{"id":158,"date":"2021-10-10T18:34:00","date_gmt":"2021-10-10T18:34:00","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=158"},"modified":"2022-02-17T20:07:44","modified_gmt":"2022-02-17T20:07:44","slug":"3e-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/3e-coreq\/","title":{"raw":"Corequisite Support Activity for Comparing Quantitative Distributions: 3E - 13","rendered":"Corequisite Support Activity for Comparing Quantitative Distributions: 3E &#8211; 13"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>What you'll need to know<\/h3>\r\nIn this support activity you'll become familiar with the following:\r\n<ul>\r\n \t<li><a href=\"#Describe\">Using the language of statistics to describe the distribution of a quantitative variable.<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the next section of the course material and in the following activity, you will need to compare the distributions of a single variable between groups. In this corequisite support activity, we will practice describing the distributions when presented with a histogram.\r\n<h2><strong>Describing Histograms<\/strong><\/h2>\r\nIn the the section <em><a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/what-to-know-about-applications-of-histograms-3d\/\">What to Know About Applications of Histograms: 3D\u00a0\u00a0<\/a><\/em>you defined the\u00a0shape, center, spread, and the presence of outliers in the\u00a0distribution of a quantitative variable. You learned about the skewness and modality of a distribution and saw how to use the range as a possible representation of spread. Then, in the activity,\u00a0<a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/forming-connections-with-applications-of-histograms-3d\/\"><em>Forming Connections in Applications of Histograms:\u00a03D<\/em><\/a>, you used these statistical terms in summary to thoroughly describe the distribution of a quantitative variable.\u00a0 \u00a0In the upcoming section and activity, you'll need to display a comfortable understanding of this statistical language so we'll spend some time analyzing some histograms and possible descriptions in this support activity.\r\n\r\nIn Questions 1\u20133 below, you will be presented with a histogram and a description of the distribution of the variable to analyze. The recall box below contains the descriptions of each of the four characteristics of a thorough description.\r\n<div class=\"textbox examples\">\r\n<h3>Recall<\/h3>\r\nRecall, from Forming Connection in Applications of Histograms: 3D, that a complete description of the distribution of a quantitative variable will include a discussion of shape, center, spread, and the presence of outliers. Refresh your understanding of the definitions of these characteristics if needed.\r\n\r\nCore skill: [reveal-answer q=\"61293\"]Define shape, center, spread, and the presence of outliers to describe the distribution of a quantitative variable.[\/reveal-answer]\r\n[hidden-answer a=\"61293\"]\r\n<p style=\"padding-left: 30px;\"><strong>Shape:\u00a0<\/strong>The overall pattern (left skewed, right skewed, symmetric) and the\u00a0number of peaks (unimodal, bimodal, multimodal, uniform)<\/p>\r\n<p style=\"padding-left: 30px;\"><strong>Center:\u00a0<\/strong>A measure that describes where the middle of the distribution is. The center is a number that describes a typical value. For example, one way to\u00a0think about center is that it could be the point in the distribution where about\u00a0half of the observations are below it and half are above it.<\/p>\r\n<p style=\"padding-left: 30px;\"><strong>Spread:\u00a0<\/strong>A measure of how far apart the data are. In the previous and\u00a0upcoming lesson, the range is used to measure spread. The range is the\u00a0difference between the maximum value and minimum value.<\/p>\r\n<p style=\"padding-left: 30px;\"><strong>Outliers:\u00a0<\/strong>Unusual observations that are outside the general pattern of the\u00a0distribution.<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"Describe\">Using the language of statistics to describe the distribution of a quantitative variable.<\/h3>\r\nFor each histogram in the questions below, identify if the description of the distribution is complete and addresses the appropriate features of a distribution. If not, identify the missing elements. Use the guidelines presented 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:\u00a03D<\/em><\/a>:\u00a0shape, center, spread, and the presence of outliers.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\nThe distribution of per capita CO<sub>2<\/sub> emissions for 28 European countries is roughly symmetric and unimodal. The emissions range from 2.5 to about 22.5 metric tons.\r\n\r\n<img class=\"alignnone wp-image-978\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11185508\/Picture16-300x133.png\" alt=\"A bar chart showing the per capita carbon dioxide emissions of EU countries in metric tons. The data primarily lies on the left side of the chart, with one symmetrical peak on the left, and one data point off to the far right.\" width=\"884\" height=\"392\" \/>\r\n\r\n[reveal-answer q=\"163169\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"163169\"]Include in your answer whether or not the description is accurate and whether or not it is complete. That is, are the statements made about the distribution correct? Are any of the four elements missing from the description?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\nThe number of hours watching TV per week in 2018 ranged from about 0 to 25 hours per week. There are a few respondents who watched an unusually high amount of TV (20 hours and 25 hours) compared to the rest.\r\n\r\n<img class=\"alignnone wp-image-979\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11185512\/Picture17-300x133.png\" alt=\"A bar chart showing the number of hours spent watching television per week in 2018. The data primarily lies on the far left of the chart, with a peak on the far left that steeply decreases as you move to the right. \" width=\"898\" height=\"398\" \/>\r\n\r\n[reveal-answer q=\"317214\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"317214\"]Include in your answer whether or not the description is accurate and whether or not it is complete. That is, are the statements made about the distribution correct? Are any of the four elements missing from the description?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 3<\/h3>\r\nThe average SAT score for the 50 states does not have any extreme observations.\r\n\r\n<img class=\"alignnone wp-image-980\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11185516\/Picture18-300x133.png\" alt=\"A bar chart showing the Average SAT scores for the 50 states. The data has two distinct peaks, with one trough separating the peaks. \" width=\"873\" height=\"387\" \/>\r\n\r\n[reveal-answer q=\"713039\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"713039\"]Include in your answer whether or not the description is accurate and whether or not it is complete. That is, are the statements made about the distribution correct? Are any of the four elements missing from the description?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\nProvide a complete description for the movie runtimes for all G-rated movies.\r\n\r\n<img class=\"alignnone wp-image-981\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11185520\/Picture19-300x133.png\" alt=\"A bar graph shows the run time in minutes for G-rated movies. The data primarily lies in the center of the chart, with only a few data points off to the far left and right of the chart.\" width=\"902\" height=\"400\" \/>\r\n\r\n[reveal-answer q=\"3512\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"3512\"]Recall that a complete description includes information about the shape, center, spread and any outliers.[\/hidden-answer]\r\n\r\n<\/div>\r\nHopefully, you have started to become more comfortable using the language of statistics to describe the distribution of a quantitative variable. It's time to move on to the next section.","rendered":"<div class=\"textbox learning-objectives\">\n<h3>What you&#8217;ll need to know<\/h3>\n<p>In this support activity you&#8217;ll become familiar with the following:<\/p>\n<ul>\n<li><a href=\"#Describe\">Using the language of statistics to describe the distribution of a quantitative variable.<\/a><\/li>\n<\/ul>\n<\/div>\n<p>In the next section of the course material and in the following activity, you will need to compare the distributions of a single variable between groups. In this corequisite support activity, we will practice describing the distributions when presented with a histogram.<\/p>\n<h2><strong>Describing Histograms<\/strong><\/h2>\n<p>In the the section <em><a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/what-to-know-about-applications-of-histograms-3d\/\">What to Know About Applications of Histograms: 3D\u00a0\u00a0<\/a><\/em>you defined the\u00a0shape, center, spread, and the presence of outliers in the\u00a0distribution of a quantitative variable. You learned about the skewness and modality of a distribution and saw how to use the range as a possible representation of spread. Then, in the activity,\u00a0<a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/forming-connections-with-applications-of-histograms-3d\/\"><em>Forming Connections in Applications of Histograms:\u00a03D<\/em><\/a>, you used these statistical terms in summary to thoroughly describe the distribution of a quantitative variable.\u00a0 \u00a0In the upcoming section and activity, you&#8217;ll need to display a comfortable understanding of this statistical language so we&#8217;ll spend some time analyzing some histograms and possible descriptions in this support activity.<\/p>\n<p>In Questions 1\u20133 below, you will be presented with a histogram and a description of the distribution of the variable to analyze. The recall box below contains the descriptions of each of the four characteristics of a thorough description.<\/p>\n<div class=\"textbox examples\">\n<h3>Recall<\/h3>\n<p>Recall, from Forming Connection in Applications of Histograms: 3D, that a complete description of the distribution of a quantitative variable will include a discussion of shape, center, spread, and the presence of outliers. Refresh your understanding of the definitions of these characteristics if needed.<\/p>\n<p>Core skill: <\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q61293\">Define shape, center, spread, and the presence of outliers to describe the distribution of a quantitative variable.<\/span><\/p>\n<div id=\"q61293\" class=\"hidden-answer\" style=\"display: none\">\n<p style=\"padding-left: 30px;\"><strong>Shape:\u00a0<\/strong>The overall pattern (left skewed, right skewed, symmetric) and the\u00a0number of peaks (unimodal, bimodal, multimodal, uniform)<\/p>\n<p style=\"padding-left: 30px;\"><strong>Center:\u00a0<\/strong>A measure that describes where the middle of the distribution is. The center is a number that describes a typical value. For example, one way to\u00a0think about center is that it could be the point in the distribution where about\u00a0half of the observations are below it and half are above it.<\/p>\n<p style=\"padding-left: 30px;\"><strong>Spread:\u00a0<\/strong>A measure of how far apart the data are. In the previous and\u00a0upcoming lesson, the range is used to measure spread. The range is the\u00a0difference between the maximum value and minimum value.<\/p>\n<p style=\"padding-left: 30px;\"><strong>Outliers:\u00a0<\/strong>Unusual observations that are outside the general pattern of the\u00a0distribution.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h3 id=\"Describe\">Using the language of statistics to describe the distribution of a quantitative variable.<\/h3>\n<p>For each histogram in the questions below, identify if the description of the distribution is complete and addresses the appropriate features of a distribution. If not, identify the missing elements. Use the guidelines presented 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:\u00a03D<\/em><\/a>:\u00a0shape, center, spread, and the presence of outliers.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p>The distribution of per capita CO<sub>2<\/sub> emissions for 28 European countries is roughly symmetric and unimodal. The emissions range from 2.5 to about 22.5 metric tons.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-978\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11185508\/Picture16-300x133.png\" alt=\"A bar chart showing the per capita carbon dioxide emissions of EU countries in metric tons. The data primarily lies on the left side of the chart, with one symmetrical peak on the left, and one data point off to the far right.\" width=\"884\" height=\"392\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q163169\">Hint<\/span><\/p>\n<div id=\"q163169\" class=\"hidden-answer\" style=\"display: none\">Include in your answer whether or not the description is accurate and whether or not it is complete. That is, are the statements made about the distribution correct? Are any of the four elements missing from the description?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p>The number of hours watching TV per week in 2018 ranged from about 0 to 25 hours per week. There are a few respondents who watched an unusually high amount of TV (20 hours and 25 hours) compared to the rest.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-979\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11185512\/Picture17-300x133.png\" alt=\"A bar chart showing the number of hours spent watching television per week in 2018. The data primarily lies on the far left of the chart, with a peak on the far left that steeply decreases as you move to the right.\" width=\"898\" height=\"398\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q317214\">Hint<\/span><\/p>\n<div id=\"q317214\" class=\"hidden-answer\" style=\"display: none\">Include in your answer whether or not the description is accurate and whether or not it is complete. That is, are the statements made about the distribution correct? Are any of the four elements missing from the description?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p>The average SAT score for the 50 states does not have any extreme observations.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-980\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11185516\/Picture18-300x133.png\" alt=\"A bar chart showing the Average SAT scores for the 50 states. The data has two distinct peaks, with one trough separating the peaks.\" width=\"873\" height=\"387\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q713039\">Hint<\/span><\/p>\n<div id=\"q713039\" class=\"hidden-answer\" style=\"display: none\">Include in your answer whether or not the description is accurate and whether or not it is complete. That is, are the statements made about the distribution correct? Are any of the four elements missing from the description?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p>Provide a complete description for the movie runtimes for all G-rated movies.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-981\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11185520\/Picture19-300x133.png\" alt=\"A bar graph shows the run time in minutes for G-rated movies. The data primarily lies in the center of the chart, with only a few data points off to the far left and right of the chart.\" width=\"902\" height=\"400\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q3512\">Hint<\/span><\/p>\n<div id=\"q3512\" class=\"hidden-answer\" style=\"display: none\">Recall that a complete description includes information about the shape, center, spread and any outliers.<\/div>\n<\/div>\n<\/div>\n<p>Hopefully, you have started to become more comfortable using the language of statistics to describe the distribution of a quantitative variable. It&#8217;s time to move on to the next section.<\/p>\n","protected":false},"author":428269,"menu_order":31,"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-158","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/158","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\/428269"}],"version-history":[{"count":23,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/158\/revisions"}],"predecessor-version":[{"id":3304,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/158\/revisions\/3304"}],"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\/158\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=158"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=158"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=158"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=158"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}