{"id":440,"date":"2021-12-20T14:32:02","date_gmt":"2021-12-20T14:32:02","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=440"},"modified":"2022-02-17T20:10:09","modified_gmt":"2022-02-17T20:10:09","slug":"forming-connections-in-4b","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/forming-connections-in-4b\/","title":{"raw":"Forming Connections in Comparing Variability of Datasets: 4B - 21","rendered":"Forming Connections in Comparing Variability of Datasets: 4B &#8211; 21"},"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\nWhen it comes to movies, have you ever sat down and thought about how long or how short some movies are? Have you 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\nDo you think the rating (G versus R) of a movie has anything to do with how long the movie is?\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: This activity will rely heavily on the tool, and it's a quick activity. The intro can be more focused on the dataset itself, to get students interested. Remind students of the three variability measures: std dev (use the tool), variance (remember to square the std dev by hand), range (remember to calculate this from min and max given in the tool).]<\/span>\r\n\r\n<\/div>\r\n<h3 id=\"TechVar\">Using Technology to Describe Variability<\/h3>\r\nLet's use a dataset of movie runtimes to explore variability using technology.\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\nFind the mean ([latex]\\bar{x}[\/latex]), median, standard deviation ([latex]s[\/latex]), and variance ([latex]s^{2}[\/latex]) for the runtimes for both the G-rated and R-rated movies and record them in the table below.\r\n<div align=\"center\">\r\n<table style=\"width: 580px;\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 41.2031px; text-align: center;\"><strong>Rating<\/strong><\/td>\r\n<td style=\"width: 120.516px;\">\r\n<p style=\"text-align: center;\"><strong>Mean<\/strong><\/p>\r\n<p style=\"text-align: center;\"><strong>([latex]\\bar{x}[\/latex])<\/strong><\/p>\r\n<\/td>\r\n<td style=\"text-align: center; width: 68.3125px;\"><strong>Median<\/strong><\/td>\r\n<td style=\"width: 133.562px;\">\r\n<p style=\"text-align: center;\"><strong>Standard Deviation<\/strong><\/p>\r\n<p style=\"text-align: center;\"><strong>([latex]s[\/latex])<\/strong><\/p>\r\n<\/td>\r\n<td style=\"width: 158.688px;\">\r\n<p style=\"text-align: center;\"><strong>Variance<\/strong><\/p>\r\n<p style=\"text-align: center;\"><strong>([latex]s^{2}[\/latex])<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 41.2031px; text-align: center;\"><strong>G<\/strong><\/td>\r\n<td style=\"width: 120.516px;\"><\/td>\r\n<td style=\"width: 68.3125px;\"><\/td>\r\n<td style=\"width: 133.562px;\"><\/td>\r\n<td style=\"width: 158.688px;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 41.2031px; text-align: center;\"><strong>R<\/strong><\/td>\r\n<td style=\"width: 120.516px;\"><\/td>\r\n<td style=\"width: 68.3125px;\"><\/td>\r\n<td style=\"width: 133.562px;\"><\/td>\r\n<td style=\"width: 158.688px;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\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\nCreate a dotplot or histogram of the data, whichever you choose. Compare the numerical value of the standard deviation to the spread that is shown in the graphical representation for each rating.\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\nWhat else do you see in the distributions of runtime that might affect the variability?\r\n\r\n<\/div>\r\n<h3 id=\"IntStdDev\">Finding and Interpreting 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 357. As illustrated in the following screenshot, highlight the value 357 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<div class=\"textbox key-takeaways\">\r\n<h3>question 5<\/h3>\r\nFind the mean ([latex]\\bar{x}[\/latex]), median, standard deviation (s), and variance (s<sup>2<\/sup>) for the G rating with and without the outlier and then record them in the table below. Refer to the preview activity if you need help remembering how to calculate variance. Enter your answers from Question 2 again in the table below to ease the comparisons.\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Rating<\/strong><\/td>\r\n<td><strong>Mean<\/strong>\r\n\r\n<strong>([latex]\\bar{x}[\/latex])<\/strong><\/td>\r\n<td><strong>Median<\/strong><\/td>\r\n<td><strong>Standard Deviation<\/strong>\r\n\r\n<strong>(s)<\/strong><\/td>\r\n<td><strong>Variance<\/strong>\r\n\r\n<strong>(s<sup>2<\/sup>)<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>G rating <span style=\"text-decoration: underline;\">with<\/span> the outlier<\/strong><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>G rating <span style=\"text-decoration: underline;\">without<\/span> the outlier<\/strong><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 6<\/h3>\r\nWhat do you notice about the effect of an outlier on standard deviation?\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 7<\/h3>\r\nDo you think standard deviation represents a \u201ctypical\u201d distance from the mean when an outlier is present?\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 is for students 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>When it comes to movies, have you ever sat down and thought about how long or how short some movies are? Have you 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-440-1\" href=\"#footnote-440-1\" 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>Do you think the rating (G versus R) of a movie has anything to do with how long the movie is?<\/p>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>video placement<\/h3>\n<p><span style=\"background-color: #e6daf7;\">[guidance: This activity will rely heavily on the tool, and it&#8217;s a quick activity. The intro can be more focused on the dataset itself, to get students interested. Remind students of the three variability measures: std dev (use the tool), variance (remember to square the std dev by hand), range (remember to calculate this from min and max given in the tool).]<\/span><\/p>\n<\/div>\n<h3 id=\"TechVar\">Using Technology to Describe Variability<\/h3>\n<p>Let&#8217;s use a dataset of movie runtimes to explore variability using technology.<\/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>Find the mean ([latex]\\bar{x}[\/latex]), median, standard deviation ([latex]s[\/latex]), and variance ([latex]s^{2}[\/latex]) for the runtimes for both the G-rated and R-rated movies and record them in the table below.<\/p>\n<div style=\"margin: auto;\">\n<table style=\"width: 580px;\">\n<tbody>\n<tr>\n<td style=\"width: 41.2031px; text-align: center;\"><strong>Rating<\/strong><\/td>\n<td style=\"width: 120.516px;\">\n<p style=\"text-align: center;\"><strong>Mean<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>([latex]\\bar{x}[\/latex])<\/strong><\/p>\n<\/td>\n<td style=\"text-align: center; width: 68.3125px;\"><strong>Median<\/strong><\/td>\n<td style=\"width: 133.562px;\">\n<p style=\"text-align: center;\"><strong>Standard Deviation<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>([latex]s[\/latex])<\/strong><\/p>\n<\/td>\n<td style=\"width: 158.688px;\">\n<p style=\"text-align: center;\"><strong>Variance<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>([latex]s^{2}[\/latex])<\/strong><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 41.2031px; text-align: center;\"><strong>G<\/strong><\/td>\n<td style=\"width: 120.516px;\"><\/td>\n<td style=\"width: 68.3125px;\"><\/td>\n<td style=\"width: 133.562px;\"><\/td>\n<td style=\"width: 158.688px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 41.2031px; text-align: center;\"><strong>R<\/strong><\/td>\n<td style=\"width: 120.516px;\"><\/td>\n<td style=\"width: 68.3125px;\"><\/td>\n<td style=\"width: 133.562px;\"><\/td>\n<td style=\"width: 158.688px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\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>Create a dotplot or histogram of the data, whichever you choose. Compare the numerical value of the standard deviation to the spread that is shown in the graphical representation for each rating.<\/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>What else do you see in the distributions of runtime that might affect the variability?<\/p>\n<\/div>\n<h3 id=\"IntStdDev\">Finding and Interpreting 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 357. As illustrated in the following screenshot, highlight the value 357 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<div class=\"textbox key-takeaways\">\n<h3>question 5<\/h3>\n<p>Find the mean ([latex]\\bar{x}[\/latex]), median, standard deviation (s), and variance (s<sup>2<\/sup>) for the G rating with and without the outlier and then record them in the table below. Refer to the preview activity if you need help remembering how to calculate variance. Enter your answers from Question 2 again in the table below to ease the comparisons.<\/p>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>Rating<\/strong><\/td>\n<td><strong>Mean<\/strong><\/p>\n<p><strong>([latex]\\bar{x}[\/latex])<\/strong><\/td>\n<td><strong>Median<\/strong><\/td>\n<td><strong>Standard Deviation<\/strong><\/p>\n<p><strong>(s)<\/strong><\/td>\n<td><strong>Variance<\/strong><\/p>\n<p><strong>(s<sup>2<\/sup>)<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>G rating <span style=\"text-decoration: underline;\">with<\/span> the outlier<\/strong><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>G rating <span style=\"text-decoration: underline;\">without<\/span> the outlier<\/strong><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 6<\/h3>\n<p>What do you notice about the effect of an outlier on standard deviation?<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 7<\/h3>\n<p>Do you think standard deviation represents a \u201ctypical\u201d distance from the mean when an outlier is present?<\/p>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>video placement<\/h3>\n<p><span style=\"background-color: #e6daf7;\">[wrap-up:\u00a0The goal is for students 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-440-1\">\u00a0<em>What do movie ratings mean?<\/em> (n.d.). Showbiz.Junkies. Retrieved from https:\/\/www.showbizjunkies.com\/mpaa-ratings\/  <a href=\"#return-footnote-440-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":25777,"menu_order":11,"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-440","chapter","type-chapter","status-publish","hentry"],"part":621,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/440","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":34,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/440\/revisions"}],"predecessor-version":[{"id":3312,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/440\/revisions\/3312"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/621"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/440\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=440"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=440"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=440"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=440"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}