{"id":6971,"date":"2021-10-22T02:23:40","date_gmt":"2021-10-21T20:53:40","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6971"},"modified":"2021-10-25T09:31:10","modified_gmt":"2021-10-25T04:01:10","slug":"if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/","title":{"rendered":"If the mean deviation about the median of numbers a, 2a, …. , 50a is 50, then |a| is equal to"},"content":{"rendered":"

Solution :<\/h2>\n

Median of a, 2a, 3a, 4a, ….. . 50a is<\/p>\n

\\(25a + 26a\\over 2\\) = 25.5a<\/p>\n

Mean deviation = \\(\\sum{|x_i – Median|}\\over N\\)<\/p>\n

\\(\\implies\\)\u00a0 50 = \\(1\\over 50\\) {2|a|.(0.5 + 1.5 + …… + 24.5)]<\/p>\n

\\(\\implies\\) 2500 = 2|a|. \\(25\\over 2\\) (25)<\/p>\n

\\(\\implies\\) |a| = 4<\/p>\n

\n

Similar Questions<\/h3>\n

The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P(X = 1) is<\/a><\/p>\n

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observation of the set is increased by 2, then the median of the new is<\/a><\/p>\n

A student obtained 75%, 80%, 85% marks in three subjects. If the marks of another subject are added then his average marks can not be less than<\/a><\/p>\n

In a series of 2n observations, half of them equals a and remaining half equal -a. If the standard deviation of the observation is 2, then |a| equal to<\/a><\/p>\n

The variance of first 50 even natural numbers is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Median of a, 2a, 3a, 4a, ….. . 50a is \\(25a + 26a\\over 2\\) = 25.5a Mean deviation = \\(\\sum{|x_i – Median|}\\over N\\) \\(\\implies\\)\u00a0 50 = \\(1\\over 50\\) {2|a|.(0.5 + 1.5 + …… + 24.5)] \\(\\implies\\) 2500 = 2|a|. \\(25\\over 2\\) (25) \\(\\implies\\) |a| = 4 Similar Questions The mean and variance of …<\/p>\n

If the mean deviation about the median of numbers a, 2a, …. , 50a is 50, then |a| is equal to<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,58],"tags":[],"yoast_head":"\nIf the mean deviation about the median of numbers a, 2a, .... , 50a is 50, then |a| is equal to<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the mean deviation about the median of numbers a, 2a, .... , 50a is 50, then |a| is equal to\" \/>\n<meta property=\"og:description\" content=\"Solution : Median of a, 2a, 3a, 4a, ….. . 50a is (25a + 26aover 2) = 25.5a Mean deviation = (sum{|x_i – Median|}over N) (implies)\u00a0 50 = (1over 50) {2|a|.(0.5 + 1.5 + …… + 24.5)] (implies) 2500 = 2|a|. (25over 2) (25) (implies) |a| = 4 Similar Questions The mean and variance of … If the mean deviation about the median of numbers a, 2a, …. , 50a is 50, then |a| is equal to Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-21T20:53:40+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-25T04:01:10+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"If the mean deviation about the median of numbers a, 2a, …. , 50a is 50, then |a| is equal to\",\"datePublished\":\"2021-10-21T20:53:40+00:00\",\"dateModified\":\"2021-10-25T04:01:10+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/\"},\"wordCount\":158,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Maths Questions\",\"Statistics Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/\",\"url\":\"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/\",\"name\":\"If the mean deviation about the median of numbers a, 2a, .... , 50a is 50, then |a| is equal to\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-21T20:53:40+00:00\",\"dateModified\":\"2021-10-25T04:01:10+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"If the mean deviation about the median of numbers a, 2a, …. , 50a is 50, then |a| is equal to\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"If the mean deviation about the median of numbers a, 2a, .... , 50a is 50, then |a| is equal to","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/","og_locale":"en_US","og_type":"article","og_title":"If the mean deviation about the median of numbers a, 2a, .... , 50a is 50, then |a| is equal to","og_description":"Solution : Median of a, 2a, 3a, 4a, ….. . 50a is (25a + 26aover 2) = 25.5a Mean deviation = (sum{|x_i – Median|}over N) (implies)\u00a0 50 = (1over 50) {2|a|.(0.5 + 1.5 + …… + 24.5)] (implies) 2500 = 2|a|. (25over 2) (25) (implies) |a| = 4 Similar Questions The mean and variance of … If the mean deviation about the median of numbers a, 2a, …. , 50a is 50, then |a| is equal to Read More »","og_url":"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/","og_site_name":"Mathemerize","article_published_time":"2021-10-21T20:53:40+00:00","article_modified_time":"2021-10-25T04:01:10+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"If the mean deviation about the median of numbers a, 2a, …. , 50a is 50, then |a| is equal to","datePublished":"2021-10-21T20:53:40+00:00","dateModified":"2021-10-25T04:01:10+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/"},"wordCount":158,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Maths Questions","Statistics Questions"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/","url":"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/","name":"If the mean deviation about the median of numbers a, 2a, .... , 50a is 50, then |a| is equal to","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-10-21T20:53:40+00:00","dateModified":"2021-10-25T04:01:10+00:00","breadcrumb":{"@id":"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/if-the-mean-deviation-about-the-median-of-numbers-a-2a-50a-is-50-then-a-is-equal-to\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"If the mean deviation about the median of numbers a, 2a, …. , 50a is 50, then |a| is equal to"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6971"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=6971"}],"version-history":[{"count":3,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6971\/revisions"}],"predecessor-version":[{"id":7479,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6971\/revisions\/7479"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=6971"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=6971"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=6971"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}