{"id":3578,"date":"2021-07-29T11:27:33","date_gmt":"2021-07-29T11:27:33","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3578"},"modified":"2021-11-29T18:40:56","modified_gmt":"2021-11-29T13:10:56","slug":"measures-of-dispersion-statistics","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/","title":{"rendered":"What are Measures of Dispersion Statistics ?"},"content":{"rendered":"

Here, you will learn what are the measures of dispersion in statistics i.e. range, mean deviation, variance and standard deviation with example.<\/p>\n

Let’s begin –<\/p>\n

Measures of Dispersion :<\/h2>\n

The dispersion of a statistical distribution is the measure of deviation of its values about the their average(central) value.<\/p>\n

It gives an idea of scatteredness of the different values from the average value.<\/p>\n

Generally these measures of dispersion are commonly used.<\/p>\n

\n

(i) Range <\/p>\n

(ii) Mean deviation <\/p>\n

(iii) Variance and standard deviation<\/p>\n<\/blockquote>\n

Range :<\/strong><\/p>\n

The difference between the greatest and least values of variate of a distribution, are called range of that distribution.<\/p>\n

If distribution is the grouped distribution, then its range is the difference between upper limit of maximum class and lower limit of a minimum class.<\/p>\n

\n

Also, coefficient of range = \\({difference of extreme values}\\over {sum of extreme values}\\)<\/p>\n<\/blockquote>\n

Mean deviation(M.D.) :<\/strong><\/p>\n

The mean deviation of a distribution is, the mean of absolute value of deviations of variate from their statistical average(Mean, Median, Mode).<\/p>\n

If A is any statistical average of a distribution that mean deviation about A is defined as<\/p>\n

\n

Mean deviation = \\({\\sum_{i=1}^{n}{|x_i – A|}}\\over n\\)    (For ungrouped distribution)<\/p>\n

Mean deviation = \\({\\sum_{i=1}^{n}{f_i|x_i – A|}}\\over N\\)  (For frequency distribution)<\/p>\n<\/blockquote>\n

NOTE : <\/strong>Mean deviation is minimum when it taken about the median.<\/p>\n\n\n

Example : <\/span>Find the mean deviation of the numbers 3, 4, 5, 6, 7.<\/p>\n

Solution : <\/span>We have n = 5, \\(\\bar{x}\\) = 5 here.

\n \\(\\therefore\\) Mean deviation = \\({\\sum_{i=1}^{n}{|x_i – A|}}\\over n\\)

\n = \\(1\\over 5\\)[|3 – 5| + |4 – 5| + |5 – 5| + |6 – 5| + |7 – 5|]

\n = \\(1\\over 5\\)[2 + 1 + 0 + 1 + 2] = 1.2

<\/p>\n\n\n

Variance and Standard Deviation :<\/strong><\/p>\n

It is defined as the mean of squares of the deviation of variate from their mean. It is denoted by \\(\\sigma^2\\) or var(x).<\/p>\n

The positive square root of variance are called the standard deviation. It is denoted by \\(\\sigma\\) or S.D.<\/p>\n

\n

Hence standard deviation = + \\(\\sqrt{variance}\\)<\/p>\n<\/blockquote>\n

Hope you learnt what are measures of dispersion in statistics, learn more concepts of statistics and practice more questions to get ahead in the competition. Good luck!<\/p>\n\n\n

\n
Next – Formula for Variance and Standard Deviation<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Mean By Step Deviation Method and By Short Method<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here, you will learn what are the measures of dispersion in statistics i.e. range, mean deviation, variance and standard deviation with example. Let’s begin – Measures of Dispersion : The dispersion of a statistical distribution is the measure of deviation of its values about the their average(central) value. It gives an idea of scatteredness of …<\/p>\n

What are Measures of Dispersion Statistics ?<\/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":[22],"tags":[606,604,605,607],"yoast_head":"\nWhat are Measures of Dispersion Statistics ?<\/title>\n<meta name=\"description\" content=\"In this post, you will learn what are the measures of dispersion in statistics i.e. range, mean deviation, variance and standard deviation.\" \/>\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\/measures-of-dispersion-statistics\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What are Measures of Dispersion Statistics ?\" \/>\n<meta property=\"og:description\" content=\"In this post, you will learn what are the measures of dispersion in statistics i.e. range, mean deviation, variance and standard deviation.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-07-29T11:27:33+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-11-29T13:10:56+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=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"What are Measures of Dispersion Statistics ?\",\"datePublished\":\"2021-07-29T11:27:33+00:00\",\"dateModified\":\"2021-11-29T13:10:56+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/\"},\"wordCount\":368,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"keywords\":[\"mean deviation\",\"measures of dispersion\",\"range\",\"variance and standard deviation\"],\"articleSection\":[\"Statistics\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/\",\"url\":\"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/\",\"name\":\"What are Measures of Dispersion Statistics ?\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-07-29T11:27:33+00:00\",\"dateModified\":\"2021-11-29T13:10:56+00:00\",\"description\":\"In this post, you will learn what are the measures of dispersion in statistics i.e. range, mean deviation, variance and standard deviation.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"What are Measures of Dispersion Statistics ?\"}]},{\"@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":"What are Measures of Dispersion Statistics ?","description":"In this post, you will learn what are the measures of dispersion in statistics i.e. range, mean deviation, variance and standard deviation.","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\/measures-of-dispersion-statistics\/","og_locale":"en_US","og_type":"article","og_title":"What are Measures of Dispersion Statistics ?","og_description":"In this post, you will learn what are the measures of dispersion in statistics i.e. range, mean deviation, variance and standard deviation.","og_url":"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/","og_site_name":"Mathemerize","article_published_time":"2021-07-29T11:27:33+00:00","article_modified_time":"2021-11-29T13:10:56+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"What are Measures of Dispersion Statistics ?","datePublished":"2021-07-29T11:27:33+00:00","dateModified":"2021-11-29T13:10:56+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/"},"wordCount":368,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"keywords":["mean deviation","measures of dispersion","range","variance and standard deviation"],"articleSection":["Statistics"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/","url":"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/","name":"What are Measures of Dispersion Statistics ?","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-07-29T11:27:33+00:00","dateModified":"2021-11-29T13:10:56+00:00","description":"In this post, you will learn what are the measures of dispersion in statistics i.e. range, mean deviation, variance and standard deviation.","breadcrumb":{"@id":"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/measures-of-dispersion-statistics\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"What are Measures of Dispersion Statistics ?"}]},{"@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\/3578"}],"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=3578"}],"version-history":[{"count":8,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/3578\/revisions"}],"predecessor-version":[{"id":6545,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/3578\/revisions\/6545"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=3578"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=3578"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=3578"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}