{"id":31,"date":"2023-11-28T17:07:25","date_gmt":"2023-11-28T22:07:25","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/median\/"},"modified":"2025-01-14T16:50:23","modified_gmt":"2025-01-14T21:50:23","slug":"median","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/median\/","title":{"raw":"The Median","rendered":"The Median"},"content":{"raw":"<div class=\"The Median\">\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Outcomes<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">Understand and calculate medians both by hand and in Excel.<\/div>\r\n<\/div>\r\n<img class=\" wp-image-426 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/11\/Median-300x52.jpg\" alt=\"\" width=\"312\" height=\"54\" \/>\r\n<ul>\r\n \t<li>The value of the middle number<\/li>\r\n \t<li>Or the mean of the two middle numbers when there are an even number of data<\/li>\r\n \t<li>To calculate: order the numbers from smallest to largest then find the middle number or average of two middle numbers (for even sized data sets)<\/li>\r\n<\/ul>\r\n<h1>Finding the median For an Odd numbers of Data (ExerCise)<\/h1>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Knowledge Check 2.1 - Finding the Median<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><strong>Step 1<\/strong>:\r\n[h5p id=\"4\"]<strong>Step 2<\/strong>:\r\n<div>[h5p id=\"5\"]<\/div>\r\n<div><\/div>\r\n<div>Conclusion: The median value of the data set is 23.<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Finding the median for AN EVEN number of Data<\/h1>\r\n<h2>Example 2.2<\/h2>\r\nFind the median of the following numbers: 25, 19, 24, 23, 28, 21\r\n\r\n<span style=\"color: #003366\"><strong>Step 1:<\/strong> <\/span>Order the data: 19, 21, 23, 24, 25, 28\r\n\r\n<span style=\"color: #003366\"><strong>Step 2:<\/strong><\/span> Find the middle values: 19, 21, <strong>23, 24<\/strong>, 25, 28\r\n\r\n<strong><span style=\"color: #003366\">Step 3:<\/span> <\/strong>Average the middle values: (23 + 24)\/ 2 = 23.5\r\n\r\n<span style=\"color: #003366\"><strong>Conclusion<\/strong><\/span>: The middle value (median) for the above data set is 23.5.\r\n<h1>Finding the median using Excel (VIDEO)<\/h1>\r\n<h2>Example 2.3.1<\/h2>\r\nFind the median using Excel.\r\n<ul>\r\n \t<li class=\"import-BodyText\">We use the =median() call in Excel to calculate the median.<\/li>\r\n \t<li>See the video below.<\/li>\r\n \t<li><a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/1-2-2.xlsx\">Click here to download the solution shown in the video below<\/a>.<\/li>\r\n<\/ul>\r\n[embed]https:\/\/youtu.be\/AUlgbNL_VF0[\/embed]\r\n<h1>Comparing the Mean and Median (VIDEO)<\/h1>\r\n<h2>Example 2.3.2<\/h2>\r\n<ul>\r\n \t<li>The mean can be greatly affected by outliers (extreme values)<\/li>\r\n \t<li>The median is a better reflection of the middle value in data set because it does not get affected by extreme values<\/li>\r\n \t<li>See the video below for an example.<\/li>\r\n \t<li><a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/1-2-3.xlsx\">Click here to download the Excel file shown in the video below<\/a>.<\/li>\r\n<\/ul>\r\n&nbsp;\r\n\r\n[embed]https:\/\/youtu.be\/mV3YXBxw-oI[\/embed]\r\n<h1>Key Takeaways (Exercise)<\/h1>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Key Takeaways: The Median<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[h5p id=\"7\"]\r\n[h5p id=\"10\"]\r\n\r\n<\/div>\r\n<\/div>\r\n<h1>Your Own Notes<\/h1>\r\n<ul>\r\n \t<li>Are there any notes you want to take from this section? Is there anything you'd like to copy and paste below?<\/li>\r\n \t<li>These notes are for you only (they will not be stored anywhere)<\/li>\r\n \t<li>Make sure to download them at the end to use as a reference<\/li>\r\n<\/ul>\r\n[h5p id=\"16\"]\r\n\r\n<\/div>","rendered":"<div class=\"The Median\">\n<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Outcomes<\/p>\n<\/header>\n<div class=\"textbox__content\">Understand and calculate medians both by hand and in Excel.<\/div>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-426 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/11\/Median-300x52.jpg\" alt=\"\" width=\"312\" height=\"54\" srcset=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/11\/Median-300x52.jpg 300w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/11\/Median-1024x179.jpg 1024w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/11\/Median-768x134.jpg 768w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/11\/Median-1536x268.jpg 1536w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/11\/Median-2048x357.jpg 2048w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/11\/Median-65x11.jpg 65w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/11\/Median-225x39.jpg 225w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/11\/Median-350x61.jpg 350w\" sizes=\"auto, (max-width: 312px) 100vw, 312px\" \/><\/p>\n<ul>\n<li>The value of the middle number<\/li>\n<li>Or the mean of the two middle numbers when there are an even number of data<\/li>\n<li>To calculate: order the numbers from smallest to largest then find the middle number or average of two middle numbers (for even sized data sets)<\/li>\n<\/ul>\n<h1>Finding the median For an Odd numbers of Data (ExerCise)<\/h1>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Knowledge Check 2.1 &#8211; Finding the Median<\/p>\n<\/header>\n<div class=\"textbox__content\"><strong>Step 1<\/strong>:<\/p>\n<div id=\"h5p-4\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-4\" class=\"h5p-iframe\" data-content-id=\"4\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"KC 1.2.1 - Order the data:\"><\/iframe><\/div>\n<\/div>\n<p><strong>Step 2<\/strong>:<\/p>\n<div>\n<div id=\"h5p-5\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-5\" class=\"h5p-iframe\" data-content-id=\"5\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"KC 1.2.1  - Determine Middle value\"><\/iframe><\/div>\n<\/div>\n<\/div>\n<div><\/div>\n<div>Conclusion: The median value of the data set is 23.<\/div>\n<\/div>\n<\/div>\n<h1>Finding the median for AN EVEN number of Data<\/h1>\n<h2>Example 2.2<\/h2>\n<p>Find the median of the following numbers: 25, 19, 24, 23, 28, 21<\/p>\n<p><span style=\"color: #003366\"><strong>Step 1:<\/strong> <\/span>Order the data: 19, 21, 23, 24, 25, 28<\/p>\n<p><span style=\"color: #003366\"><strong>Step 2:<\/strong><\/span> Find the middle values: 19, 21, <strong>23, 24<\/strong>, 25, 28<\/p>\n<p><strong><span style=\"color: #003366\">Step 3:<\/span> <\/strong>Average the middle values: (23 + 24)\/ 2 = 23.5<\/p>\n<p><span style=\"color: #003366\"><strong>Conclusion<\/strong><\/span>: The middle value (median) for the above data set is 23.5.<\/p>\n<h1>Finding the median using Excel (VIDEO)<\/h1>\n<h2>Example 2.3.1<\/h2>\n<p>Find the median using Excel.<\/p>\n<ul>\n<li class=\"import-BodyText\">We use the =median() call in Excel to calculate the median.<\/li>\n<li>See the video below.<\/li>\n<li><a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/1-2-2.xlsx\">Click here to download the solution shown in the video below<\/a>.<\/li>\n<\/ul>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Calculating the median using Excel\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/AUlgbNL_VF0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h1>Comparing the Mean and Median (VIDEO)<\/h1>\n<h2>Example 2.3.2<\/h2>\n<ul>\n<li>The mean can be greatly affected by outliers (extreme values)<\/li>\n<li>The median is a better reflection of the middle value in data set because it does not get affected by extreme values<\/li>\n<li>See the video below for an example.<\/li>\n<li><a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/1-2-3.xlsx\">Click here to download the Excel file shown in the video below<\/a>.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Comparing the mean and median\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/mV3YXBxw-oI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h1>Key Takeaways (Exercise)<\/h1>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Key Takeaways: The Median<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"h5p-7\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-7\" class=\"h5p-iframe\" data-content-id=\"7\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"1.2 Key Takeaways\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-10\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-10\" class=\"h5p-iframe\" data-content-id=\"10\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"1.2 Key Takeaways Accordion\"><\/iframe><\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Your Own Notes<\/h1>\n<ul>\n<li>Are there any notes you want to take from this section? Is there anything you&#8217;d like to copy and paste below?<\/li>\n<li>These notes are for you only (they will not be stored anywhere)<\/li>\n<li>Make sure to download them at the end to use as a reference<\/li>\n<\/ul>\n<div id=\"h5p-16\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-16\" class=\"h5p-iframe\" data-content-id=\"16\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Key takeaways, notes and comments from this section document tool.\"><\/iframe><\/div>\n<\/div>\n<\/div>\n","protected":false},"author":865,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-31","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/31","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/users\/865"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/31\/revisions"}],"predecessor-version":[{"id":2982,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/31\/revisions\/2982"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/31\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/media?parent=31"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=31"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/contributor?post=31"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/license?post=31"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}