{"id":3662,"date":"2022-03-09T14:21:46","date_gmt":"2022-03-09T14:21:46","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=3662"},"modified":"2022-03-16T17:43:56","modified_gmt":"2022-03-16T17:43:56","slug":"4b-comparing-variability-model-page-fc","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/4b-comparing-variability-model-page-fc\/","title":{"raw":"For UTC Testing -- Comparing Variability of Datasets: Forming Connections","rendered":"For UTC Testing &#8212; Comparing Variability of Datasets: Forming Connections"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>objectives for this activity<\/h3>\r\nDuring this activity, you will:\r\n<ul>\r\n \t<li><a href=\"#TechVar\">Use a data analysis tool to describe variability of data.<\/a><\/li>\r\n \t<li><a href=\"#IntStdDev\">Find and interpret the standard deviation of data.<\/a><\/li>\r\n<\/ul>\r\nClick on a skill above to jump to its location in this activity.\r\n\r\n<\/div>\r\n<h2>It\u2019s Showtime!<\/h2>\r\nHave you ever thought about how long or how short some movies are? You might have the idea that a typical movie runs a little under two hours but movie runtimes cover a broad range. The shortest feature films have run just over an hour, while the longest run three and even four hours. Have you ever thought about why there is such variability in the length of movies?\r\n\r\n<strong><img class=\"aligncenter wp-image-1000\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11192315\/Picture33-300x200.jpg\" alt=\"A mom and two children looking at a tablet together and smiling\" width=\"465\" height=\"310\" \/><\/strong>\r\n\r\nIn this activity we'll explore movie lengths or \u201cruntimes\u201d and the ratings that go along with the runtimes. Let\u2019s compare the movie runtimes for rated G (General Audiences, All Ages Admitted) and rated R (Restricted, Children Under 17 Require Accompanying Parent or Adult Guardian) movies.[footnote]\u00a0<em>What do movie ratings mean?<\/em> (n.d.). Showbiz.Junkies. Retrieved from https:\/\/www.showbizjunkies.com\/mpaa-ratings\/ [\/footnote]\u00a0Along the way, you'll gain an understanding of how variability is reflected in graphical displays and described using numerical summaries.\r\n\r\nBefore beginning, consider the following question.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\n[ohm_question]241063[\/ohm_question]\r\n\r\n[reveal-answer q=\"243063\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"243063\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>video placement<\/h3>\r\n<span style=\"background-color: #e6daf7;\">[Guidance: Think about your answer to Question 1. What kind of movies do you prefer watching? How long do they tend to be? Do you tend to watch a particular movie rating more often than the others? This activity explores the variability in movie runtimes across different ratings. The activity is a quick one, and relies heavily on the data analysis tool. You'll need an understanding of the three variability measures: standard deviation (which you calculate using technology), variance (which you'll need to calculate by hand; it's the square of the standard deviation), and range (which you'll calculate by hand using the minimum and maximum values given in the tool)].\u00a0<\/span>\r\n\r\n<\/div>\r\n<h3 id=\"TechVar\">Variability<\/h3>\r\nLet's use a dataset of movie runtimes to explore variability using technology. Follow the directions below to display the descriptive statistics for the database: Movie Run Time, and use the results to answer Questions 2 - 4 below.\r\n<div class=\"textbox\">\r\n\r\nGo to the Describing and Exploring Quantitative Variables tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\" target=\"_blank\" rel=\"noopener\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>.\r\n<p style=\"padding-left: 30px;\">Step 1) Select the <strong>Several Groups<\/strong> tab.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 2) Locate the drop-down menu under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 3) Locate the drop-down menu under <strong>Dataset<\/strong> and select <strong>Movie Run Time<\/strong>.<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\n[ohm_question]241064[\/ohm_question]\r\n\r\n[reveal-answer q=\"442878\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"442878\"]Make sure the Several Groups tab is selected and refer to the Descriptive Statistics. Recall that variance is the square of standard deviation.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 3<\/h3>\r\n[ohm_question]241065[\/ohm_question]\r\n\r\n[reveal-answer q=\"866059\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"866059\"]Which type of display helps you see the spread of larger datasets more clearly? How much space does the data take up? [\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\n[ohm_question]241066[\/ohm_question]\r\n\r\n[reveal-answer q=\"435162\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"435162\"]Look at the distributions as histograms and as dotplots. Which is easier for seeing extreme values? Do you see anything of interest when viewing the dotplots?[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"IntStdDev\">Standard Deviation<\/h3>\r\nLet\u2019s explore the impact of the outlier on the variability of the G-rated movies. In the G-rated group, select and remove the outlier of\u00a0[latex]357[\/latex]. As illustrated in the following screenshot, highlight the value\u00a0[latex]357[\/latex] and delete.\r\n\r\n<strong><img class=\"alignnone wp-image-1001\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11192513\/Picture34-300x223.png\" alt=\"A selection menu, showing headings &quot;Group Name,&quot; &quot;Group Labels,&quot; &quot;G,&quot; &quot;PG,&quot; &quot;PG-13,&quot; and &quot;R.&quot; In the &quot;G&quot; section, 357 is highlighted.\" width=\"487\" height=\"362\" \/><\/strong>\r\n\r\nExplore the impact of removing the outlier by answering Questions 5 - 7 below. What do you notice about the varia\r\n<div class=\"textbox key-takeaways\">\r\n<h3><img class=\"wp-image-3719 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/03\/09220443\/stars.jpg\" alt=\"\" width=\"44\" height=\"45\" \/>question 5<\/h3>\r\n[ohm_question]241067[\/ohm_question]\r\n\r\n[reveal-answer q=\"802577\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"802577\"]Refer to your answers to Question 2 for G rating with the outlier. [\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 6<\/h3>\r\n[ohm_question]241068[\/ohm_question]\r\n\r\n[reveal-answer q=\"451535\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"451535\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3><img class=\"wp-image-3719 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/03\/09220443\/stars.jpg\" alt=\"\" width=\"44\" height=\"45\" \/>question 7<\/h3>\r\n[ohm_question]241069[\/ohm_question]\r\n[reveal-answer q=\"483415\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"483415\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>video placement<\/h3>\r\n<span style=\"background-color: #e6daf7;\">[wrap-up:\u00a0The goal of this activity is to understand\u00a0that standard deviation is sensitive to outliers and is not a perfect\u00a0measure of variability. \"What did you think about how sensitive std dev is to the presence of outliers?\u00a0 How did the dot in the G-rated distribution affect the numerical summary? Let's examine the range of the G-rated distribution. Note that the max value is 357, but the data is clearly concentrated between about 70 and120. Let's look again at what happens to the mean of the distribution when we remove the outlier. The median stays about the same, which makes sense since it's the middle data value. But the mean drops from a position well to the right of the median back to even with the median. And the variance drops from about 625 to about 121 -- pretty significant! The key take-away is that our ideas of center and spread are affected greatly by the presence of outliers, and they should be used responsibly. Standard Deviation can give us an idea of variability, along with other characteristic about a distribution, but it is not a perfect measure. ]<\/span>\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>objectives for this activity<\/h3>\n<p>During this activity, you will:<\/p>\n<ul>\n<li><a href=\"#TechVar\">Use a data analysis tool to describe variability of data.<\/a><\/li>\n<li><a href=\"#IntStdDev\">Find and interpret the standard deviation of data.<\/a><\/li>\n<\/ul>\n<p>Click on a skill above to jump to its location in this activity.<\/p>\n<\/div>\n<h2>It\u2019s Showtime!<\/h2>\n<p>Have you ever thought about how long or how short some movies are? You might have the idea that a typical movie runs a little under two hours but movie runtimes cover a broad range. The shortest feature films have run just over an hour, while the longest run three and even four hours. Have you ever thought about why there is such variability in the length of movies?<\/p>\n<p><strong><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1000\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11192315\/Picture33-300x200.jpg\" alt=\"A mom and two children looking at a tablet together and smiling\" width=\"465\" height=\"310\" \/><\/strong><\/p>\n<p>In this activity we&#8217;ll explore movie lengths or \u201cruntimes\u201d and the ratings that go along with the runtimes. Let\u2019s compare the movie runtimes for rated G (General Audiences, All Ages Admitted) and rated R (Restricted, Children Under 17 Require Accompanying Parent or Adult Guardian) movies.<a class=\"footnote\" title=\"\u00a0What do movie ratings mean? (n.d.). Showbiz.Junkies. Retrieved from https:\/\/www.showbizjunkies.com\/mpaa-ratings\/\" id=\"return-footnote-3662-1\" href=\"#footnote-3662-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a>\u00a0Along the way, you&#8217;ll gain an understanding of how variability is reflected in graphical displays and described using numerical summaries.<\/p>\n<p>Before beginning, consider the following question.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241063\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241063&theme=oea&iframe_resize_id=ohm241063&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q243063\">Hint<\/span><\/p>\n<div id=\"q243063\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>video placement<\/h3>\n<p><span style=\"background-color: #e6daf7;\">[Guidance: Think about your answer to Question 1. What kind of movies do you prefer watching? How long do they tend to be? Do you tend to watch a particular movie rating more often than the others? This activity explores the variability in movie runtimes across different ratings. The activity is a quick one, and relies heavily on the data analysis tool. You&#8217;ll need an understanding of the three variability measures: standard deviation (which you calculate using technology), variance (which you&#8217;ll need to calculate by hand; it&#8217;s the square of the standard deviation), and range (which you&#8217;ll calculate by hand using the minimum and maximum values given in the tool)].\u00a0<\/span><\/p>\n<\/div>\n<h3 id=\"TechVar\">Variability<\/h3>\n<p>Let&#8217;s use a dataset of movie runtimes to explore variability using technology. Follow the directions below to display the descriptive statistics for the database: Movie Run Time, and use the results to answer Questions 2 &#8211; 4 below.<\/p>\n<div class=\"textbox\">\n<p>Go to the Describing and Exploring Quantitative Variables tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\" target=\"_blank\" rel=\"noopener\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>.<\/p>\n<p style=\"padding-left: 30px;\">Step 1) Select the <strong>Several Groups<\/strong> tab.<\/p>\n<p style=\"padding-left: 30px;\">Step 2) Locate the drop-down menu under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.<\/p>\n<p style=\"padding-left: 30px;\">Step 3) Locate the drop-down menu under <strong>Dataset<\/strong> and select <strong>Movie Run Time<\/strong>.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241064\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241064&theme=oea&iframe_resize_id=ohm241064&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q442878\">Hint<\/span><\/p>\n<div id=\"q442878\" class=\"hidden-answer\" style=\"display: none\">Make sure the Several Groups tab is selected and refer to the Descriptive Statistics. Recall that variance is the square of standard deviation.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241065\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241065&theme=oea&iframe_resize_id=ohm241065&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q866059\">Hint<\/span><\/p>\n<div id=\"q866059\" class=\"hidden-answer\" style=\"display: none\">Which type of display helps you see the spread of larger datasets more clearly? How much space does the data take up? <\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241066\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241066&theme=oea&iframe_resize_id=ohm241066&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q435162\">Hint<\/span><\/p>\n<div id=\"q435162\" class=\"hidden-answer\" style=\"display: none\">Look at the distributions as histograms and as dotplots. Which is easier for seeing extreme values? Do you see anything of interest when viewing the dotplots?<\/div>\n<\/div>\n<\/div>\n<h3 id=\"IntStdDev\">Standard Deviation<\/h3>\n<p>Let\u2019s explore the impact of the outlier on the variability of the G-rated movies. In the G-rated group, select and remove the outlier of\u00a0[latex]357[\/latex]. As illustrated in the following screenshot, highlight the value\u00a0[latex]357[\/latex] and delete.<\/p>\n<p><strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1001\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11192513\/Picture34-300x223.png\" alt=\"A selection menu, showing headings &quot;Group Name,&quot; &quot;Group Labels,&quot; &quot;G,&quot; &quot;PG,&quot; &quot;PG-13,&quot; and &quot;R.&quot; In the &quot;G&quot; section, 357 is highlighted.\" width=\"487\" height=\"362\" \/><\/strong><\/p>\n<p>Explore the impact of removing the outlier by answering Questions 5 &#8211; 7 below. What do you notice about the varia<\/p>\n<div class=\"textbox key-takeaways\">\n<h3><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3719 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/03\/09220443\/stars.jpg\" alt=\"\" width=\"44\" height=\"45\" \/>question 5<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241067\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241067&theme=oea&iframe_resize_id=ohm241067&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q802577\">Hint<\/span><\/p>\n<div id=\"q802577\" class=\"hidden-answer\" style=\"display: none\">Refer to your answers to Question 2 for G rating with the outlier. <\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 6<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241068\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241068&theme=oea&iframe_resize_id=ohm241068&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q451535\">Hint<\/span><\/p>\n<div id=\"q451535\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3719 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/03\/09220443\/stars.jpg\" alt=\"\" width=\"44\" height=\"45\" \/>question 7<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241069\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241069&theme=oea&iframe_resize_id=ohm241069&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q483415\">Hint<\/span><\/p>\n<div id=\"q483415\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>video placement<\/h3>\n<p><span style=\"background-color: #e6daf7;\">[wrap-up:\u00a0The goal of this activity is to understand\u00a0that standard deviation is sensitive to outliers and is not a perfect\u00a0measure of variability. &#8220;What did you think about how sensitive std dev is to the presence of outliers?\u00a0 How did the dot in the G-rated distribution affect the numerical summary? Let&#8217;s examine the range of the G-rated distribution. Note that the max value is 357, but the data is clearly concentrated between about 70 and120. Let&#8217;s look again at what happens to the mean of the distribution when we remove the outlier. The median stays about the same, which makes sense since it&#8217;s the middle data value. But the mean drops from a position well to the right of the median back to even with the median. And the variance drops from about 625 to about 121 &#8212; pretty significant! The key take-away is that our ideas of center and spread are affected greatly by the presence of outliers, and they should be used responsibly. Standard Deviation can give us an idea of variability, along with other characteristic about a distribution, but it is not a perfect measure. ]<\/span><\/p>\n<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-3662-1\">\u00a0<em>What do movie ratings mean?<\/em> (n.d.). Showbiz.Junkies. Retrieved from https:\/\/www.showbizjunkies.com\/mpaa-ratings\/  <a href=\"#return-footnote-3662-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":25777,"menu_order":7,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3662","chapter","type-chapter","status-publish","hentry"],"part":3887,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3662","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3662\/revisions"}],"predecessor-version":[{"id":3721,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3662\/revisions\/3721"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/3887"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3662\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=3662"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=3662"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=3662"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=3662"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}