2013 20<\/p>\n<\/td>\n<td colspan=\"2\" width=\"125\">\n<p>20<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"107\">\n<p>100 \u2013 150<\/p>\n<\/td>\n<td width=\"101\">\n<p>18<\/p>\n<\/td>\n<td width=\"39\">\n<p>125<\/p>\n<\/td>\n<td width=\"83\">\n<p>0<\/p>\n<\/td>\n<td width=\"102\">\n<p>0<\/p>\n<\/td>\n<td width=\"36\">\n<p>0<\/p>\n<\/td>\n<td width=\"104\">\n<p>0<\/p>\n<\/td>\n<td colspan=\"2\" width=\"125\">\n<p>0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"107\">\n<p>150 \u2013 200<\/p>\n<\/td>\n<td width=\"101\">\n<p>25<\/p>\n<\/td>\n<td width=\"39\">\n<p>175<\/p>\n<\/td>\n<td width=\"83\">\n<p>50<\/p>\n<\/td>\n<td width=\"102\">\n<p>1<\/p>\n<\/td>\n<td width=\"36\">\n<p>1<\/p>\n<\/td>\n<td width=\"104\">\n<p>25<\/p>\n<\/td>\n<td colspan=\"2\" width=\"125\">\n<p>25<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"107\">\n<p>200 \u2013 250<\/p>\n<\/td>\n<td width=\"101\">\n<p>22<\/p>\n<\/td>\n<td width=\"39\">\n<p>225<\/p>\n<\/td>\n<td width=\"83\">\n<p>100<\/p>\n<\/td>\n<td width=\"102\">\n<p>2<\/p>\n<\/td>\n<td width=\"36\">\n<p>4<\/p>\n<\/td>\n<td width=\"104\">\n<p>44<\/p>\n<\/td>\n<td colspan=\"2\" width=\"125\">\n<p>88<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"107\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"101\">\u00a0<\/td>\n<td width=\"39\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"83\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"102\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"36\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"104\">\u00a0<\/td>\n<td colspan=\"2\" width=\"125\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td width=\"107\">\u00a0<\/td>\n<td width=\"101\">\u00a0<\/td>\n<td width=\"39\">\u00a0<\/td>\n<td width=\"83\">\u00a0<\/td>\n<td width=\"102\">\u00a0<\/td>\n<td width=\"36\">\u00a0<\/td>\n<td width=\"104\">\u00a0<\/td>\n<td width=\"124\">\u00a0<\/td>\n<td width=\"1\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<table>\n<tbody>\n<tr>\n<td colspan=\"8\" width=\"767\">\n<p><b><strong>For Brand B<\/strong><\/b><\/p>\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"1\">\n<p>\u00a0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"91\">\n<p><b><strong>Life (in hrs)<\/strong><\/b><\/p>\n<\/td>\n<td width=\"102\">\n<p><b><strong>No. of bulbs<em>\u00a0(f)<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"84\">\n<p><b><strong>Mid value<em>\u00a0m<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"102\">\n<p><b><strong><em>A =\u00a0<\/em>125<\/strong><\/b><\/p>\n<\/td>\n<td width=\"108\">\u00a0<\/td>\n<td width=\"54\">\n<p><b><strong><em>d&#8217;<\/em><sup>2<\/sup><\/strong><\/b><\/p>\n<\/td>\n<td width=\"108\">\n<p><b><strong><em>fd&#8217;<\/em><\/strong><\/b><\/p>\n<\/td>\n<td colspan=\"2\" width=\"119\">\n<p><b><strong><em>fd&#8217;<\/em><sup>2<\/sup><\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"91\">\n<p>0 \u2013 50<\/p>\n<\/td>\n<td width=\"102\">\n<p>2<\/p>\n<\/td>\n<td width=\"84\">\n<p>25<\/p>\n<\/td>\n<td width=\"102\">\n<p>\u2013 100<\/p>\n<\/td>\n<td width=\"108\">\n<p>\u2013 2<\/p>\n<\/td>\n<td width=\"54\">\n<p>4<\/p>\n<\/td>\n<td width=\"108\">\n<p>\u2013 4<\/p>\n<\/td>\n<td colspan=\"2\" width=\"119\">\n<p>8<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"91\">\n<p>50 \u2013 100<\/p>\n<\/td>\n<td width=\"102\">\n<p>8<\/p>\n<\/td>\n<td width=\"84\">\n<p>75<\/p>\n<\/td>\n<td width=\"102\">\n<p>\u2013 50<\/p>\n<\/td>\n<td width=\"108\">\n<p>\u2013 1<\/p>\n<\/td>\n<td width=\"54\">\n<p>1<\/p>\n<\/td>\n<td width=\"108\">\n<p>\u2013 8<\/p>\n<\/td>\n<td colspan=\"2\" width=\"119\">\n<p>8<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"91\">\n<p>100 \u2013 150<\/p>\n<\/td>\n<td width=\"102\">\n<p>60<\/p>\n<\/td>\n<td width=\"84\">\n<p>125<\/p>\n<\/td>\n<td width=\"102\">\n<p>0<\/p>\n<\/td>\n<td width=\"108\">\n<p>0<\/p>\n<\/td>\n<td width=\"54\">\n<p>0<\/p>\n<\/td>\n<td width=\"108\">\n<p>0<\/p>\n<\/td>\n<td colspan=\"2\" width=\"119\">\n<p>0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"91\">\n<p>150 \u2013 200<\/p>\n<\/td>\n<td width=\"102\">\n<p>25<\/p>\n<\/td>\n<td width=\"84\">\n<p>175<\/p>\n<\/td>\n<td width=\"102\">\n<p>50<\/p>\n<\/td>\n<td width=\"108\">\n<p>1<\/p>\n<\/td>\n<td width=\"54\">\n<p>1<\/p>\n<\/td>\n<td width=\"108\">\n<p>25<\/p>\n<\/td>\n<td colspan=\"2\" width=\"119\">\n<p>25<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"91\">\n<p>200 \u2013 250<\/p>\n<\/td>\n<td width=\"102\">\n<p>5<\/p>\n<\/td>\n<td width=\"84\">\n<p>225<\/p>\n<\/td>\n<td width=\"102\">\n<p>100<\/p>\n<\/td>\n<td width=\"108\">\n<p>2<\/p>\n<\/td>\n<td width=\"54\">\n<p>4<\/p>\n<\/td>\n<td width=\"108\">\n<p>10<\/p>\n<\/td>\n<td colspan=\"2\" width=\"119\">\n<p>20<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"91\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"102\">\u00a0<\/td>\n<td width=\"84\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"102\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"108\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"54\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"108\">\u00a0<\/td>\n<td colspan=\"2\" width=\"119\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td width=\"87\">\u00a0<\/td>\n<td width=\"101\">\u00a0<\/td>\n<td width=\"81\">\u00a0<\/td>\n<td width=\"97\">\u00a0<\/td>\n<td width=\"107\">\u00a0<\/td>\n<td width=\"52\">\u00a0<\/td>\n<td width=\"107\">\u00a0<\/td>\n<td width=\"117\">\u00a0<\/td>\n<td width=\"1\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<p>(i) The average life of bulb of Brand B has comparatively\u00a0 higher life than the bulb of Brand A.<\/p>\n<p>(ii) The\u00a0 bulbs\u00a0 of Brand B is more dependable as CV of Brand B is lesser than CV of Brand A.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"question-9\"><\/span>Question 9:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Average daily wage of 50 workers of a factory was Rs 200 with a Standard Deviation of Rs 40. Each worker is given a raise of Rs 20. What is the new average daily wage and Standard Deviation? Have the wages become more or less uniform?<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-9\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><em>N<\/em>\u00a0= 50<\/p>\n<p>\u00a0= 200<\/p>\n<p><em>s<\/em>\u00a0= 40<\/p>\n<p>So, Total Wages = 200 \u00d7 50<\/p>\n<p>= Rs 10,000<\/p>\n<p>Now, increased wage rate = Rs 20<\/p>\n<p>Total raise = 50 \u00d7 20 = Rs 1,000<\/p>\n<p>Total Wage after raise = 10,000 + 1,000<\/p>\n<p>=Rs 11,000<\/p>\n<p>= Rs 220<\/p>\n<p>Initial Standard Deviation = Rs 40<\/p>\n<p>So, New Standard Deviation = Rs 40 + Rs 20<\/p>\n<p>= Rs 60<\/p>\n<p><b><strong><u>Note<\/u><\/strong><\/b>: New Standard Deviation will rise by the same amount as the wage of each worker has increased.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"question-10\"><\/span>Question 10:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>If in the previous question, each worker is given a hike of 10% in wages, how are the Mean and Standard Deviation values affected?<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-10\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Average wage = Rs 200<\/p>\n<p>Hike in wages = 10% of Rs 200<\/p>\n<p>= Rs 20<\/p>\n<p>Individual raise given to each worker = Rs 20<\/p>\n<p>Total raise in wage = 50 \u00d7 20 = Rs 1,000<\/p>\n<p>New Total Wage = Rs 10,000 + Rs 1000<\/p>\n<p>= Rs 11,000<\/p>\n<p>\u00a0<\/p>\n<p>Initial Standard Deviation = Rs 40<\/p>\n<p>So, New Standard Deviation = Rs 40 + 20<\/p>\n<p>= Rs 60<\/p>\n<h4><span class=\"ez-toc-section\" id=\"page-no-90\"><\/span>Page No 90:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"question-11\"><\/span>Question 11:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Calculate the Mean Deviation using mean and Standard Deviation for the following distribution.<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"86\">\n<p><b><strong>Classes<\/strong><\/b><\/p>\n<\/td>\n<td width=\"104\">\n<p><b><strong>Frequencies<\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"86\">\n<p>20 \u2013 40<\/p>\n<\/td>\n<td width=\"104\">\n<p>3<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"86\">\n<p>40 \u2013 80<\/p>\n<\/td>\n<td width=\"104\">\n<p>6<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"86\">\n<p>80 \u2013 100<\/p>\n<\/td>\n<td width=\"104\">\n<p>20<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"86\">\n<p>100 \u2013 120<\/p>\n<\/td>\n<td width=\"104\">\n<p>12<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"86\">\n<p>120 \u2013 140<\/p>\n<\/td>\n<td width=\"104\">\n<p>9<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"86\">\n<p>Total<\/p>\n<\/td>\n<td width=\"104\">\n<p>50<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-11\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<table>\n<tbody>\n<tr>\n<td width=\"79\">\n<p><b><strong>Classes<\/strong><\/b><\/p>\n<\/td>\n<td width=\"96\">\n<p><b><strong>Frequency<\/strong><\/b><\/p>\n<\/td>\n<td width=\"42\">\n<p><b><strong><em>m<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"84\">\n<p><b><strong><em>A = 90<\/em><\/strong><\/b><\/p>\n<p><b><strong><em>d = X \u2013 A<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"42\">\u00a0<\/td>\n<td width=\"124\">\u00a0<\/td>\n<td width=\"124\">\u00a0<\/td>\n<td width=\"113\">\n<p><b><strong><em>fd&#8217;<\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"53\">\n<p><b><strong><em>d&#8217;<sup>2<\/sup><\/em><\/strong><\/b><\/p>\n<\/td>\n<td width=\"109\">\n<p><b><strong><em>fd&#8217;<sup>2<\/sup><\/em><\/strong><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"79\">\n<p>20 \u2013 40<\/p>\n<\/td>\n<td width=\"96\">\n<p>3<\/p>\n<\/td>\n<td width=\"42\">\n<p>30<\/p>\n<\/td>\n<td width=\"84\">\n<p>\u2013 60<\/p>\n<\/td>\n<td width=\"42\">\n<p>60<\/p>\n<\/td>\n<td width=\"124\">\n<p>180<\/p>\n<\/td>\n<td width=\"124\">\n<p>\u2013 6<\/p>\n<\/td>\n<td width=\"113\">\n<p>\u2013 18<\/p>\n<\/td>\n<td width=\"53\">\n<p>36<\/p>\n<\/td>\n<td width=\"109\">\n<p>108<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"79\">\n<p>40 \u2013 80<\/p>\n<\/td>\n<td width=\"96\">\n<p>6<\/p>\n<\/td>\n<td width=\"42\">\n<p>60<\/p>\n<\/td>\n<td width=\"84\">\n<p>\u2013 30<\/p>\n<\/td>\n<td width=\"42\">\n<p>30<\/p>\n<\/td>\n<td width=\"124\">\n<p>180<\/p>\n<\/td>\n<td width=\"124\">\n<p>\u2013 3<\/p>\n<\/td>\n<td width=\"113\">\n<p>\u2013 18<\/p>\n<\/td>\n<td width=\"53\">\n<p>9<\/p>\n<\/td>\n<td width=\"109\">\n<p>54<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"79\">\n<p>80 \u2013 100<\/p>\n<\/td>\n<td width=\"96\">\n<p>20<\/p>\n<\/td>\n<td width=\"42\">\n<p>90<\/p>\n<\/td>\n<td width=\"84\">\n<p>0<\/p>\n<\/td>\n<td width=\"42\">\n<p>0<\/p>\n<\/td>\n<td width=\"124\">\n<p>0<\/p>\n<\/td>\n<td width=\"124\">\n<p>0<\/p>\n<\/td>\n<td width=\"113\">\n<p>0<\/p>\n<\/td>\n<td width=\"53\">\n<p>0<\/p>\n<\/td>\n<td width=\"109\">\n<p>0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"79\">\n<p>100 \u2013 120<\/p>\n<\/td>\n<td width=\"96\">\n<p>12<\/p>\n<\/td>\n<td width=\"42\">\n<p>110<\/p>\n<\/td>\n<td width=\"84\">\n<p>20<\/p>\n<\/td>\n<td width=\"42\">\n<p>20<\/p>\n<\/td>\n<td width=\"124\">\n<p>240<\/p>\n<\/td>\n<td width=\"124\">\n<p>2<\/p>\n<\/td>\n<td width=\"113\">\n<p>24<\/p>\n<\/td>\n<td width=\"53\">\n<p>4<\/p>\n<\/td>\n<td width=\"109\">\n<p>48<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"79\">\n<p>120 \u2013 140<\/p>\n<\/td>\n<td width=\"96\">\n<p>9<\/p>\n<\/td>\n<td width=\"42\">\n<p>130<\/p>\n<\/td>\n<td width=\"84\">\n<p>40<\/p>\n<\/td>\n<td width=\"42\">\n<p>40<\/p>\n<\/td>\n<td width=\"124\">\n<p>360<\/p>\n<\/td>\n<td width=\"124\">\n<p>4<\/p>\n<\/td>\n<td width=\"113\">\n<p>36<\/p>\n<\/td>\n<td width=\"53\">\n<p>16<\/p>\n<\/td>\n<td width=\"109\">\n<p>144<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"79\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"96\">\u00a0<\/td>\n<td width=\"42\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"84\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"42\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"124\">\u00a0<\/td>\n<td width=\"124\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"113\">\u00a0<\/td>\n<td width=\"53\">\n<p>\u00a0<\/p>\n<\/td>\n<td width=\"109\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><b><strong>Mean Deviation from mean<\/strong><\/b><\/p>\n<h4><span class=\"ez-toc-section\" id=\"question-12\"><\/span>Question 12:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>The sum of 10 values is 100 and the sum of their squares is 1090. Find out the Coefficient of Variation.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"answer-12\"><\/span>ANSWER:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><img class=\"progressive\" src=\"https:\/\/img-nm.mnimgs.com\/img\/study_content\/editlive_ncert\/image6914698646333600083.jpg\" alt=\"\" width=\"164\" height=\"363\" data-href=\"https:\/\/img-nm.mnimgs.com\/img\/study_content\/editlive_ncert\/image6914698646333600083.jpg\"><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-other-ncert-chapters-solutions-of-class-11-statistics\"><\/span><strong>Access Other NCERT Chapters Solutions of Class 11 Statistics <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>You can download the PDF of NCERT Solutions Class 11 Accountancy for other chapters:\u00a0<\/strong><\/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<\/ul>\n<ul>\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<\/ul>\n<ul>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-3\/\"><strong>Chapter-3 Organisation Of Data<\/strong><\/a><\/li>\n<\/ul>\n<ul>\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<\/ul>\n<ul>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-5\/\"><strong>Chapter-5 Measures of Central Tendency<\/strong><\/a><\/li>\n<\/ul>\n<ul>\n<li><strong>Chapter-7 Correlation<\/strong><\/li>\n<\/ul>\n<ul>\n<li><strong>Chapter-8 Index Numbers<\/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 of class 11 Statistics Chapter 6. If you have any queries, you can mention them in the comment section.<\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"faq-frequently-asked-questions-ncert-solutions-for-class-11-statistics-chapter-6\"><\/span><strong>FAQ (Frequently Asked Questions): NCERT Solutions for Class 11 Statistics Chapter 6<\/strong><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-1626934274329\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-steps-involved-in-the-construction-of-the-lorenz-curve\"><\/span><strong>What are the steps involved in the construction of the Lorenz Curve?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The procedure involves a set of nine steps.<br \/>Determine the class midpoints. Table 2: Col. 2<br \/>Multiply the midpoint of the class by the frequency in the class to get the anticipated total income of employees in each c ss. As a result, Col. (4) of Table is obtained.<br \/>Calculate the frequency of each class as a proportion of the total frequency. Col. (5) of Table is thus obtained.<br \/>Calculate the total income of each class as a percentage (%) of the total income of all classes. Col. (6) of Table 5 was so obtained.\u00a0<br \/>Prepare a table with less than cumulative frequency and a table with cumulative income.<br \/>Col. 6 (2) Employees&#8217; cumulative frequency is shown in Table 6.5.<br \/>Table 6.5 displays the total income received by these individuals.<br \/>Draw a line from Coordinate(0,0) to Co-ordinate(0,0) (100,100). The line of equal distribution is what it&#8217;s called.<br \/>Plot the cumulative percentages of employees on the horizontal axis and cumulative income on the vertical axis.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1626934398713\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-measures-used-for-the-dispersion-of-values\"><\/span><strong>What are the measures used for the Dispersion of Values?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>There are four main measures that users can utilize to further disperse scatter values. They&#8217;re\u00a0<br \/>Range<br \/>Quartile Dispersion<br \/>Mean Deviation<br \/>Standard Deviation.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1626934447563\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"define-mean-deviation\"><\/span><strong>Define mean deviation.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The mean deviation is the average of all the deviations of all the principles taken from an average value (mean, median, mode) of the series while ignoring the signs (+ or -) of the deviation.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1626934476681\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-is-the-standard-deviation\"><\/span><strong>What is the standard deviation?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>It is the square root of the arithmetic mean of the squared deviations of the items from their mean value.<br \/><strong>Define range.<\/strong><br \/>The range is the variance between the lowest and the highest values in a series.\u00a0<br \/>Range = Highest value in the series \u2013 Lowest value in the series<br \/>\u00a0<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 11 Statistics Chapter 6: We are always concerned with the students&#8217; development. NCERT Solutions For Class 11 Statistics Chapter 6 enable students to comprehend each topic in depth, resulting in good knowledge and the development of expertise in that topic, chapter, or subject. The resources were created by a group of &#8230; <a title=\"Class 11 Statistics NCERT Solutions for Chapter 6 2021: Download PDF\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-statistics-chapter-6\/\" aria-label=\"More on Class 11 Statistics NCERT Solutions for Chapter 6 2021: Download PDF\">Read more<\/a><\/p>\n","protected":false},"author":250,"featured_media":107130,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73413,2985,73410],"tags":[3570,76233,76483],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/107096"}],"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=107096"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/107096\/revisions"}],"predecessor-version":[{"id":113058,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/107096\/revisions\/113058"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/107130"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=107096"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=107096"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=107096"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}