{"id":2438,"date":"2022-06-23T06:36:55","date_gmt":"2022-06-23T06:36:55","guid":{"rendered":"https:\/\/swatilathia.com\/?page_id=2438"},"modified":"2022-06-30T05:10:32","modified_gmt":"2022-06-30T05:10:32","slug":"introduction-to-measure-of-dispersion","status":"publish","type":"page","link":"https:\/\/swatilathia.com\/?page_id=2438","title":{"rendered":"Introduction to Measure of Dispersion"},"content":{"rendered":"<body>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-6a2cc1dddc878\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" 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: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-6a2cc1dddc878\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/swatilathia.com\/?page_id=2438\/#What_is_Measure_of_Dispersion\" >What is Measure of Dispersion?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/swatilathia.com\/?page_id=2438\/#Range_and_Co-efficient_of_Range\" >Range and Co-efficient of Range<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/swatilathia.com\/?page_id=2438\/#Calculate_Range_and_Co-efficient_of_Range_for_Ungrouped_Discrete_series_and_Continuous_series\" >Calculate Range and Co-efficient of Range for Ungrouped, Discrete series and Continuous series<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/swatilathia.com\/?page_id=2438\/#Interquartile_Range_and_Quartile_Deviation_and_Co-efficient_of_Quartile_Deviation\" >Interquartile Range and Quartile Deviation and Co-efficient of Quartile Deviation<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/swatilathia.com\/?page_id=2438\/#Calculate_QD_Quartile_Deviation_and_Co-efficient_of_QD_from_Ungrouped_Data\" >Calculate Q.D. (Quartile Deviation) and Co-efficient of Q.D. from Ungrouped Data<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/swatilathia.com\/?page_id=2438\/#Calculate_QD_and_Co-efficient_of_QD_from_Discrete_Series\" >Calculate Q.D. and Co-efficient of Q.D. from Discrete Series<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/swatilathia.com\/?page_id=2438\/#Calculate_QD_and_Co-efficient_of_QD_from_Continuous_Series\" >Calculate Q.D. and Co-efficient of Q.D. from Continuous Series<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/swatilathia.com\/?page_id=2438\/#What_is_Standard_Deviation\" >What is Standard Deviation ?<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/swatilathia.com\/?page_id=2438\/#Calculate_Standard_DeviationVariance_using_Direct_Method\" >Calculate Standard Deviation\/Variance using Direct Method<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/swatilathia.com\/?page_id=2438\/#Calculate_Standard_DeviationVariance_using_square_of_value_method_and_shortcut_method\" >Calculate Standard Deviation\/Variance using square of value method and shortcut method<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/swatilathia.com\/?page_id=2438\/#Calculate_Combined_Standard_Deviation\" >Calculate Combined Standard Deviation<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"What_is_Measure_of_Dispersion\"><\/span>What is Measure of Dispersion?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">The measure of central tendency tells something about the general level of a frequency distribution but it fails to give its complete description. This does not tell how the items are scattered around it. Sometimes it might happen that averages of two set of data are equal but the scattering of the observations from the mean and internal variations among individual observation could be different. So the direct comparison of two set of data on the basis of mean without truly estimating the variation is not feasible.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Introduction to Measure of Dispersion with example\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/1HQBbcrowxs?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Range_and_Co-efficient_of_Range\"><\/span>Range and Co-efficient of Range<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Range is the simplest method of studying Dispersion. Range is defined as the difference between te value of the smallest observation and the value of the largest observation present in the distribution and it is denoted by R.<\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">To calculate Range, <strong>R = L \u2013 S<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Calculate_Range_and_Co-efficient_of_Range_for_Ungrouped_Discrete_series_and_Continuous_series\"><\/span>Calculate Range and Co-efficient of Range for Ungrouped, Discrete series and Continuous series<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"What is Range | Example to calculate range from ungrouped, discrete and continuous data\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/BINgWlW4Bys?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Interquartile_Range_and_Quartile_Deviation_and_Co-efficient_of_Quartile_Deviation\"><\/span>Interquartile Range and Quartile Deviation and Co-efficient of Quartile Deviation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Introduction to Interquartile range and Quartile Deviation\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/Xy0Ef8jMuF0?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Calculate_QD_Quartile_Deviation_and_Co-efficient_of_QD_from_Ungrouped_Data\"><\/span>Calculate Q.D. (Quartile Deviation) and Co-efficient of Q.D. from Ungrouped Data <span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Calculate Quartile Deviation from Ungrouped Data | Example\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/vz-3OT9kCfQ?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Calculate_QD_and_Co-efficient_of_QD_from_Discrete_Series\"><\/span>Calculate Q.D. and Co-efficient of Q.D. from Discrete Series<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Calculate QD from Discrete Series | Examples\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/-MugfKFi88A?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Calculate_QD_and_Co-efficient_of_QD_from_Continuous_Series\"><\/span>Calculate Q.D. and Co-efficient of Q.D. from Continuous Series<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Calculate Quartile Deviation from Continuous Series | Example\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/x-fS3USxOxw?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"What_is_Standard_Deviation\"><\/span>What is Standard Deviation ?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A standard deviation (or \u03c3) is\u00a0<strong>a measure of how dispersed the data is in relation to the mean<\/strong>.\u00a0\u00a0It is useful in comparing sets of data which may have the same mean but a different range.\u00a0<\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">To calculate Standard Deviation, <\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Step 1:<\/strong> Find the mean. <\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Step 2:<\/strong> For each data point, find the square of its distance to the mean. <\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Step 3:<\/strong> Sum the values from Step 2. <\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Step 4:<\/strong> Divide by the number of data points.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Calculate_Standard_DeviationVariance_using_Direct_Method\"><\/span>Calculate Standard Deviation\/Variance using Direct Method<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"What is Standard Deviation | Example with Direct Method\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/yL0JwBpdQWI?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Calculate_Standard_DeviationVariance_using_square_of_value_method_and_shortcut_method\"><\/span>Calculate Standard Deviation\/Variance using square of value method and shortcut method<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Calculate Standard Deviation with Square of value method and shortcut method\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/qB6zglFAF_s?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Calculate_Combined_Standard_Deviation\"><\/span>Calculate Combined Standard Deviation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Calculate Combined Standard Deviation | Example\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/b96ePnpN1nY?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n<\/body>","protected":false},"excerpt":{"rendered":"<p>What is Measure of Dispersion? The measure of central tendency tells something about the general level of a frequency distribution but it fails to give its complete description. This does not tell how the items are scattered around it. Sometimes it might happen that averages of two set of data are equal but the scattering [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"zakra_page_container_layout":"customizer","zakra_page_sidebar_layout":"customizer","zakra_remove_content_margin":false,"zakra_sidebar":"customizer","zakra_transparent_header":"customizer","zakra_logo":0,"zakra_main_header_style":"default","zakra_menu_item_color":"","zakra_menu_item_hover_color":"","zakra_menu_item_active_color":"","zakra_menu_active_style":"","zakra_page_header":true,"om_disable_all_campaigns":false,"footnotes":""},"class_list":["post-2438","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2438","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swatilathia.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2438"}],"version-history":[{"count":9,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2438\/revisions"}],"predecessor-version":[{"id":2457,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2438\/revisions\/2457"}],"wp:attachment":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2438"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}