{"id":145424,"date":"2024-09-27T05:56:32","date_gmt":"2024-09-27T05:56:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=145424"},"modified":"2024-09-27T05:56:34","modified_gmt":"2024-09-27T05:56:34","slug":"what-is-the-interquartile-range-of-this-set-of-data","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/27\/what-is-the-interquartile-range-of-this-set-of-data\/","title":{"rendered":"What is the interquartile range of this set of data"},"content":{"rendered":"\n<p>What is the interquartile range of this set of data? 15, 19, 20, 25, 31, 38, 41 6 13 19 26<\/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 interquartile range (IQR) of the given data set, we first need to organize the data in ascending order and then determine the quartiles.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Organize the Data<\/h3>\n\n\n\n<p>The provided data set is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>15, 19, 20, 25, 31, 38, 41, 6, 13, 19, 26<\/li>\n<\/ul>\n\n\n\n<p>First, let&#8217;s arrange the numbers in ascending order:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Ordered Data<\/strong>: 6, 13, 15, 19, 19, 20, 25, 26, 31, 38, 41<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Determine Quartiles<\/h3>\n\n\n\n<p>The quartiles divide the data set into four equal parts:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Q1 (First Quartile)<\/strong>: The median of the first half of the data.<\/li>\n\n\n\n<li><strong>Q2 (Second Quartile)<\/strong>: The median of the entire data set.<\/li>\n\n\n\n<li><strong>Q3 (Third Quartile)<\/strong>: The median of the second half of the data.<\/li>\n<\/ul>\n\n\n\n<p><strong>Finding Q2 (Median)<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The data set has 11 values. The median (Q2) is the middle value, which is the 6th value:<\/li>\n\n\n\n<li><strong>Q2 = 20<\/strong><\/li>\n<\/ul>\n\n\n\n<p><strong>Finding Q1<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The first half of the data (before the median) is:<\/li>\n\n\n\n<li>6, 13, 15, 19, 19<\/li>\n\n\n\n<li>Q1 is the median of this half. Since there are 5 values, the median is the 3rd value:<\/li>\n\n\n\n<li><strong>Q1 = 15<\/strong><\/li>\n<\/ul>\n\n\n\n<p><strong>Finding Q3<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The second half of the data (after the median) is:<\/li>\n\n\n\n<li>25, 26, 31, 38, 41<\/li>\n\n\n\n<li>Q3 is the median of this half. With 5 values, the median is again the 3rd value:<\/li>\n\n\n\n<li><strong>Q3 = 31<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate the Interquartile Range (IQR)<\/h3>\n\n\n\n<p>The IQR is calculated as:<br>[<br>\\text{IQR} = Q3 &#8211; Q1<br>]<br>Substituting in our values:<br>[<br>\\text{IQR} = 31 &#8211; 15 = 16<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The interquartile range (IQR) of the given data set is <strong>16<\/strong>. The IQR is a measure of statistical dispersion and represents the range within which the central 50% of the data falls, effectively providing insight into the spread of the middle portion of the data while reducing the influence of outliers. In this case, the IQR indicates a moderate spread of the values between the lower and upper quartiles, which can be useful for understanding the variability in the dataset.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the interquartile range of this set of data? 15, 19, 20, 25, 31, 38, 41 6 13 19 26 The Correct Answer and Explanation is : To find the interquartile range (IQR) of the given data set, we first need to organize the data in ascending order and then determine the quartiles. Step [&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-145424","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145424","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=145424"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145424\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=145424"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=145424"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=145424"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}