{"id":291,"date":"2022-02-18T23:58:03","date_gmt":"2022-02-18T23:58:03","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/?post_type=chapter&#038;p=291"},"modified":"2022-05-20T16:43:10","modified_gmt":"2022-05-20T16:43:10","slug":"calculating-mean-and-median-of-a-dataset-corequisite-support-activity","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/chapter\/calculating-mean-and-median-of-a-dataset-corequisite-support-activity\/","title":{"raw":"Calculating the Mean and Median of a Data Set: Corequisite Support Activity","rendered":"Calculating the Mean and Median of a Data Set: 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=\"#CompareDotplot\">Compare a single variable across groups using dotplots.<\/a><\/li>\r\n \t<li><a href=\"#CompareHist\">Compare a single variable across groups using histograms<\/a><a href=\"#CompareDist\">.<\/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=\"#ReadDotplot\">Read and interpret a dotplot.<\/a><\/li>\r\n \t<li><a href=\"#ReadHistogram\">Read and interpret a histogram.<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the next section of the course material you will refresh your knowledge of mean and median by calculating them for a small data set. In the following activity, you'll use technology to calculate them for larger data sets in order to read, interpret, and make comparisons of centers between histograms. In this support activity, you'll review reading and interpreting graphs that display the distribution of quantitative data, dotplots and histograms.\r\n<h2>Graphical Displays Illustrating Frequency<\/h2>\r\nLet's begin by re-visiting data from a sleep study [footnote] Onyper, S. V., Thacher, P. V., Gilbert, J. W., &amp; Gradess, S. G. (2012). Class start times, sleep, and academic performance in college: A path analysis. <em>Chronobiology International<\/em>, 29(3), 318-335. [\/footnote] of college students that we saw in <a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/3a-forming-connections-with-categorical-variables\/\"><em>Forming Connections in Displaying Categorical Data: 3A<\/em><\/a>.\u00a0We'll explore and compare the distributions of a few of the numerical variables from the study, including alcoholic drinks consumed per week, hours of sleep per night on the weekends, and classes missed in a semester.\r\n<h3 id=\"ReadDotplot\">Dotplots<\/h3>\r\nBelow we are given a dotplot for the variable <em>Alcoholic Drinks Per Week<\/em>. Recall that a dotplot is used to display the frequency and distribution of a quantitative variable. Use this dotplot to answer Questions 1-3.\r\n<div class=\"textbox examples\">\r\n<h3>Recall<\/h3>\r\nYou may wish to refresh your understanding of how data is represented in a dotplot.\r\n\r\nCore skill:\r\n[reveal-answer q=\"839004\"]Understand the features of a dotplot[\/reveal-answer]\r\n[hidden-answer a=\"839004\"]A dotplot is a graph for displaying the distribution of a quantitative variable, in which the frequency of each value is represented by a stack of dots, one dot per observation. [\/hidden-answer]\r\n\r\n<\/div>\r\n<img class=\"alignnone wp-image-985\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11190634\/Picture211-300x133.png\" alt=\"A dot plot showing the average number of Alcoholic drinks consumed per week by college students. A count of 33 students drank 0. A count of 9 students drank 1. A count of 16 students drank 2. A count of 30 students drank 3. A count of 18 students drank 4. A count of 31 students drank 5. A count of 23 students drank 6. A count of 22 students drank 7. A count of 14 students drank 8. A count of 11 students drank 9. A count of 26 students drank 10. Zero students drank 11. A count of 9 students drank 12. A count of 3 students drank 13. One student drank 14. A count of 3 students drank 15. One student drank 18. A count of 2 students drank 20. One student drank 24. \" width=\"900\" height=\"399\" \/>\r\n\r\nIn order to use a graphical display to answer questions about the data set, it helps to first ask yourself a question or two to become familiar with the visualization. We'd like to know what information this dotplot conveys about the participating students in the study. Then we can use it to answer questions about the data. Question 1 will help orient you to the information presented in the dotplot. Questions 2 and 3 ask specifically about the data.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\n[ohm_question hide_question_numbers=1]240942[\/ohm_question]\r\n\r\n[reveal-answer q=\"76977\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"76977\"]See the recall box above for an explanation of the characteristics of a dotplot.[\/hidden-answer]\r\n\r\n<\/div>\r\nNow that you are familiar with the information presented in the display, you can use it to answer questions about the data.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\n[ohm_question hide_question_numbers=1]240943[\/ohm_question]\r\n\r\n[reveal-answer q=\"502081\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"502081\"]The data presented in a dotplot is usually small enough that the number of observations can be counted from the graph. [\/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]240944[\/ohm_question]\r\n\r\n[reveal-answer q=\"391331\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"391331\"]What do <em>you <\/em>think?[\/hidden-answer]\r\n\r\n<\/div>\r\nNext, we'll see how a histogram presents information about the distribution of a quantitative variable.\r\n<h3 id=\"ReadHistogram\">Histograms<\/h3>\r\nBelow we are given a histogram for the variable <em>Hours of Sleep Per Night (Weekend)<\/em>. Recall that a histogram displays the distribution of a quantitative variable but, unlike the dotplot in which each observation is stacked above each value appearing, a histogram gathers groups of observations up into its bars.\r\n<div class=\"textbox examples\">\r\n<h3>recall<\/h3>\r\nYou may wish to refresh your understanding of how data is represented in a histogram.\r\n\r\nCore skill: [reveal-answer q=\"819814\"]Understand the features of a histogram[\/reveal-answer]\r\n[hidden-answer a=\"819814\"]A histogram is a graph for displaying the distribution of a quantitative variable in which the frequency of an interval of values is represented by the height of a rectangular bar that summarizes a group of observations over an interval of values. The width, called <em>binwidth<\/em>, of each bar is equivalent and can represent any interval of values desired.\u00a0[\/hidden-answer]\r\n\r\n<\/div>\r\nUse the following histogram to address Questions 4-7.\r\n\r\n<img class=\"alignnone wp-image-1453\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/17233338\/Picture195-300x135.png\" alt=\"A histogram of labeled &quot;Hours of Sleep Per Night (Weekend)&quot; on the x-axis and &quot;Count&quot; on the y-axis. For 4-5, the count is approximately 4. For 5-6, the count is approximately 8. For 6-7, the count is approximately 33. For 7-8, the count is approximately 57. For 8-9, the count is approximately 70. For 9-10, the count is approximately 54. For 10-11, the count is approximately 23. For 11-12, the count is approximately 4. For 12-13, the count is approximately 2.\" width=\"1110\" height=\"503\" \/>\r\n\r\nAs you did with for the dotplot above, first orient yourself to the information conveyed in the histogram by answering Question 4.\u00a0 Then, compare and contrast the histogram to the dotplot in Question 5. Finally, read and interpret the histogram to answer Questions 6 and 7.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\n[ohm_question hide_question_numbers=1]240947[\/ohm_question]\r\n\r\n[reveal-answer q=\"941946\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"941946\"]See the recall box above for a description of the features of a histogram.[\/hidden-answer]\r\n\r\n<\/div>\r\nNow that you are familiar with the information presented in the histogram, look back at the dotplot and consider general differences and similarities in the two types of displays.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 5<\/h3>\r\n[ohm_question hide_question_numbers=1]240948[\/ohm_question]\r\n\r\n[reveal-answer q=\"207574\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"207574\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\nHistograms are more commonly encountered than dotplots as a visualization of quantitative data since they can more concisely display large data sets. Dotplots are more appropriate for smaller sets of data in which the observations (the dots) are not overwhelmingly numerous.\r\n\r\nNow use the histogram to answer questions about the variable\u00a0<em>Hours of Sleep Per Night (Weekend)<\/em>.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 6<\/h3>\r\n[ohm_question hide_question_numbers=1]240951[\/ohm_question]\r\n\r\n[reveal-answer q=\"350070\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"350070\"]The height of each bar represents the observations grouped within the bar.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 7<\/h3>\r\n[ohm_question hide_question_numbers=1]240952[\/ohm_question]\r\n\r\n[reveal-answer q=\"107203\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"107203\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\nLet's examine the distribution of a variable from another data set.\r\n\r\nThe histogram below displays the frequency of sodium content per serving for\u00a0[latex]20[\/latex] different varieties of cereals.[footnote] Agresti, A., Franklin, C. A., &amp; Klingenberg, B. (2021). Statistics: The art and science of learning from data, 5th edition. Pearson. https:\/\/www.pearson.com\/us\/higher-education\/program\/Agresti-My-Lab-Statistics-with-Pearson-e-Text-Access-Card-for-Statistics-The-Art-and-Science-of-Learning-from-Data-18-Weeks-5th-Edition\/PGM2788191.html [\/footnote]\r\n\r\n<img class=\"alignnone wp-image-1458\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/17234959\/Picture196-300x129.png\" alt=\"A histogram labeled &quot;Cereal Sodium Content (mg)&quot; on the horizontal axis, which is numbered in increments of 50 from 0 to 100, and labeled &quot;Count&quot; on the vertical axis. For 0-25, the count is 1. For 50-75, the count is 2. For 100-125, the count is 1. For 125-150, the count is 3. For 150-175, the count is 2. For 175-200, the count is 4. For 200-225, the count is 5. For 275-300, the count is 1. For 325-350, the count is 1.\" width=\"1260\" height=\"542\" \/>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 8<\/h3>\r\n[ohm_question hide_question_numbers=1]240955[\/ohm_question]\r\n\r\n[reveal-answer q=\"357681\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"357681\"]Count all the bars that represent sodium of at least\u00a0[latex]200[\/latex] mg.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 9<\/h3>\r\n[ohm_question hide_question_numbers=1]240957[\/ohm_question]\r\n\r\n[reveal-answer q=\"779992\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"779992\"]Count all the bars that represent sodium less than [latex]200[\/latex] mg.[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2 id=\"CompareDotplot\">Comparing Variables Across Groups<\/h2>\r\nNow let's make comparisons of a single variable across two groups using first dotplots, then histograms.\r\n<div class=\"textbox exercises\">\r\n<h3>interactive example<\/h3>\r\nWhen making comparisons of a single variable across two groups, we are often looking for clues that let us know which group is larger or in which group more data appears to the left or right of a particular value of the variable.\r\n<ol>\r\n \t<li>Based on what you know about dotplots and histograms, which graph would be more helpful for determining which group is larger?<\/li>\r\n \t<li>Which graph would be more helpful for determining in which group the bulk of the data lies more to one side of a particular value of the variable?<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"637164\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"637164\"]\r\n<ol>\r\n \t<li>The dotplot, since it shows exact number of observations, would be more helpful to determine which group is larger. The histogram doesn't give us information about exactly how many of each value are in each bin of the graph.<\/li>\r\n \t<li>The histogram, since it shows the data in block (bins), is better for seeing large trends in the distribution. The fine detail in the dotplot can be difficult to use to draw conclusions about broader questions.<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<h3>Comparing with Dotplots<\/h3>\r\nThe following dotplots compare the numbers of classes missed between two groups of students: those who abstain from drinking alcohol (\u201cAbstain\u201d) and those who consume large amounts of alcohol each week (\u201cHeavy\u201d). Note that \u201cModerate\u201d and \u201cLight\u201d drinkers are excluded here.\r\n\r\n<img class=\"alignnone wp-image-986\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11190639\/Picture22-300x253.png\" alt=\"Two dot plots are shown. In the first, it shows the number of classes missed by students who abstain from drinking alcohol. 16 students missed 0 classes. 10 students missed 1 class. 4 students missed 2 classes. One student missed 4 classes. One student missed 14 classes. One student missed 15 classes. One student missed 20 classes. The second dot plot shows the number of classes missed by students who drink heavily. 4 students missed 0 classes. 2 students missed 1 class. 3 students missed 2 classes. 4 students missed 3 classes. 1 student missed 4 classes. 1 student missed 5 classes. 1 student missed 6 classes.\" width=\"905\" height=\"763\" \/>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 10<\/h3>\r\n[ohm_question hide_question_numbers=1]240958[\/ohm_question]\r\n\r\n[reveal-answer q=\"698730\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"698730\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 11<\/h3>\r\n[ohm_question hide_question_numbers=1]240959[\/ohm_question]\r\n\r\n[reveal-answer q=\"514538\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"514538\"]Recall that the number of observations are represented by individual dots, one per observation.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 12<\/h3>\r\n[ohm_question hide_question_numbers=1]240960[\/ohm_question]\r\n\r\n[reveal-answer q=\"302235\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"302235\"]Recall that the number of observations are represented by individual dots, one per observation.[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3>Comparing with Histograms<\/h3>\r\nThe following graph compares the distribution of per capita CO<sub>2<\/sub> emissions between two groups: countries in Central and South America and countries in Europe.\r\n\r\n<img class=\"alignnone wp-image-987\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11190644\/Picture23-300x158.png\" alt=\"Two histograms are shown. In the first histogram, it shows the per capita CO2 Emission in metric tons (x-axis) and the number of Central and South American countries that produce those amounts of emissions. 14 countries emitted between 0 and 2 metric tons. 9 countries emitted between 2 and 4 metric tons. 8 countries emitted between 4 and 6 metric tons. 4 countries emitted between 6 to 8 metric tons. 1 country emitted between 8 and 10 metric tons. 2 countries emitted between 10 and 12 metric tons. In the second histogram, it shows the per capita CO2 Emission in metric tons (x-axis) and the number of European countries that produce those amounts of emissions. 1 country emitted between 0 and 2 metric tons. 4 countries emitted between 2 and 4 metric tons. 7 countries emitted between 4 and 6 metric tons. 7 countries emitted between 6 and 8 metric tons. 9 countries emitted between 8 and 10 metric tons. 1 country emitted between 10 and 12 metric tons. 2 countries emitted 12 or more metric tons.\" width=\"879\" height=\"463\" \/>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 13<\/h3>\r\n[ohm_question hide_question_numbers=1]240961[\/ohm_question]\r\n\r\n[reveal-answer q=\"347026\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"347026\"]What do <em>you\u00a0<\/em>think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 14<\/h3>\r\n[ohm_question hide_question_numbers=1]240963[\/ohm_question]\r\n\r\n[reveal-answer q=\"708487\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"708487\"]What do <em>you\u00a0<\/em>think?[\/hidden-answer]\r\n\r\n<\/div>\r\nIf you feel comfortable reading, interpreting, and comparing histograms, please move on to the next section and activity.","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=\"#CompareDotplot\">Compare a single variable across groups using dotplots.<\/a><\/li>\n<li><a href=\"#CompareHist\">Compare a single variable across groups using histograms<\/a><a href=\"#CompareDist\">.<\/a><\/li>\n<\/ul>\n<p>You will also have an opportunity to refresh the following skills:<\/p>\n<ul>\n<li><a href=\"#ReadDotplot\">Read and interpret a dotplot.<\/a><\/li>\n<li><a href=\"#ReadHistogram\">Read and interpret a histogram.<\/a><\/li>\n<\/ul>\n<\/div>\n<p>In the next section of the course material you will refresh your knowledge of mean and median by calculating them for a small data set. In the following activity, you&#8217;ll use technology to calculate them for larger data sets in order to read, interpret, and make comparisons of centers between histograms. In this support activity, you&#8217;ll review reading and interpreting graphs that display the distribution of quantitative data, dotplots and histograms.<\/p>\n<h2>Graphical Displays Illustrating Frequency<\/h2>\n<p>Let&#8217;s begin by re-visiting data from a sleep study <a class=\"footnote\" title=\"Onyper, S. V., Thacher, P. V., Gilbert, J. W., &amp; Gradess, S. G. (2012). Class start times, sleep, and academic performance in college: A path analysis. Chronobiology International, 29(3), 318-335.\" id=\"return-footnote-291-1\" href=\"#footnote-291-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> of college students that we saw in <a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/3a-forming-connections-with-categorical-variables\/\"><em>Forming Connections in Displaying Categorical Data: 3A<\/em><\/a>.\u00a0We&#8217;ll explore and compare the distributions of a few of the numerical variables from the study, including alcoholic drinks consumed per week, hours of sleep per night on the weekends, and classes missed in a semester.<\/p>\n<h3 id=\"ReadDotplot\">Dotplots<\/h3>\n<p>Below we are given a dotplot for the variable <em>Alcoholic Drinks Per Week<\/em>. Recall that a dotplot is used to display the frequency and distribution of a quantitative variable. Use this dotplot to answer Questions 1-3.<\/p>\n<div class=\"textbox examples\">\n<h3>Recall<\/h3>\n<p>You may wish to refresh your understanding of how data is represented in a dotplot.<\/p>\n<p>Core skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q839004\">Understand the features of a dotplot<\/span><\/p>\n<div id=\"q839004\" class=\"hidden-answer\" style=\"display: none\">A dotplot is a graph for displaying the distribution of a quantitative variable, in which the frequency of each value is represented by a stack of dots, one dot per observation. <\/div>\n<\/div>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-985\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11190634\/Picture211-300x133.png\" alt=\"A dot plot showing the average number of Alcoholic drinks consumed per week by college students. A count of 33 students drank 0. A count of 9 students drank 1. A count of 16 students drank 2. A count of 30 students drank 3. A count of 18 students drank 4. A count of 31 students drank 5. A count of 23 students drank 6. A count of 22 students drank 7. A count of 14 students drank 8. A count of 11 students drank 9. A count of 26 students drank 10. Zero students drank 11. A count of 9 students drank 12. A count of 3 students drank 13. One student drank 14. A count of 3 students drank 15. One student drank 18. A count of 2 students drank 20. One student drank 24.\" width=\"900\" height=\"399\" \/><\/p>\n<p>In order to use a graphical display to answer questions about the data set, it helps to first ask yourself a question or two to become familiar with the visualization. We&#8217;d like to know what information this dotplot conveys about the participating students in the study. Then we can use it to answer questions about the data. Question 1 will help orient you to the information presented in the dotplot. Questions 2 and 3 ask specifically about the data.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240942\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240942&theme=oea&iframe_resize_id=ohm240942\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q76977\">Hint<\/span><\/p>\n<div id=\"q76977\" class=\"hidden-answer\" style=\"display: none\">See the recall box above for an explanation of the characteristics of a dotplot.<\/div>\n<\/div>\n<\/div>\n<p>Now that you are familiar with the information presented in the display, you can use it to answer questions about the data.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240943\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240943&theme=oea&iframe_resize_id=ohm240943\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q502081\">Hint<\/span><\/p>\n<div id=\"q502081\" class=\"hidden-answer\" style=\"display: none\">The data presented in a dotplot is usually small enough that the number of observations can be counted from the graph. <\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240944\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240944&theme=oea&iframe_resize_id=ohm240944\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q391331\">Hint<\/span><\/p>\n<div id=\"q391331\" class=\"hidden-answer\" style=\"display: none\">What do <em>you <\/em>think?<\/div>\n<\/div>\n<\/div>\n<p>Next, we&#8217;ll see how a histogram presents information about the distribution of a quantitative variable.<\/p>\n<h3 id=\"ReadHistogram\">Histograms<\/h3>\n<p>Below we are given a histogram for the variable <em>Hours of Sleep Per Night (Weekend)<\/em>. Recall that a histogram displays the distribution of a quantitative variable but, unlike the dotplot in which each observation is stacked above each value appearing, a histogram gathers groups of observations up into its bars.<\/p>\n<div class=\"textbox examples\">\n<h3>recall<\/h3>\n<p>You may wish to refresh your understanding of how data is represented in a histogram.<\/p>\n<p>Core skill: <\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q819814\">Understand the features of a histogram<\/span><\/p>\n<div id=\"q819814\" class=\"hidden-answer\" style=\"display: none\">A histogram is a graph for displaying the distribution of a quantitative variable in which the frequency of an interval of values is represented by the height of a rectangular bar that summarizes a group of observations over an interval of values. The width, called <em>binwidth<\/em>, of each bar is equivalent and can represent any interval of values desired.\u00a0<\/div>\n<\/div>\n<\/div>\n<p>Use the following histogram to address Questions 4-7.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1453\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/17233338\/Picture195-300x135.png\" alt=\"A histogram of labeled &quot;Hours of Sleep Per Night (Weekend)&quot; on the x-axis and &quot;Count&quot; on the y-axis. For 4-5, the count is approximately 4. For 5-6, the count is approximately 8. For 6-7, the count is approximately 33. For 7-8, the count is approximately 57. For 8-9, the count is approximately 70. For 9-10, the count is approximately 54. For 10-11, the count is approximately 23. For 11-12, the count is approximately 4. For 12-13, the count is approximately 2.\" width=\"1110\" height=\"503\" \/><\/p>\n<p>As you did with for the dotplot above, first orient yourself to the information conveyed in the histogram by answering Question 4.\u00a0 Then, compare and contrast the histogram to the dotplot in Question 5. Finally, read and interpret the histogram to answer Questions 6 and 7.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240947\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240947&theme=oea&iframe_resize_id=ohm240947\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q941946\">Hint<\/span><\/p>\n<div id=\"q941946\" class=\"hidden-answer\" style=\"display: none\">See the recall box above for a description of the features of a histogram.<\/div>\n<\/div>\n<\/div>\n<p>Now that you are familiar with the information presented in the histogram, look back at the dotplot and consider general differences and similarities in the two types of displays.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 5<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240948\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240948&theme=oea&iframe_resize_id=ohm240948\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q207574\">Hint<\/span><\/p>\n<div id=\"q207574\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<p>Histograms are more commonly encountered than dotplots as a visualization of quantitative data since they can more concisely display large data sets. Dotplots are more appropriate for smaller sets of data in which the observations (the dots) are not overwhelmingly numerous.<\/p>\n<p>Now use the histogram to answer questions about the variable\u00a0<em>Hours of Sleep Per Night (Weekend)<\/em>.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 6<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240951\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240951&theme=oea&iframe_resize_id=ohm240951\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q350070\">Hint<\/span><\/p>\n<div id=\"q350070\" class=\"hidden-answer\" style=\"display: none\">The height of each bar represents the observations grouped within the bar.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 7<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240952\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240952&theme=oea&iframe_resize_id=ohm240952\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q107203\">Hint<\/span><\/p>\n<div id=\"q107203\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<p>Let&#8217;s examine the distribution of a variable from another data set.<\/p>\n<p>The histogram below displays the frequency of sodium content per serving for\u00a0[latex]20[\/latex] different varieties of cereals.<a class=\"footnote\" title=\"Agresti, A., Franklin, C. A., &amp; Klingenberg, B. (2021). Statistics: The art and science of learning from data, 5th edition. Pearson. https:\/\/www.pearson.com\/us\/higher-education\/program\/Agresti-My-Lab-Statistics-with-Pearson-e-Text-Access-Card-for-Statistics-The-Art-and-Science-of-Learning-from-Data-18-Weeks-5th-Edition\/PGM2788191.html\" id=\"return-footnote-291-2\" href=\"#footnote-291-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1458\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/17234959\/Picture196-300x129.png\" alt=\"A histogram labeled &quot;Cereal Sodium Content (mg)&quot; on the horizontal axis, which is numbered in increments of 50 from 0 to 100, and labeled &quot;Count&quot; on the vertical axis. For 0-25, the count is 1. For 50-75, the count is 2. For 100-125, the count is 1. For 125-150, the count is 3. For 150-175, the count is 2. For 175-200, the count is 4. For 200-225, the count is 5. For 275-300, the count is 1. For 325-350, the count is 1.\" width=\"1260\" height=\"542\" \/><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 8<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240955\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240955&theme=oea&iframe_resize_id=ohm240955\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q357681\">Hint<\/span><\/p>\n<div id=\"q357681\" class=\"hidden-answer\" style=\"display: none\">Count all the bars that represent sodium of at least\u00a0[latex]200[\/latex] mg.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 9<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240957\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240957&theme=oea&iframe_resize_id=ohm240957\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q779992\">Hint<\/span><\/p>\n<div id=\"q779992\" class=\"hidden-answer\" style=\"display: none\">Count all the bars that represent sodium less than [latex]200[\/latex] mg.<\/div>\n<\/div>\n<\/div>\n<h2 id=\"CompareDotplot\">Comparing Variables Across Groups<\/h2>\n<p>Now let&#8217;s make comparisons of a single variable across two groups using first dotplots, then histograms.<\/p>\n<div class=\"textbox exercises\">\n<h3>interactive example<\/h3>\n<p>When making comparisons of a single variable across two groups, we are often looking for clues that let us know which group is larger or in which group more data appears to the left or right of a particular value of the variable.<\/p>\n<ol>\n<li>Based on what you know about dotplots and histograms, which graph would be more helpful for determining which group is larger?<\/li>\n<li>Which graph would be more helpful for determining in which group the bulk of the data lies more to one side of a particular value of the variable?<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q637164\">Show Answer<\/span><\/p>\n<div id=\"q637164\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>The dotplot, since it shows exact number of observations, would be more helpful to determine which group is larger. The histogram doesn&#8217;t give us information about exactly how many of each value are in each bin of the graph.<\/li>\n<li>The histogram, since it shows the data in block (bins), is better for seeing large trends in the distribution. The fine detail in the dotplot can be difficult to use to draw conclusions about broader questions.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<h3>Comparing with Dotplots<\/h3>\n<p>The following dotplots compare the numbers of classes missed between two groups of students: those who abstain from drinking alcohol (\u201cAbstain\u201d) and those who consume large amounts of alcohol each week (\u201cHeavy\u201d). Note that \u201cModerate\u201d and \u201cLight\u201d drinkers are excluded here.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-986\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11190639\/Picture22-300x253.png\" alt=\"Two dot plots are shown. In the first, it shows the number of classes missed by students who abstain from drinking alcohol. 16 students missed 0 classes. 10 students missed 1 class. 4 students missed 2 classes. One student missed 4 classes. One student missed 14 classes. One student missed 15 classes. One student missed 20 classes. The second dot plot shows the number of classes missed by students who drink heavily. 4 students missed 0 classes. 2 students missed 1 class. 3 students missed 2 classes. 4 students missed 3 classes. 1 student missed 4 classes. 1 student missed 5 classes. 1 student missed 6 classes.\" width=\"905\" height=\"763\" \/><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 10<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240958\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240958&theme=oea&iframe_resize_id=ohm240958\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q698730\">Hint<\/span><\/p>\n<div id=\"q698730\" 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>question 11<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240959\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240959&theme=oea&iframe_resize_id=ohm240959\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q514538\">Hint<\/span><\/p>\n<div id=\"q514538\" class=\"hidden-answer\" style=\"display: none\">Recall that the number of observations are represented by individual dots, one per observation.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 12<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240960\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240960&theme=oea&iframe_resize_id=ohm240960\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q302235\">Hint<\/span><\/p>\n<div id=\"q302235\" class=\"hidden-answer\" style=\"display: none\">Recall that the number of observations are represented by individual dots, one per observation.<\/div>\n<\/div>\n<\/div>\n<h3>Comparing with Histograms<\/h3>\n<p>The following graph compares the distribution of per capita CO<sub>2<\/sub> emissions between two groups: countries in Central and South America and countries in Europe.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-987\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11190644\/Picture23-300x158.png\" alt=\"Two histograms are shown. In the first histogram, it shows the per capita CO2 Emission in metric tons (x-axis) and the number of Central and South American countries that produce those amounts of emissions. 14 countries emitted between 0 and 2 metric tons. 9 countries emitted between 2 and 4 metric tons. 8 countries emitted between 4 and 6 metric tons. 4 countries emitted between 6 to 8 metric tons. 1 country emitted between 8 and 10 metric tons. 2 countries emitted between 10 and 12 metric tons. In the second histogram, it shows the per capita CO2 Emission in metric tons (x-axis) and the number of European countries that produce those amounts of emissions. 1 country emitted between 0 and 2 metric tons. 4 countries emitted between 2 and 4 metric tons. 7 countries emitted between 4 and 6 metric tons. 7 countries emitted between 6 and 8 metric tons. 9 countries emitted between 8 and 10 metric tons. 1 country emitted between 10 and 12 metric tons. 2 countries emitted 12 or more metric tons.\" width=\"879\" height=\"463\" \/><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 13<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240961\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240961&theme=oea&iframe_resize_id=ohm240961\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q347026\">Hint<\/span><\/p>\n<div id=\"q347026\" class=\"hidden-answer\" style=\"display: none\">What do <em>you\u00a0<\/em>think?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 14<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240963\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240963&theme=oea&iframe_resize_id=ohm240963\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q708487\">Hint<\/span><\/p>\n<div id=\"q708487\" class=\"hidden-answer\" style=\"display: none\">What do <em>you\u00a0<\/em>think?<\/div>\n<\/div>\n<\/div>\n<p>If you feel comfortable reading, interpreting, and comparing histograms, please move on to the next section and activity.<\/p>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-291-1\"> Onyper, S. V., Thacher, P. V., Gilbert, J. W., &amp; Gradess, S. G. (2012). Class start times, sleep, and academic performance in college: A path analysis. <em>Chronobiology International<\/em>, 29(3), 318-335.  <a href=\"#return-footnote-291-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-291-2\"> Agresti, A., Franklin, C. A., &amp; Klingenberg, B. (2021). Statistics: The art and science of learning from data, 5th edition. Pearson. https:\/\/www.pearson.com\/us\/higher-education\/program\/Agresti-My-Lab-Statistics-with-Pearson-e-Text-Access-Card-for-Statistics-The-Art-and-Science-of-Learning-from-Data-18-Weeks-5th-Edition\/PGM2788191.html  <a href=\"#return-footnote-291-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":175116,"menu_order":28,"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-291","chapter","type-chapter","status-publish","hentry"],"part":1252,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/291","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":12,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/291\/revisions"}],"predecessor-version":[{"id":1256,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/291\/revisions\/1256"}],"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\/291\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/media?parent=291"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapter-type?post=291"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/contributor?post=291"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/license?post=291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}