{"id":153638,"date":"2024-10-13T07:43:03","date_gmt":"2024-10-13T07:43:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=153638"},"modified":"2024-10-13T07:43:06","modified_gmt":"2024-10-13T07:43:06","slug":"what-is-the-mean-absolute-deviation-of-the-following-set-of-data-10-8-10-6-6-2-10-4","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/13\/what-is-the-mean-absolute-deviation-of-the-following-set-of-data-10-8-10-6-6-2-10-4\/","title":{"rendered":"What is the mean absolute deviation of the following set of data 10 8 10 6 6 2 10 4"},"content":{"rendered":"\n<p>What is the mean absolute deviation of the following set of data 10 8 10 6 6 2 10 4<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To find the mean absolute deviation (MAD) of the data set (10, 8, 10, 6, 6, 2, 10, 4), we can follow these steps:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate the Mean<\/h3>\n\n\n\n<p>First, we need to find the mean of the data set.<\/p>\n\n\n\n<p>[<br>\\text{Mean} = \\frac{\\text{Sum of all data points}}{\\text{Number of data points}}<br>]<\/p>\n\n\n\n<p>Calculating the sum:<\/p>\n\n\n\n<p>[<br>10 + 8 + 10 + 6 + 6 + 2 + 10 + 4 = 56<br>]<\/p>\n\n\n\n<p>The number of data points is 8. Therefore:<\/p>\n\n\n\n<p>[<br>\\text{Mean} = \\frac{56}{8} = 7<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate the Absolute Deviations<\/h3>\n\n\n\n<p>Next, we need to calculate the absolute deviation of each data point from the mean. The absolute deviation is found using the formula:<\/p>\n\n\n\n<p>[<br>\\text{Absolute Deviation} = |x &#8211; \\text{Mean}|<br>]<\/p>\n\n\n\n<p>Calculating the absolute deviations:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For 10: (|10 &#8211; 7| = 3)<\/li>\n\n\n\n<li>For 8: (|8 &#8211; 7| = 1)<\/li>\n\n\n\n<li>For 10: (|10 &#8211; 7| = 3)<\/li>\n\n\n\n<li>For 6: (|6 &#8211; 7| = 1)<\/li>\n\n\n\n<li>For 6: (|6 &#8211; 7| = 1)<\/li>\n\n\n\n<li>For 2: (|2 &#8211; 7| = 5)<\/li>\n\n\n\n<li>For 10: (|10 &#8211; 7| = 3)<\/li>\n\n\n\n<li>For 4: (|4 &#8211; 7| = 3)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate the Mean Absolute Deviation<\/h3>\n\n\n\n<p>Now we calculate the mean of these absolute deviations:<\/p>\n\n\n\n<p>[<br>\\text{Sum of Absolute Deviations} = 3 + 1 + 3 + 1 + 1 + 5 + 3 + 3 = 18<br>]<\/p>\n\n\n\n<p>The mean absolute deviation is then calculated as follows:<\/p>\n\n\n\n<p>[<br>\\text{MAD} = \\frac{\\text{Sum of Absolute Deviations}}{\\text{Number of data points}} = \\frac{18}{8} = 2.25<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The mean absolute deviation of the data set (10, 8, 10, 6, 6, 2, 10, 4) is <strong>2.25<\/strong>. The MAD provides a measure of the dispersion of the data points around the mean. A lower MAD indicates that the data points are closer to the mean, while a higher MAD signifies a greater spread of values. This measure is particularly useful in fields such as statistics and data analysis for assessing variability without being overly affected by extreme values.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the mean absolute deviation of the following set of data 10 8 10 6 6 2 10 4 The Correct Answer and Explanation is : To find the mean absolute deviation (MAD) of the data set (10, 8, 10, 6, 6, 2, 10, 4), we can follow these steps: Step 1: Calculate the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-153638","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/153638","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=153638"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/153638\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=153638"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=153638"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=153638"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}