{"id":305,"date":"2022-02-19T00:03:10","date_gmt":"2022-02-19T00:03:10","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/?post_type=chapter&#038;p=305"},"modified":"2022-05-20T16:44:11","modified_gmt":"2022-05-20T16:44:11","slug":"comparing-variability-of-datasets-corequisite-support-activity","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/chapter\/comparing-variability-of-datasets-corequisite-support-activity\/","title":{"raw":"Comparing Variability of Data Sets: Corequisite Support Activity","rendered":"Comparing Variability of Data Sets: Corequisite Support Activity"},"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=\"#DevMean\">Calculate the deviation from the mean of an observation in a data set.<\/a><\/li>\r\n<\/ul>\r\nYou will also have an opportunity to refresh the following skills:\r\n<ul>\r\n \t<li><a href=\"#MeanMedian\">Understand the difference between mean and median.<\/a><\/li>\r\n \t<li><a href=\"#SampleSizeMean\">Use technology to calculate the sample size and mean of a distribution.<\/a><\/li>\r\n \t<li><a href=\"#LargeNumbers\">Interpret large numbers.<\/a><\/li>\r\n \t<li><a href=\"#name\">Compare differently signed numbers.<\/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 understand and calculate the deviation from the mean. You will be extending this knowledge in the course section to understanding what the spread of a data set is and how it is calculated. For now, let's concentrate on refreshing necessary skills and learning about\u00a0<strong>deviation from the mean<\/strong>.\r\n<h2>Deviation from the Mean<\/h2>\r\nConsider the following dotplot of the exam scores for two different math classes on their midterm. The class average was\u00a0[latex]70[\/latex] points for both Class 1 and Class 2.\r\n\r\n<strong><img class=\"alignnone wp-image-999\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11192200\/Picture32-300x139.png\" alt=\"Two dot plots of exam scores. One shows dots clustered primarily between 60 and 80, while the other shows dots spread out between 40 and 100.\" width=\"900\" height=\"417\" \/><\/strong>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\n[ohm_question hide_question_numbers=1]241043[\/ohm_question]\r\n\r\n[reveal-answer q=\"282689\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"282689\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the next activity, we will be measuring the variability of a data set. We do this by measuring the distance, known as <strong>deviation<\/strong>, of an observed value from the mean. Let\u2019s look at an example from the real world.\r\n\r\n<img class=\"gnt_em_img_i aligncenter\" style=\"height: 339px;\" src=\"https:\/\/www.gannett-cdn.com\/media\/2018\/07\/08\/USATODAY\/usatsports\/hurricane-sandy-damage1.jpg?width=660&amp;height=372&amp;fit=crop&amp;format=pjpg&amp;auto=webp\" srcset=\"https:\/\/www.gannett-cdn.com\/media\/2018\/07\/08\/USATODAY\/usatsports\/hurricane-sandy-damage1.jpg?width=1320&amp;height=744&amp;fit=crop&amp;format=pjpg&amp;auto=webp 2x\" alt=\"The 2018 extreme weather season continues to unfold. A city is shown in the aftermath of a hurricane.\" width=\"601\" height=\"372\" \/>\r\n\r\nHurricanes cause extensive amounts of damage. In this corequisite support activity, we will consider the amount of damage in dollars of the\u00a0[latex]30[\/latex] most expensive hurricanes to have hit the U.S. mainland between 1990 and 2010. In order to explore this data set, you will need to recall what you have learned about measures of center. We'll concentrate on the mean of a quantitative distribution in this activity.\r\n<h3>Mean vs. median<\/h3>\r\n<span id=\"MeanMedian\">Before we move on, take a moment to recall the difference between mean and median.<\/span>\r\n<div class=\"textbox examples\">\r\n<h3>recall<\/h3>\r\nDo you recall the two measures of center you learned about in the previous section of the course: mean and median?\r\n\r\nCore skill: [reveal-answer q=\"127055\"]Define the mean and the median of a data set[\/reveal-answer]\r\n[hidden-answer a=\"127055\"]\r\n\r\nThe\u00a0<strong>mean<\/strong> of a data set is the \"balancing weight\" of the data values, what is commonly called the \"average.\"\r\n<ul>\r\n \t<li>To calculate the mean, divide the sum of all the data values by the number of them.<\/li>\r\n<\/ul>\r\nThe\u00a0<strong>median<\/strong> of a data set is the \"middle-most\" of the data values, the\u00a0[latex]50[\/latex]<sup>th<\/sup> percentile, and splits the data in half.\r\n<ul>\r\n \t<li>To identify the median, order the numbers then locate the middle number. Half the data will be above the median and half will be below it. If the data set contains an even amount of values, take the mean of the middle two values.<\/li>\r\n<\/ul>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nLet's go to the technology to analyze the data set \"Hurricane Damage.\"\r\n<h3 id=\"SampleSizeMean\">Sample size and mean<\/h3>\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>Single Group<\/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>Data Set<\/strong> and select <strong>Hurricane Damage<\/strong>.<\/p>\r\n\r\n<\/div>\r\nIn the descriptive statistics at the top of the applet, you will see the sample size [latex]\\left(n\\right)[\/latex] and the mean [latex]\\left(\\bar{x}\\right)[\/latex] of the data set.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\n[ohm_question hide_question_numbers=1]241044[\/ohm_question]\r\n\r\n[reveal-answer q=\"943053\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"943053\"]Make sure the Data Set \"Hurricane Damage\" is selected then locate the Sample Size in Descriptive Statistics.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 3<\/h3>\r\n[ohm_question hide_question_numbers=1]241045[\/ohm_question]\r\n\r\n[reveal-answer q=\"77790\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"77790\"]What is the name of the variable of interest? Use units when expressing your answer to put it in context.[\/hidden-answer]\r\n\r\n<\/div>\r\nOn the next page, you will continue to learn more about deviation from the mean.","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=\"#DevMean\">Calculate the deviation from the mean of an observation in a data set.<\/a><\/li>\n<\/ul>\n<p>You will also have an opportunity to refresh the following skills:<\/p>\n<ul>\n<li><a href=\"#MeanMedian\">Understand the difference between mean and median.<\/a><\/li>\n<li><a href=\"#SampleSizeMean\">Use technology to calculate the sample size and mean of a distribution.<\/a><\/li>\n<li><a href=\"#LargeNumbers\">Interpret large numbers.<\/a><\/li>\n<li><a href=\"#name\">Compare differently signed numbers.<\/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 understand and calculate the deviation from the mean. You will be extending this knowledge in the course section to understanding what the spread of a data set is and how it is calculated. For now, let&#8217;s concentrate on refreshing necessary skills and learning about\u00a0<strong>deviation from the mean<\/strong>.<\/p>\n<h2>Deviation from the Mean<\/h2>\n<p>Consider the following dotplot of the exam scores for two different math classes on their midterm. The class average was\u00a0[latex]70[\/latex] points for both Class 1 and Class 2.<\/p>\n<p><strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-999\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11192200\/Picture32-300x139.png\" alt=\"Two dot plots of exam scores. One shows dots clustered primarily between 60 and 80, while the other shows dots spread out between 40 and 100.\" width=\"900\" height=\"417\" \/><\/strong><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241043\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241043&theme=oea&iframe_resize_id=ohm241043\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q282689\">Hint<\/span><\/p>\n<div id=\"q282689\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<p>In the next activity, we will be measuring the variability of a data set. We do this by measuring the distance, known as <strong>deviation<\/strong>, of an observed value from the mean. Let\u2019s look at an example from the real world.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"gnt_em_img_i aligncenter\" style=\"height: 339px;\" src=\"https:\/\/www.gannett-cdn.com\/media\/2018\/07\/08\/USATODAY\/usatsports\/hurricane-sandy-damage1.jpg?width=660&amp;height=372&amp;fit=crop&amp;format=pjpg&amp;auto=webp\" srcset=\"https:\/\/www.gannett-cdn.com\/media\/2018\/07\/08\/USATODAY\/usatsports\/hurricane-sandy-damage1.jpg?width=1320&amp;height=744&amp;fit=crop&amp;format=pjpg&amp;auto=webp 2x\" alt=\"The 2018 extreme weather season continues to unfold. A city is shown in the aftermath of a hurricane.\" width=\"601\" height=\"372\" \/><\/p>\n<p>Hurricanes cause extensive amounts of damage. In this corequisite support activity, we will consider the amount of damage in dollars of the\u00a0[latex]30[\/latex] most expensive hurricanes to have hit the U.S. mainland between 1990 and 2010. In order to explore this data set, you will need to recall what you have learned about measures of center. We&#8217;ll concentrate on the mean of a quantitative distribution in this activity.<\/p>\n<h3>Mean vs. median<\/h3>\n<p><span id=\"MeanMedian\">Before we move on, take a moment to recall the difference between mean and median.<\/span><\/p>\n<div class=\"textbox examples\">\n<h3>recall<\/h3>\n<p>Do you recall the two measures of center you learned about in the previous section of the course: mean and median?<\/p>\n<p>Core skill: <\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q127055\">Define the mean and the median of a data set<\/span><\/p>\n<div id=\"q127055\" class=\"hidden-answer\" style=\"display: none\">\n<p>The\u00a0<strong>mean<\/strong> of a data set is the &#8220;balancing weight&#8221; of the data values, what is commonly called the &#8220;average.&#8221;<\/p>\n<ul>\n<li>To calculate the mean, divide the sum of all the data values by the number of them.<\/li>\n<\/ul>\n<p>The\u00a0<strong>median<\/strong> of a data set is the &#8220;middle-most&#8221; of the data values, the\u00a0[latex]50[\/latex]<sup>th<\/sup> percentile, and splits the data in half.<\/p>\n<ul>\n<li>To identify the median, order the numbers then locate the middle number. Half the data will be above the median and half will be below it. If the data set contains an even amount of values, take the mean of the middle two values.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<p>Let&#8217;s go to the technology to analyze the data set &#8220;Hurricane Damage.&#8221;<\/p>\n<h3 id=\"SampleSizeMean\">Sample size and mean<\/h3>\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>Single Group<\/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>Data Set<\/strong> and select <strong>Hurricane Damage<\/strong>.<\/p>\n<\/div>\n<p>In the descriptive statistics at the top of the applet, you will see the sample size [latex]\\left(n\\right)[\/latex] and the mean [latex]\\left(\\bar{x}\\right)[\/latex] of the data set.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241044\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241044&theme=oea&iframe_resize_id=ohm241044\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q943053\">Hint<\/span><\/p>\n<div id=\"q943053\" class=\"hidden-answer\" style=\"display: none\">Make sure the Data Set &#8220;Hurricane Damage&#8221; is selected then locate the Sample Size in Descriptive Statistics.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241045\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241045&theme=oea&iframe_resize_id=ohm241045\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q77790\">Hint<\/span><\/p>\n<div id=\"q77790\" class=\"hidden-answer\" style=\"display: none\">What is the name of the variable of interest? Use units when expressing your answer to put it in context.<\/div>\n<\/div>\n<\/div>\n<p>On the next page, you will continue to learn more about deviation from the mean.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-305\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Damage shown from 2018 extreme weather season. <strong>Authored by<\/strong>: Spencer Platt \/ Getty Images. <strong>Provided by<\/strong>: USA Today. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.usatoday.com\/story\/money\/2018\/09\/12\/most-destructive-hurricanes-of-all-time\/36697269\/\">https:\/\/www.usatoday.com\/story\/money\/2018\/09\/12\/most-destructive-hurricanes-of-all-time\/36697269\/<\/a>. <strong>License<\/strong>: <em>All Rights Reserved<\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":175116,"menu_order":33,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Damage shown from 2018 extreme weather season\",\"author\":\"Spencer Platt \/ Getty Images\",\"organization\":\"USA Today\",\"url\":\"https:\/\/www.usatoday.com\/story\/money\/2018\/09\/12\/most-destructive-hurricanes-of-all-time\/36697269\/\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-305","chapter","type-chapter","status-publish","hentry"],"part":1252,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/305","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/users\/175116"}],"version-history":[{"count":26,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/305\/revisions"}],"predecessor-version":[{"id":1241,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/305\/revisions\/1241"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/parts\/1252"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/305\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/media?parent=305"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapter-type?post=305"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/contributor?post=305"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/license?post=305"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}