{"id":911,"date":"2024-04-19T03:35:17","date_gmt":"2024-04-19T07:35:17","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=chapter&#038;p=911"},"modified":"2024-06-11T15:57:46","modified_gmt":"2024-06-11T19:57:46","slug":"percentiles-quartiles-and-five-number-summaries","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/percentiles-quartiles-and-five-number-summaries\/","title":{"raw":"Percentiles, Quartiles and Five Number Summaries","rendered":"Percentiles, Quartiles and Five Number Summaries"},"content":{"raw":"<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">\u00a0Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nCalculate and understand percentiles, quartiles and five number summaries\r\n\r\n<\/div>\r\n<\/div>\r\n<h2>Percentiles:<\/h2>\r\n<ul>\r\n \t<li>The value such that a specified percent of the data is below that value<\/li>\r\n \t<li><em>Example<\/em>: If the 80% percentile (P<sub>80<\/sub>) = 179, then 80% of the data is below 179.<\/li>\r\n \t<li>We will use = <a href=\"https:\/\/support.microsoft.com\/en-us\/office\/percentile-inc-function-680f9539-45eb-410b-9a5e-c1355e5fe2ed#:~:text=INC%20function,-Excel%20for%20Microsoft&amp;text=Returns%20the%20k%2Dth%20percentile,establish%20a%20threshold%20of%20acceptance.\">PERCENTILE.INC(<em>array<\/em>,\u00a0<em>k<\/em>)<\/a> in Excel to determine these values<\/li>\r\n<\/ul>\r\n<h2>Quartiles:<\/h2>\r\n<ul>\r\n \t<li>The data can be 'split' into four quarters<\/li>\r\n \t<li>Q<sub>1<\/sub> is the value such that 25% of the data is below this value (=P<sub>25<\/sub>)<\/li>\r\n \t<li>Q<sub>2<\/sub> is the value such that 50% of the data is below this value (=P<sub>50<\/sub>)<\/li>\r\n \t<li><em>Note:<\/em> Q<sub>2<\/sub> is also the <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/median\/\">median<\/a><\/li>\r\n \t<li>Q<sub>3<\/sub> is the value such that 75% of the data is below this value (=P<sub>75<\/sub>)<\/li>\r\n \t<li>We will use = <a href=\"https:\/\/support.microsoft.com\/en-us\/office\/quartile-inc-function-1bbacc80-5075-42f1-aed6-47d735c4819d\">QUARTILE.INC(<em>array<\/em>, <em>quart<\/em>)<\/a> in Excel to determine the quartiles<\/li>\r\n<\/ul>\r\n<h2>Five Number Summaries<\/h2>\r\nData can be 'summarized' by its five number summary. This summary is used to determine the shape of the data and generate boxplots.\r\n<ol>\r\n \t<li>Minimum (min) - the minimum value in the data<\/li>\r\n \t<li>First quartile (Q<sub>1<\/sub>) - the first quartile value<\/li>\r\n \t<li>Median\u00a0(Q<sub>2<\/sub>) - the second quartile value<\/li>\r\n \t<li>Third quartile (Q<sub>3<\/sub>) - the third quartile value<\/li>\r\n \t<li>Maximum - the maximum value in the data<\/li>\r\n<\/ol>\r\n<h1>Generating the five number summary in Excel (video)<\/h1>\r\n<h2>Example 11.1.1<\/h2>\r\n<span style=\"color: #003366\"><strong>Problem Setup: <\/strong><\/span>Again, we are working with the 30 students' heights from BCIT (<a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/9-1-1-1.xlsx\">click here to download as Excel sheet<\/a>) and see the table of values below. We want to create the five number summary for their heights:\r\n<table style=\"height: 54px;margin-left: 40px\">\r\n<tbody style=\"padding-left: 40px\">\r\n<tr style=\"height: 18px;padding-left: 40px\">\r\n<td style=\"height: 18px;width: 41.6875px;padding-left: 40px\">173<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">153<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">172<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">191<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">173<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">167<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">156<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">169<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">175<\/td>\r\n<td style=\"height: 18px;width: 41.9792px;padding-left: 40px\">169<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;padding-left: 40px\">\r\n<td style=\"height: 18px;width: 41.6875px;padding-left: 40px\">159<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">163<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">177<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">155<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">152<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">178<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">172<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">188<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">152<\/td>\r\n<td style=\"height: 18px;width: 41.9792px;padding-left: 40px\">171<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;padding-left: 40px\">\r\n<td style=\"height: 18px;width: 41.6875px;padding-left: 40px\">174<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">183<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">192<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">151<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">159<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">184<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">170<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">186<\/td>\r\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">155<\/td>\r\n<td style=\"height: 18px;width: 41.9792px;padding-left: 40px\">156<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<span style=\"color: #003366\"><strong>Question: <\/strong><\/span>What is the five number summary for the above students' heights?\r\n\r\n[embed]https:\/\/youtu.be\/mzwV8w2g248[\/embed]\r\n\r\n<span style=\"color: #003366\"><strong>Solution: <\/strong><a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/04\/11-1-1_Solutions.xlsx\">Click here<\/a><\/span>\u00a0to view the solutions (five number summary) shown in the above video:\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: Percentiles, Quartiles and Five Number Summaries<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[h5p id=\"25\"]\r\n\r\n[h5p id=\"26\"]\r\n\r\n<\/div>\r\n<\/div>\r\n<h1>Your Own Notes (EXERCISE)<\/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\"]","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">\u00a0Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Calculate and understand percentiles, quartiles and five number summaries<\/p>\n<\/div>\n<\/div>\n<h2>Percentiles:<\/h2>\n<ul>\n<li>The value such that a specified percent of the data is below that value<\/li>\n<li><em>Example<\/em>: If the 80% percentile (P<sub>80<\/sub>) = 179, then 80% of the data is below 179.<\/li>\n<li>We will use = <a href=\"https:\/\/support.microsoft.com\/en-us\/office\/percentile-inc-function-680f9539-45eb-410b-9a5e-c1355e5fe2ed#:~:text=INC%20function,-Excel%20for%20Microsoft&amp;text=Returns%20the%20k%2Dth%20percentile,establish%20a%20threshold%20of%20acceptance.\">PERCENTILE.INC(<em>array<\/em>,\u00a0<em>k<\/em>)<\/a> in Excel to determine these values<\/li>\n<\/ul>\n<h2>Quartiles:<\/h2>\n<ul>\n<li>The data can be &#8216;split&#8217; into four quarters<\/li>\n<li>Q<sub>1<\/sub> is the value such that 25% of the data is below this value (=P<sub>25<\/sub>)<\/li>\n<li>Q<sub>2<\/sub> is the value such that 50% of the data is below this value (=P<sub>50<\/sub>)<\/li>\n<li><em>Note:<\/em> Q<sub>2<\/sub> is also the <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/median\/\">median<\/a><\/li>\n<li>Q<sub>3<\/sub> is the value such that 75% of the data is below this value (=P<sub>75<\/sub>)<\/li>\n<li>We will use = <a href=\"https:\/\/support.microsoft.com\/en-us\/office\/quartile-inc-function-1bbacc80-5075-42f1-aed6-47d735c4819d\">QUARTILE.INC(<em>array<\/em>, <em>quart<\/em>)<\/a> in Excel to determine the quartiles<\/li>\n<\/ul>\n<h2>Five Number Summaries<\/h2>\n<p>Data can be &#8216;summarized&#8217; by its five number summary. This summary is used to determine the shape of the data and generate boxplots.<\/p>\n<ol>\n<li>Minimum (min) &#8211; the minimum value in the data<\/li>\n<li>First quartile (Q<sub>1<\/sub>) &#8211; the first quartile value<\/li>\n<li>Median\u00a0(Q<sub>2<\/sub>) &#8211; the second quartile value<\/li>\n<li>Third quartile (Q<sub>3<\/sub>) &#8211; the third quartile value<\/li>\n<li>Maximum &#8211; the maximum value in the data<\/li>\n<\/ol>\n<h1>Generating the five number summary in Excel (video)<\/h1>\n<h2>Example 11.1.1<\/h2>\n<p><span style=\"color: #003366\"><strong>Problem Setup: <\/strong><\/span>Again, we are working with the 30 students&#8217; heights from BCIT (<a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/9-1-1-1.xlsx\">click here to download as Excel sheet<\/a>) and see the table of values below. We want to create the five number summary for their heights:<\/p>\n<table style=\"height: 54px;margin-left: 40px\">\n<tbody style=\"padding-left: 40px\">\n<tr style=\"height: 18px;padding-left: 40px\">\n<td style=\"height: 18px;width: 41.6875px;padding-left: 40px\">173<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">153<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">172<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">191<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">173<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">167<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">156<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">169<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">175<\/td>\n<td style=\"height: 18px;width: 41.9792px;padding-left: 40px\">169<\/td>\n<\/tr>\n<tr style=\"height: 18px;padding-left: 40px\">\n<td style=\"height: 18px;width: 41.6875px;padding-left: 40px\">159<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">163<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">177<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">155<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">152<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">178<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">172<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">188<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">152<\/td>\n<td style=\"height: 18px;width: 41.9792px;padding-left: 40px\">171<\/td>\n<\/tr>\n<tr style=\"height: 18px;padding-left: 40px\">\n<td style=\"height: 18px;width: 41.6875px;padding-left: 40px\">174<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">183<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">192<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">151<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">159<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">184<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">170<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">186<\/td>\n<td style=\"height: 18px;width: 41.1875px;padding-left: 40px\">155<\/td>\n<td style=\"height: 18px;width: 41.9792px;padding-left: 40px\">156<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"color: #003366\"><strong>Question: <\/strong><\/span>What is the five number summary for the above students&#8217; heights?<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"How to calculate the five number summary in Excel\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/mzwV8w2g248?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><span style=\"color: #003366\"><strong>Solution: <\/strong><a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/04\/11-1-1_Solutions.xlsx\">Click here<\/a><\/span>\u00a0to view the solutions (five number summary) shown in the above video:<\/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: Percentiles, Quartiles and Five Number Summaries<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"h5p-25\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-25\" class=\"h5p-iframe\" data-content-id=\"25\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Key Takeaways for Percentiles, Quartiles and Five Number Summaries\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-26\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-26\" class=\"h5p-iframe\" data-content-id=\"26\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Key Takeaways for Percentiles, Quartiles and Five Number Summaries Solutions\"><\/iframe><\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Your Own Notes (EXERCISE)<\/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","protected":false},"author":865,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-911","chapter","type-chapter","status-publish","hentry"],"part":160,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/911","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":10,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/911\/revisions"}],"predecessor-version":[{"id":1944,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/911\/revisions\/1944"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/160"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/911\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/media?parent=911"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=911"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/contributor?post=911"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/license?post=911"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}