{"id":295,"date":"2021-10-27T21:44:36","date_gmt":"2021-10-27T21:44:36","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=295"},"modified":"2022-02-17T20:07:53","modified_gmt":"2022-02-17T20:07:53","slug":"what-to-know-about-comparing-quantitative-distributions-3e","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/what-to-know-about-comparing-quantitative-distributions-3e\/","title":{"raw":"What to Know About Comparing Quantitative Distributions: 3E - 14","rendered":"What to Know About Comparing Quantitative Distributions: 3E &#8211; 14"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>goals for this section<\/h3>\r\nAfter completing this section, you should feel comfortable performing these skills.\r\n<ul>\r\n \t<li><a href=\"#CompareCenters\">Compare centers of distributions of a quantitative variable.<\/a><\/li>\r\n \t<li><a href=\"#CompareSpread\">Compare the spread in distributions of a quantitative variable.<\/a><\/li>\r\n<\/ul>\r\nClick on a skill above to jump to its location in this section.\r\n\r\n<\/div>\r\nWhen describing and summarizing data, you will frequently need to be able to describe the shape of the distribution of a quantitative variable and compare centers and spreads of distributions of a quantitative variable. You will also need to determine the presence of outliers in the distribution of a quantitative variable.\r\n\r\nIn <a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/forming-connections-with-applications-of-histograms-3d\/\"><em>Forming Connections in Applications of Histograms: 3D<\/em><\/a>, we learned to describe the distribution of one variable at a time. Recall that the description of a distribution includes shape, center, spread, and the presence or absence of outliers. In the next activity, you will need to use technology to create and interpret histograms and dotplots for a quantitative variable compared across groups. To prepare for the activity, in this section you'll practice describing the shape of distributions and identifying the presence of outliers while using graphs to compare the center and spread of several groups at once.\r\n\r\nLet's start by going to the data analysis tool to create a set of histograms for a variable in a dataset that contains several groups. Follow the directions below to create stacked histograms of the price of a room rental in New York City across different types of rooms.\r\n\r\nFor Questions 1\u20133 below:\r\n<div class=\"textbox\">\r\n\r\nGo to the <em>Describing and Exploring Quantitative Variables<\/em> tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\" target=\"_blank\" rel=\"noopener\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/.\u00a0<\/a>\r\n<p style=\"padding-left: 30px;\">Step 1) Select the <strong>Several Groups<\/strong> tab at the top of the page.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 2) Locate the dropdown under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 3) Locate the dropdown under <strong>Dataset<\/strong> and select <strong>Airbnb Price by Type of Room<\/strong>.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 4) Under\u00a0<span style=\"font-size: 1em;\"><strong>Choose Type of Plot<\/strong>: select\u00a0<strong>Histogram<\/strong><\/span><\/p>\r\n<p style=\"padding-left: 30px;\">Step 5) Under <strong>Histogram Options<\/strong>: select <strong>stacked<\/strong>.<\/p>\r\n\r\n<\/div>\r\nUse the displayed histograms of Airbnb rental prices in New York City (in $) to answer Questions 1 - 3 below.\r\n<div class=\"textbox examples\">\r\n<h3>Recall<\/h3>\r\nIn the previous section,\u00a0<em>What to Know About Applications of Histograms: 3D<\/em>, you learned how to visually assess center and spread. Do you recall those techniques?\r\n\r\nCore skill:\r\n[reveal-answer q=\"727094\"]Visually approximate the center of a distribution displayed as a histogram.[\/reveal-answer]\r\n[hidden-answer a=\"727094\"]The\u00a0<strong>center<\/strong>\u00a0describes the location of the middle of the distribution. The center is a number that describes a typical value. For example, one way to think about the center is that it could be the point in the distribution where about half of the observations are below it and half are above it.[\/hidden-answer]\r\n\r\nCore skill:\r\n[reveal-answer q=\"509061\"]Visually approximate the spread of a distribution displayed as a histogram.[\/reveal-answer]\r\n[hidden-answer a=\"509061\"]The\u00a0<strong>spread<\/strong>\u00a0is a measure of how much the values in a dataset tend to differ from one another. One way we can find the spread is by finding the minimum and maximum values in the data and calculating the difference between them. This difference is called the\u00a0<strong>range.<\/strong>[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\nDescribe the shape of the distribution of Airbnb prices for renting an entire apartment. Select the best description.\r\n<p style=\"padding-left: 30px;\">a) Approximately symmetric<\/p>\r\n<p style=\"padding-left: 30px;\">b) Right skewed<\/p>\r\n<p style=\"padding-left: 30px;\">c) Left skewed<\/p>\r\n<p style=\"padding-left: 30px;\">d) Bimodal<\/p>\r\n[reveal-answer q=\"677028\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"677028\"]Look at the legend to identify which plot is the distribution of the entire apartment.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>comparing centers and spread<\/h3>\r\n<span style=\"background-color: #99cc00;\">[Perspective Video -- a 3-instructor video that shows how to think about comparisons of centers and spread in a stacked histogram that displays a quantitative variable across more than one group]<\/span>\r\n\r\n<\/div>\r\n<h3 id=\"CompareCenters\">Comparing centers<\/h3>\r\nNow, instead of looking at just one of the distributions, let's compare the centers of all three plots to answer a question. Recall that we think of the center of quantitative data as the location of the middle of the data (a \"typical\" observation value).\u00a0 Later, we'll identify the numerical value of the center precisely using descriptive statistics. For now, just use the graphs to compare the centers of the different groups.\r\n\r\nExamine the stacked histograms that appear in the analysis tool to compare their centers. Use your observations to answer Question 2 below.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\nWhich of the three Airbnb room types has the smallest typical price?\r\n<p style=\"padding-left: 30px;\">a) Shared room<\/p>\r\n<p style=\"padding-left: 30px;\">b) Private room<\/p>\r\n<p style=\"padding-left: 30px;\">c) Entire apartment<\/p>\r\n<p style=\"padding-left: 30px;\">d) All three have similar centers<\/p>\r\n[reveal-answer q=\"510937\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"510937\"]Which center appears furthest to the left?[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"CompareSpread\">Comparing Spread<\/h3>\r\nRecall that spread is a measure of how much the values in a dataset tend to differ from one another. You saw in the previous section that one way we can describe spread is to calculate the range of the data: the difference between the minimum and maximum values in the data.\r\n\r\nWe'll see later that there are other ways to assign a numerical value to spread, but for now just use the graphs to visually compare the range of each distribution.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 3<\/h3>\r\nWhich of the three Airbnb room types has the greatest range?\r\n<p style=\"padding-left: 30px;\">a) Shared room<\/p>\r\n<p style=\"padding-left: 30px;\">b) Private room<\/p>\r\n<p style=\"padding-left: 30px;\">c) Entire apartment<\/p>\r\n<p style=\"padding-left: 30px;\">d) All three have similar ranges<\/p>\r\n[reveal-answer q=\"646684\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"646684\"]Recall that range is calculated as the difference (the distance) between the least and greatest observation values.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>using technology to interpret distributions<\/h3>\r\n<span style=\"background-color: #99cc00;\">[Worked example - a 3-instructor video works through an example like questions 4 - 6 below]<\/span>\r\n\r\n<\/div>\r\nFor Questions 4\u20136, change the tool inputs to the following:\r\n<ul>\r\n \t<li>Dataset: CO<sub>2<\/sub> Emissions by Continent<\/li>\r\n \t<li>Choose Type of Plot: Dotplot<\/li>\r\n \t<li>Select Dot Size: Choose an appropriate size to visualize the data efficiently<\/li>\r\n<\/ul>\r\nUse the displayed dotplot\u00a0of per capita CO<sub>2<\/sub> emissions (in metric tons) to answer the following questions.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\nDescribe the shape of the distribution of per capita CO<sub>2<\/sub> emissions for Europe. Select the best description.\r\n<p style=\"padding-left: 30px;\">a) Approximately symmetric<\/p>\r\n<p style=\"padding-left: 30px;\">b) Right skewed<\/p>\r\n<p style=\"padding-left: 30px;\">c)Left skewed<\/p>\r\n<p style=\"padding-left: 30px;\">d) Bimodal<\/p>\r\n[reveal-answer q=\"550079\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"550079\"]To identify symmetry or skew, look for long tails of data. To identify modality, look for one or more discernable maximum frequencies.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 5<\/h3>\r\nAre there any outliers in the distribution of per capita CO<sub>2<\/sub> emissions for Central and South America? If so, what are the approximate values of the outliers?\r\n\r\n[reveal-answer q=\"766474\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"766474\"]We'll have a numerical strategy for determining outliers later. For now, just locate any unusual observations in the data. [\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 6<\/h3>\r\nWhich of the two distributions of per capita CO<sub>2<\/sub> emissions has the greatest range of values?\r\n<p style=\"padding-left: 30px;\">a) Central and South America<\/p>\r\n<p style=\"padding-left: 30px;\">b) Europe<\/p>\r\n<p style=\"padding-left: 30px;\">c) The two distributions have similar ranges.<\/p>\r\n[reveal-answer q=\"526711\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"526711\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Summary<\/h2>\r\nIn this section, you've gained practice with distributions of quantitative variables by examining distributions of a single variable across several groups. You've described their shapes, identified centers and spread, and made comparisons between more than one distribution. You've also had practice in identifying outliers in a distribution. Let's summarize what you've seen so far.\r\n<ul>\r\n \t<li>In questions 1 and 4, you used technology to create a distribution as a histogram or a dotplot and described the shape of the distribution you created.<\/li>\r\n \t<li>In question 2, you compared centers of distributions of a quantitative variable.<\/li>\r\n \t<li>In questions 3 and 6, you compared the spread in distributions.<\/li>\r\n \t<li>In question 5, you determined the presence of outliers in the distribution of a quantitative variable.<\/li>\r\n<\/ul>\r\nBeing able to describe the center, spread, and shape, and detect outliers are essential to being able to complete the next Forming Connections activity. If you ready, then it's time to move on!\r\n<h3><\/h3>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>goals for this section<\/h3>\n<p>After completing this section, you should feel comfortable performing these skills.<\/p>\n<ul>\n<li><a href=\"#CompareCenters\">Compare centers of distributions of a quantitative variable.<\/a><\/li>\n<li><a href=\"#CompareSpread\">Compare the spread in distributions of a quantitative variable.<\/a><\/li>\n<\/ul>\n<p>Click on a skill above to jump to its location in this section.<\/p>\n<\/div>\n<p>When describing and summarizing data, you will frequently need to be able to describe the shape of the distribution of a quantitative variable and compare centers and spreads of distributions of a quantitative variable. You will also need to determine the presence of outliers in the distribution of a quantitative variable.<\/p>\n<p>In <a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/forming-connections-with-applications-of-histograms-3d\/\"><em>Forming Connections in Applications of Histograms: 3D<\/em><\/a>, we learned to describe the distribution of one variable at a time. Recall that the description of a distribution includes shape, center, spread, and the presence or absence of outliers. In the next activity, you will need to use technology to create and interpret histograms and dotplots for a quantitative variable compared across groups. To prepare for the activity, in this section you&#8217;ll practice describing the shape of distributions and identifying the presence of outliers while using graphs to compare the center and spread of several groups at once.<\/p>\n<p>Let&#8217;s start by going to the data analysis tool to create a set of histograms for a variable in a dataset that contains several groups. Follow the directions below to create stacked histograms of the price of a room rental in New York City across different types of rooms.<\/p>\n<p>For Questions 1\u20133 below:<\/p>\n<div class=\"textbox\">\n<p>Go to the <em>Describing and Exploring Quantitative Variables<\/em> tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\" target=\"_blank\" rel=\"noopener\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/.\u00a0<\/a><\/p>\n<p style=\"padding-left: 30px;\">Step 1) Select the <strong>Several Groups<\/strong> tab at the top of the page.<\/p>\n<p style=\"padding-left: 30px;\">Step 2) Locate the dropdown under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.<\/p>\n<p style=\"padding-left: 30px;\">Step 3) Locate the dropdown under <strong>Dataset<\/strong> and select <strong>Airbnb Price by Type of Room<\/strong>.<\/p>\n<p style=\"padding-left: 30px;\">Step 4) Under\u00a0<span style=\"font-size: 1em;\"><strong>Choose Type of Plot<\/strong>: select\u00a0<strong>Histogram<\/strong><\/span><\/p>\n<p style=\"padding-left: 30px;\">Step 5) Under <strong>Histogram Options<\/strong>: select <strong>stacked<\/strong>.<\/p>\n<\/div>\n<p>Use the displayed histograms of Airbnb rental prices in New York City (in $) to answer Questions 1 &#8211; 3 below.<\/p>\n<div class=\"textbox examples\">\n<h3>Recall<\/h3>\n<p>In the previous section,\u00a0<em>What to Know About Applications of Histograms: 3D<\/em>, you learned how to visually assess center and spread. Do you recall those techniques?<\/p>\n<p>Core skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q727094\">Visually approximate the center of a distribution displayed as a histogram.<\/span><\/p>\n<div id=\"q727094\" class=\"hidden-answer\" style=\"display: none\">The\u00a0<strong>center<\/strong>\u00a0describes the location of the middle of the distribution. The center is a number that describes a typical value. For example, one way to think about the center is that it could be the point in the distribution where about half of the observations are below it and half are above it.<\/div>\n<\/div>\n<p>Core skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q509061\">Visually approximate the spread of a distribution displayed as a histogram.<\/span><\/p>\n<div id=\"q509061\" class=\"hidden-answer\" style=\"display: none\">The\u00a0<strong>spread<\/strong>\u00a0is a measure of how much the values in a dataset tend to differ from one another. One way we can find the spread is by finding the minimum and maximum values in the data and calculating the difference between them. This difference is called the\u00a0<strong>range.<\/strong><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p>Describe the shape of the distribution of Airbnb prices for renting an entire apartment. Select the best description.<\/p>\n<p style=\"padding-left: 30px;\">a) Approximately symmetric<\/p>\n<p style=\"padding-left: 30px;\">b) Right skewed<\/p>\n<p style=\"padding-left: 30px;\">c) Left skewed<\/p>\n<p style=\"padding-left: 30px;\">d) Bimodal<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q677028\">Hint<\/span><\/p>\n<div id=\"q677028\" class=\"hidden-answer\" style=\"display: none\">Look at the legend to identify which plot is the distribution of the entire apartment.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>comparing centers and spread<\/h3>\n<p><span style=\"background-color: #99cc00;\">[Perspective Video &#8212; a 3-instructor video that shows how to think about comparisons of centers and spread in a stacked histogram that displays a quantitative variable across more than one group]<\/span><\/p>\n<\/div>\n<h3 id=\"CompareCenters\">Comparing centers<\/h3>\n<p>Now, instead of looking at just one of the distributions, let&#8217;s compare the centers of all three plots to answer a question. Recall that we think of the center of quantitative data as the location of the middle of the data (a &#8220;typical&#8221; observation value).\u00a0 Later, we&#8217;ll identify the numerical value of the center precisely using descriptive statistics. For now, just use the graphs to compare the centers of the different groups.<\/p>\n<p>Examine the stacked histograms that appear in the analysis tool to compare their centers. Use your observations to answer Question 2 below.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p>Which of the three Airbnb room types has the smallest typical price?<\/p>\n<p style=\"padding-left: 30px;\">a) Shared room<\/p>\n<p style=\"padding-left: 30px;\">b) Private room<\/p>\n<p style=\"padding-left: 30px;\">c) Entire apartment<\/p>\n<p style=\"padding-left: 30px;\">d) All three have similar centers<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q510937\">Hint<\/span><\/p>\n<div id=\"q510937\" class=\"hidden-answer\" style=\"display: none\">Which center appears furthest to the left?<\/div>\n<\/div>\n<\/div>\n<h3 id=\"CompareSpread\">Comparing Spread<\/h3>\n<p>Recall that spread is a measure of how much the values in a dataset tend to differ from one another. You saw in the previous section that one way we can describe spread is to calculate the range of the data: the difference between the minimum and maximum values in the data.<\/p>\n<p>We&#8217;ll see later that there are other ways to assign a numerical value to spread, but for now just use the graphs to visually compare the range of each distribution.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p>Which of the three Airbnb room types has the greatest range?<\/p>\n<p style=\"padding-left: 30px;\">a) Shared room<\/p>\n<p style=\"padding-left: 30px;\">b) Private room<\/p>\n<p style=\"padding-left: 30px;\">c) Entire apartment<\/p>\n<p style=\"padding-left: 30px;\">d) All three have similar ranges<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q646684\">Hint<\/span><\/p>\n<div id=\"q646684\" class=\"hidden-answer\" style=\"display: none\">Recall that range is calculated as the difference (the distance) between the least and greatest observation values.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>using technology to interpret distributions<\/h3>\n<p><span style=\"background-color: #99cc00;\">[Worked example &#8211; a 3-instructor video works through an example like questions 4 &#8211; 6 below]<\/span><\/p>\n<\/div>\n<p>For Questions 4\u20136, change the tool inputs to the following:<\/p>\n<ul>\n<li>Dataset: CO<sub>2<\/sub> Emissions by Continent<\/li>\n<li>Choose Type of Plot: Dotplot<\/li>\n<li>Select Dot Size: Choose an appropriate size to visualize the data efficiently<\/li>\n<\/ul>\n<p>Use the displayed dotplot\u00a0of per capita CO<sub>2<\/sub> emissions (in metric tons) to answer the following questions.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p>Describe the shape of the distribution of per capita CO<sub>2<\/sub> emissions for Europe. Select the best description.<\/p>\n<p style=\"padding-left: 30px;\">a) Approximately symmetric<\/p>\n<p style=\"padding-left: 30px;\">b) Right skewed<\/p>\n<p style=\"padding-left: 30px;\">c)Left skewed<\/p>\n<p style=\"padding-left: 30px;\">d) Bimodal<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q550079\">Hint<\/span><\/p>\n<div id=\"q550079\" class=\"hidden-answer\" style=\"display: none\">To identify symmetry or skew, look for long tails of data. To identify modality, look for one or more discernable maximum frequencies.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 5<\/h3>\n<p>Are there any outliers in the distribution of per capita CO<sub>2<\/sub> emissions for Central and South America? If so, what are the approximate values of the outliers?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q766474\">Hint<\/span><\/p>\n<div id=\"q766474\" class=\"hidden-answer\" style=\"display: none\">We&#8217;ll have a numerical strategy for determining outliers later. For now, just locate any unusual observations in the data. <\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 6<\/h3>\n<p>Which of the two distributions of per capita CO<sub>2<\/sub> emissions has the greatest range of values?<\/p>\n<p style=\"padding-left: 30px;\">a) Central and South America<\/p>\n<p style=\"padding-left: 30px;\">b) Europe<\/p>\n<p style=\"padding-left: 30px;\">c) The two distributions have similar ranges.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q526711\">Hint<\/span><\/p>\n<div id=\"q526711\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<h2>Summary<\/h2>\n<p>In this section, you&#8217;ve gained practice with distributions of quantitative variables by examining distributions of a single variable across several groups. You&#8217;ve described their shapes, identified centers and spread, and made comparisons between more than one distribution. You&#8217;ve also had practice in identifying outliers in a distribution. Let&#8217;s summarize what you&#8217;ve seen so far.<\/p>\n<ul>\n<li>In questions 1 and 4, you used technology to create a distribution as a histogram or a dotplot and described the shape of the distribution you created.<\/li>\n<li>In question 2, you compared centers of distributions of a quantitative variable.<\/li>\n<li>In questions 3 and 6, you compared the spread in distributions.<\/li>\n<li>In question 5, you determined the presence of outliers in the distribution of a quantitative variable.<\/li>\n<\/ul>\n<p>Being able to describe the center, spread, and shape, and detect outliers are essential to being able to complete the next Forming Connections activity. If you ready, then it&#8217;s time to move on!<\/p>\n<h3><\/h3>\n","protected":false},"author":25777,"menu_order":32,"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-295","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/295","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":31,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/295\/revisions"}],"predecessor-version":[{"id":3305,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/295\/revisions\/3305"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/295\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=295"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=295"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=295"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}