{"id":167341,"date":"2024-11-15T16:13:20","date_gmt":"2024-11-15T16:13:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=167341"},"modified":"2024-11-15T16:13:22","modified_gmt":"2024-11-15T16:13:22","slug":"in-a-study-of-the-lizard-sceloporus-occidentalis-biologists-measured-the-distance-m-run-in-2-minutes-for-each-of-15-animals","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/15\/in-a-study-of-the-lizard-sceloporus-occidentalis-biologists-measured-the-distance-m-run-in-2-minutes-for-each-of-15-animals\/","title":{"rendered":"In a study of the lizard Sceloporus occidentalis, biologists measured the distance (m) run in 2 minutes for each of 15 animals."},"content":{"rendered":"\n<p>In a study of the lizard Sceloporus occidentalis, biologists measured the distance (m) run in 2 minutes for each of 15 animals. The results (listed in increasing order) were as follows:42 18.4 22.2 24.5 26.4 27.5 28.7 30.6 32.9 32.9 34.0 34.8 37.5 42.1 45.5 45.5 (a) Determine the quartiles and the interquartile range. (b) Determine the range.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, let&#8217;s break it down step by step.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part (a) Determine the Quartiles and Interquartile Range (IQR)<\/h3>\n\n\n\n<p><strong>Step 1: Organize the Data<\/strong><br>The data set is already ordered in increasing order:<br>[ 18.4, 22.2, 24.5, 26.4, 27.5, 28.7, 30.6, 32.9, 32.9, 34.0, 34.8, 37.5, 42.1, 42.0, 45.5, 45.5 ]<\/p>\n\n\n\n<p>There are 16 data points, so:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Median (Q2)<\/strong>: The median is the middle value. Since there are an even number of data points (16), we take the average of the two middle values (the 8th and 9th values):<br>[<br>Q2 = \\frac{32.9 + 32.9}{2} = 32.9<br>]<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 2: Find Q1 and Q3<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Q1 (First Quartile)<\/strong>: This is the median of the lower half of the data (excluding the median). The lower half of the data set is:<br>[<br>18.4, 22.2, 24.5, 26.4, 27.5, 28.7, 30.6, 32.9<br>]<br>The median of this group is the average of the 4th and 5th values:<br>[<br>Q1 = \\frac{26.4 + 27.5}{2} = 26.95<br>]<\/li>\n\n\n\n<li><strong>Q3 (Third Quartile)<\/strong>: This is the median of the upper half of the data (excluding the median). The upper half of the data set is:<br>[<br>32.9, 34.0, 34.8, 37.5, 42.1, 42.0, 45.5, 45.5<br>]<br>The median of this group is the average of the 4th and 5th values:<br>[<br>Q3 = \\frac{37.5 + 42.1}{2} = 39.8<br>]<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 3: Calculate the Interquartile Range (IQR)<\/strong><br>The IQR is the difference between the third quartile (Q3) and the first quartile (Q1):<br>[<br>IQR = Q3 &#8211; Q1 = 39.8 &#8211; 26.95 = 12.85<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part (b) Determine the Range<\/h3>\n\n\n\n<p>The <strong>range<\/strong> is the difference between the largest and smallest values in the data set:<br>[<br>\\text{Range} = 45.5 &#8211; 18.4 = 27.1<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Quartiles<\/strong>:<\/li>\n\n\n\n<li>Q1 = 26.95<\/li>\n\n\n\n<li>Q2 (Median) = 32.9<\/li>\n\n\n\n<li>Q3 = 39.8<\/li>\n\n\n\n<li><strong>Interquartile Range (IQR)<\/strong> = 12.85<\/li>\n\n\n\n<li><strong>Range<\/strong> = 27.1<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>To find the quartiles, we divided the data into four parts. The <strong>first quartile (Q1)<\/strong> represents the value below which 25% of the data falls, and the <strong>third quartile (Q3)<\/strong> represents the value below which 75% of the data falls. The <strong>median (Q2)<\/strong> splits the data in half. The <strong>interquartile range (IQR)<\/strong> measures the spread of the middle 50% of the data, which is the difference between Q3 and Q1. The <strong>range<\/strong> gives the overall spread of the data by subtracting the smallest value from the largest value.<\/p>\n\n\n\n<p>The quartiles and IQR are useful for understanding the distribution of data, as they provide insight into the central tendency and variability, excluding outliers. The range is a simpler measure but can be influenced by extreme values.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In a study of the lizard Sceloporus occidentalis, biologists measured the distance (m) run in 2 minutes for each of 15 animals. The results (listed in increasing order) were as follows:42 18.4 22.2 24.5 26.4 27.5 28.7 30.6 32.9 32.9 34.0 34.8 37.5 42.1 45.5 45.5 (a) Determine the quartiles and the interquartile range. (b) [&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-167341","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167341","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=167341"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167341\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167341"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167341"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167341"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}