{"id":259,"date":"2022-02-18T23:48:06","date_gmt":"2022-02-18T23:48:06","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/?post_type=chapter&#038;p=259"},"modified":"2022-03-31T16:43:35","modified_gmt":"2022-03-31T16:43:35","slug":"applications-of-histograms-corequisite-support-activity","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/chapter\/applications-of-histograms-corequisite-support-activity\/","title":{"raw":"Applications of Histograms: Corequisite Support Activity","rendered":"Applications of Histograms: 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=\"#ReadInterpret\">Read and interpret a data table and data dictionary.<\/a><\/li>\r\n \t<li><a href=\"#HistFromData Set\">Create a histogram from a data set using technology.<\/a><\/li>\r\n \t<li><a href=\"#AnswerQuestHist\">Use a histogram to answer questions about a variable.<\/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=\"#Proportion\">Write a proportion and express it as a percentage<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the section,\u00a0<a href=\"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/chapter\/applications-of-histograms-what-to-know\/\"><em>Applications of Histograms: What to Know<\/em><\/a>,\u00a0and in the following activity, you will need to be able to use technology to visualize the distribution of quantitative variables and use the visualization to answer questions about the distribution.\r\n<h2><strong>Analyzing Course Evaluations<\/strong><\/h2>\r\nIn this corequisite support activity, you will use the <em>evals<\/em> data set,[footnote] Professor evaluations and beauty. (n.d.). OpenIntro. Retrieved from https:\/\/www.openintro.org\/data\/index.php?data=evals[\/footnote] which includes information collected from student evaluations for a sample of\u00a0[latex]463[\/latex] courses taught by\u00a0[latex]94[\/latex] professors at The University of Texas at Austin. Each row is a different course, and the columns have information about the professor and summary information from the course.\r\n\r\nThe objective of this analysis is to explore the distribution of age of the professor for the\u00a0[latex]463[\/latex] courses. To do so, you\u2019ll use technology to make a histogram to visualize the distribution of professor ages.\r\n<h3 id=\"ReadInterpret\">Data Tables<\/h3>\r\nA data table contains raw data, collected observation by observation. The columns of the table list the variables for each observation. Each row contains data collected from one observational unit.\u00a0 See the demonstration in the interactive example below to understand how to read the table.\r\n<div class=\"textbox exercises\">\r\n<h3>interactive example<\/h3>\r\nA few observations of the Teaching Evaluations data table have been extracted and are shown here along with the data dictionary. The data displayed in each row was collected from a different course taught at the university.\r\n<table>\r\n<tbody>\r\n<tr style=\"height: 23px;\">\r\n<td style=\"text-align: center; height: 23px; width: 402.5px;\" colspan=\"5\"><strong>Teaching Evaluations<\/strong><strong>\r\n<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\"><strong>score<\/strong><\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\"><strong>rank<\/strong><\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\"><strong>cls_profs<\/strong><\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\"><strong>cls_students<\/strong><\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\"><strong>age<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.7[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenure track<\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]43[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]36[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.6[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">multiple<\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]20[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]59[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]3.9[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]195[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]51[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<ul>\r\n \t<li><em><strong>score<\/strong>: <\/em>Average professor evaluation score<\/li>\r\n \t<li><em><strong>rank<\/strong>: <\/em>Rank of professor (teaching, tenure track, tenured)<\/li>\r\n \t<li><em><strong>cls_profs<\/strong>: <\/em>Number of professors teaching sections in course in sample (single, multiple)<\/li>\r\n \t<li><em><strong>cls_students<\/strong>: <\/em>Number of students in the class<\/li>\r\n \t<li><em><strong>age<\/strong>: <\/em>Age of professor in years<\/li>\r\n<\/ul>\r\n<ol>\r\n \t<li>What was the rank of the professor teaching the course section that had an average professor evaluation score of\u00a0[latex]4.6[\/latex]?<\/li>\r\n \t<li>What was the average professor evaluation score taught by a [latex]36[\/latex] year old tenure track professor?<\/li>\r\n \t<li>How many students were in the course section with the score of [latex]3.9[\/latex]?<\/li>\r\n \t<li>How many professors taught the course section with [latex]43[\/latex] students in the class?<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"655712\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"655712\"]\r\n\r\nThe middle row above shows an average score of\u00a0[latex]4.6[\/latex]. All the answers can be located in that row.\r\n<ol>\r\n \t<li>Tenured<\/li>\r\n \t<li>[latex]4.7[\/latex]<\/li>\r\n \t<li>[latex]195[\/latex]<\/li>\r\n \t<li>Single<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe first\u00a0[latex]10[\/latex] observations of the selected variables within the \u201cTeaching Evaluations\u201d data set are displayed in the following table. Use it to answer Questions 1 and 2 below.\r\n<div align=\"center\">\r\n<table style=\"height: 177px;\">\r\n<tbody>\r\n<tr style=\"height: 23px;\">\r\n<td style=\"text-align: center; height: 23px; width: 402.5px;\" colspan=\"5\"><strong>Teaching Evaluations<\/strong><strong>\r\n<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\"><strong>score<\/strong><\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\"><strong>rank<\/strong><\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\"><strong>cls_profs<\/strong><\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\"><strong>cls_students<\/strong><\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\"><strong>age<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.7[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenure track<\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]43[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]36[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.1[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenure track<\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]125[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]36[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]3.9[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenure track<\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]125[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]36[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.8[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenure track<\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]123[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]36[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.6[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">multiple<\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]20[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]59[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.3[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">multiple<\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]40[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]59[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]2.8[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">multiple<\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]44[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]59[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.1[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]55[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]51[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]3.4[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]195[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]51[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.5[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\r\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\r\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]46[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]40[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nThe following is a <strong>data dictionary<\/strong> of the selected variables:\r\n<ul>\r\n \t<li><em><strong>score<\/strong>: <\/em>Average professor evaluation score<\/li>\r\n \t<li><em><strong>rank<\/strong>: <\/em>Rank of professor (teaching, tenure track, tenured)<\/li>\r\n \t<li><em><strong>cls_profs<\/strong>: <\/em>Number of professors teaching sections in course in sample (single, multiple)<\/li>\r\n \t<li><em><strong>cls_students<\/strong>: <\/em>Number of students in the class<\/li>\r\n \t<li><em><strong>age<\/strong>: <\/em>Age of professor in years<\/li>\r\n<\/ul>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\n[ohm_question hide_question_numbers=1]241030[\/ohm_question]\r\n\r\n[reveal-answer q=\"852290\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"852290\"]From what person, item, or entity have the observations been taken?\u00a0 [\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\n[ohm_question hide_question_numbers=1]240861[\/ohm_question]\r\n[reveal-answer q=\"327228\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"327228\"]Remember that quantitative observations are in numerical form and can be manipulated arithmetically.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div>Now let's examine the distribution of the variable <em>age <\/em>by creating a histogram and using it to answer some questions about the variable.<\/div>\r\n<h3 id=\"HistFromData Set\">Histograms<\/h3>\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\/<\/a> and select the data set <strong>Teaching Evaluations - Age\"\u00a0<\/strong>to\u00a0make a histogram of the distribution of professor ages. Select\u00a0<strong>Binwidth<\/strong> to 5.\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]240862[\/ohm_question]\r\n\r\n[reveal-answer q=\"805230\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"805230\"]Make sure that you have selected the correct data set, Teaching Evaluations - Age. [\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"AnswerQuestHist\">Answering Questions<\/h3>\r\nUse the histogram to answer the following questions. You may wish to refresh the mathematical skill needed for Question 4 in the recall box before beginning. Also see the Student Resources:\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Fractions%2C+Decimals%2C+Percentages.pdf\"><em>Fractions, Decimals, Percentages<\/em><\/a> and\u00a0<em><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Ratios+and+Fractions.pdf\">Ratios and Fractions<\/a>.<\/em>\r\n<div id=\"Proportion\" class=\"textbox examples\">\r\n<h3>Recall<\/h3>\r\nFor question 4 below, recall from 1E and 2D Corequisite Activities how to write a proportion.\r\n\r\nCore Skill:\r\n[reveal-answer q=\"130155\"]Write a proportion then convert to a percent.[\/reveal-answer]\r\n[hidden-answer a=\"130155\"]\r\n\r\nEx: A class of\u00a0[latex]30[\/latex] students has\u00a0[latex]13[\/latex] student athletes enrolled.\u00a0[latex]6[\/latex] play soccer,\u00a0[latex]3[\/latex] play football, and\u00a0[latex]3[\/latex] are swimmers, and\u00a0[latex]1[\/latex] plays baseball. What proportion of the students in the class play soccer?\r\n\r\n[latex]6[\/latex] of the\u00a0[latex]30[\/latex] play soccer.\r\n<p style=\"padding-left: 30px;\">[latex]\\dfrac{6}{30} \\Rightarrow \\dfrac{1}{5}[\/latex], reduce the ratio by dividing the common factor of\u00a0[latex]6[\/latex] from the numerator and denominator.<\/p>\r\n<p style=\"padding-left: 30px;\">[latex]1\\div 5 = 0.2[\/latex] perform the division to obtain the proportion.<\/p>\r\n<p style=\"padding-left: 30px;\">[latex]0.2\\Rightarrow 20\\%[\/latex] move the decimal two places to the right and append the percent symbol to write the proportion as a percentage.<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>interactive example<\/h3>\r\nIn Questions 4 - 7, you'll use the histogram you created for the variable\u00a0<em>age<\/em> to answer questions about the data. Let's answer a few practice questions to warm up.\r\n\r\nHere is an image of the histogram you created. You can hover over the bars of the graph in the tool to get information about count and endpoints for the bins. Use the histogram in your tool to answer the following questions.\r\n\r\n<img class=\"aligncenter size-full wp-image-1170\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/16143201\/TeachingEval_Age.png\" alt=\"A histogram of the variable Age from the Teaching Evaluations dataset. \" width=\"700\" height=\"310\" \/>\r\n<ol>\r\n \t<li>About what proportion of courses are taught by a professor older than 60? Remember to hover over the bars of the graph in the tool to get the counts. The sample size is given in Descriptive Statistics.<\/li>\r\n \t<li>What does the graph suggest for the median age, and what does the median imply for the data?<\/li>\r\n \t<li>Which would be more likely: that a course is taught by a professor close to 32 years old or 62 years old?<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"643249\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"643249\"]\r\n<ol>\r\n \t<li>[latex]16.7\\%[\/latex]. You can hover over the bars in the tool to find the counts of ages over [latex]60[\/latex]. Remember the left endpoint is included in the bin. There are two bins to count, [latex]60-64[\/latex] and [latex]70-74[\/latex]. These total [latex]77[\/latex] out of the sample size of [latex]463[\/latex]. See the recall box above if you need to refresh how to change a proportion to a percent.<\/li>\r\n \t<li>To answer this question, the idea is to use the graph, not the descriptive statistics. Where does the center of data appear to lie in the graph? That is, since we are looking for a median and not mean, what age appears to split the data in half?\u00a0 It looks like about half the ages are under 50 and half over. If you refer to the descriptive statistics, you'll see that's a close approximation for the actual median.<\/li>\r\n \t<li>It appears that more data is located in the bin containing 62 than the one containing 32. It would be more likely that a professor is closer to 62.<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\nNow it's your turn to try answering questions about the data using a histogram.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\n[ohm_question hide_question_numbers=1]240863[\/ohm_question]\r\n\r\n[reveal-answer q=\"978862\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"978862\"]The number of observations in each group can be easily seen by hovering over the bar on the histogram. Recall that a proportion is a part out of a whole, often expressed as a percentage. There were\u00a0[latex]463[\/latex] courses in total.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 5<\/h3>\r\n[ohm_question hide_question_numbers=1]240864[\/ohm_question]\r\n\r\n[reveal-answer q=\"152137\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"152137\"]Where do about half the observations of the distribution appear to lie?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 6<\/h3>\r\n[ohm_question hide_question_numbers=1]240865[\/ohm_question]\r\n\r\n[reveal-answer q=\"807097\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"807097\"]The minimum and maximum values can estimated from the graph.[\/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]240866[\/ohm_question]\r\n\r\n[reveal-answer q=\"221296\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"221296\"]Which age is associated with more observations?[\/hidden-answer]\r\n\r\n<\/div>\r\nNow that you've gained some valuable practice creating and interpreting a histogram, it's time to move on to the next section and activity.\r\n<div>\r\n<div><\/div>\r\n<\/div>","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=\"#ReadInterpret\">Read and interpret a data table and data dictionary.<\/a><\/li>\n<li><a href=\"#HistFromData Set\">Create a histogram from a data set using technology.<\/a><\/li>\n<li><a href=\"#AnswerQuestHist\">Use a histogram to answer questions about a variable.<\/a><\/li>\n<\/ul>\n<p>You will also have an opportunity to refresh the following skills:<\/p>\n<ul>\n<li><a href=\"#Proportion\">Write a proportion and express it as a percentage<\/a><\/li>\n<\/ul>\n<\/div>\n<p>In the section,\u00a0<a href=\"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/chapter\/applications-of-histograms-what-to-know\/\"><em>Applications of Histograms: What to Know<\/em><\/a>,\u00a0and in the following activity, you will need to be able to use technology to visualize the distribution of quantitative variables and use the visualization to answer questions about the distribution.<\/p>\n<h2><strong>Analyzing Course Evaluations<\/strong><\/h2>\n<p>In this corequisite support activity, you will use the <em>evals<\/em> data set,<a class=\"footnote\" title=\"Professor evaluations and beauty. (n.d.). OpenIntro. Retrieved from https:\/\/www.openintro.org\/data\/index.php?data=evals\" id=\"return-footnote-259-1\" href=\"#footnote-259-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> which includes information collected from student evaluations for a sample of\u00a0[latex]463[\/latex] courses taught by\u00a0[latex]94[\/latex] professors at The University of Texas at Austin. Each row is a different course, and the columns have information about the professor and summary information from the course.<\/p>\n<p>The objective of this analysis is to explore the distribution of age of the professor for the\u00a0[latex]463[\/latex] courses. To do so, you\u2019ll use technology to make a histogram to visualize the distribution of professor ages.<\/p>\n<h3 id=\"ReadInterpret\">Data Tables<\/h3>\n<p>A data table contains raw data, collected observation by observation. The columns of the table list the variables for each observation. Each row contains data collected from one observational unit.\u00a0 See the demonstration in the interactive example below to understand how to read the table.<\/p>\n<div class=\"textbox exercises\">\n<h3>interactive example<\/h3>\n<p>A few observations of the Teaching Evaluations data table have been extracted and are shown here along with the data dictionary. The data displayed in each row was collected from a different course taught at the university.<\/p>\n<table>\n<tbody>\n<tr style=\"height: 23px;\">\n<td style=\"text-align: center; height: 23px; width: 402.5px;\" colspan=\"5\"><strong>Teaching Evaluations<\/strong><strong><br \/>\n<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\"><strong>score<\/strong><\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\"><strong>rank<\/strong><\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\"><strong>cls_profs<\/strong><\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\"><strong>cls_students<\/strong><\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\"><strong>age<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.7[\/latex]<\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenure track<\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]43[\/latex]<\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]36[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.6[\/latex]<\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">multiple<\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]20[\/latex]<\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]59[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]3.9[\/latex]<\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]195[\/latex]<\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]51[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul>\n<li><em><strong>score<\/strong>: <\/em>Average professor evaluation score<\/li>\n<li><em><strong>rank<\/strong>: <\/em>Rank of professor (teaching, tenure track, tenured)<\/li>\n<li><em><strong>cls_profs<\/strong>: <\/em>Number of professors teaching sections in course in sample (single, multiple)<\/li>\n<li><em><strong>cls_students<\/strong>: <\/em>Number of students in the class<\/li>\n<li><em><strong>age<\/strong>: <\/em>Age of professor in years<\/li>\n<\/ul>\n<ol>\n<li>What was the rank of the professor teaching the course section that had an average professor evaluation score of\u00a0[latex]4.6[\/latex]?<\/li>\n<li>What was the average professor evaluation score taught by a [latex]36[\/latex] year old tenure track professor?<\/li>\n<li>How many students were in the course section with the score of [latex]3.9[\/latex]?<\/li>\n<li>How many professors taught the course section with [latex]43[\/latex] students in the class?<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q655712\">Show Answer<\/span><\/p>\n<div id=\"q655712\" class=\"hidden-answer\" style=\"display: none\">\n<p>The middle row above shows an average score of\u00a0[latex]4.6[\/latex]. All the answers can be located in that row.<\/p>\n<ol>\n<li>Tenured<\/li>\n<li>[latex]4.7[\/latex]<\/li>\n<li>[latex]195[\/latex]<\/li>\n<li>Single<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p>The first\u00a0[latex]10[\/latex] observations of the selected variables within the \u201cTeaching Evaluations\u201d data set are displayed in the following table. Use it to answer Questions 1 and 2 below.<\/p>\n<div style=\"margin: auto;\">\n<table style=\"height: 177px;\">\n<tbody>\n<tr style=\"height: 23px;\">\n<td style=\"text-align: center; height: 23px; width: 402.5px;\" colspan=\"5\"><strong>Teaching Evaluations<\/strong><strong><br \/>\n<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\"><strong>score<\/strong><\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\"><strong>rank<\/strong><\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\"><strong>cls_profs<\/strong><\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\"><strong>cls_students<\/strong><\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\"><strong>age<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.7[\/latex]<\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenure track<\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]43[\/latex]<\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]36[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.1[\/latex]<\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenure track<\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]125[\/latex]<\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]36[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]3.9[\/latex]<\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenure track<\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]125[\/latex]<\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]36[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.8[\/latex]<\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenure track<\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]123[\/latex]<\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]36[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.6[\/latex]<\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">multiple<\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]20[\/latex]<\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]59[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.3[\/latex]<\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">multiple<\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]40[\/latex]<\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]59[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]2.8[\/latex]<\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">multiple<\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]44[\/latex]<\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]59[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.1[\/latex]<\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]55[\/latex]<\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]51[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]3.4[\/latex]<\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]195[\/latex]<\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]51[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 47.7188px; text-align: center;\">[latex]4.5[\/latex]<\/td>\n<td style=\"height: 14px; width: 90.8906px; text-align: center;\">tenured<\/td>\n<td style=\"height: 14px; width: 77.1094px; text-align: center;\">single<\/td>\n<td style=\"height: 14px; width: 104.641px; text-align: center;\">[latex]46[\/latex]<\/td>\n<td style=\"height: 14px; width: 32.1406px; text-align: center;\">[latex]40[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>The following is a <strong>data dictionary<\/strong> of the selected variables:<\/p>\n<ul>\n<li><em><strong>score<\/strong>: <\/em>Average professor evaluation score<\/li>\n<li><em><strong>rank<\/strong>: <\/em>Rank of professor (teaching, tenure track, tenured)<\/li>\n<li><em><strong>cls_profs<\/strong>: <\/em>Number of professors teaching sections in course in sample (single, multiple)<\/li>\n<li><em><strong>cls_students<\/strong>: <\/em>Number of students in the class<\/li>\n<li><em><strong>age<\/strong>: <\/em>Age of professor in years<\/li>\n<\/ul>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241030\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241030&theme=oea&iframe_resize_id=ohm241030\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q852290\">Hint<\/span><\/p>\n<div id=\"q852290\" class=\"hidden-answer\" style=\"display: none\">From what person, item, or entity have the observations been taken?\u00a0 <\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240861\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240861&theme=oea&iframe_resize_id=ohm240861\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q327228\">Hint<\/span><\/p>\n<div id=\"q327228\" class=\"hidden-answer\" style=\"display: none\">Remember that quantitative observations are in numerical form and can be manipulated arithmetically.<\/div>\n<\/div>\n<\/div>\n<div>Now let&#8217;s examine the distribution of the variable <em>age <\/em>by creating a histogram and using it to answer some questions about the variable.<\/div>\n<h3 id=\"HistFromData Set\">Histograms<\/h3>\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\/<\/a> and select the data set <strong>Teaching Evaluations &#8211; Age&#8221;\u00a0<\/strong>to\u00a0make a histogram of the distribution of professor ages. Select\u00a0<strong>Binwidth<\/strong> to 5.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240862\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240862&theme=oea&iframe_resize_id=ohm240862\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q805230\">Hint<\/span><\/p>\n<div id=\"q805230\" class=\"hidden-answer\" style=\"display: none\">Make sure that you have selected the correct data set, Teaching Evaluations &#8211; Age. <\/div>\n<\/div>\n<\/div>\n<h3 id=\"AnswerQuestHist\">Answering Questions<\/h3>\n<p>Use the histogram to answer the following questions. You may wish to refresh the mathematical skill needed for Question 4 in the recall box before beginning. Also see the Student Resources:\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Fractions%2C+Decimals%2C+Percentages.pdf\"><em>Fractions, Decimals, Percentages<\/em><\/a> and\u00a0<em><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Ratios+and+Fractions.pdf\">Ratios and Fractions<\/a>.<\/em><\/p>\n<div id=\"Proportion\" class=\"textbox examples\">\n<h3>Recall<\/h3>\n<p>For question 4 below, recall from 1E and 2D Corequisite Activities how to write a proportion.<\/p>\n<p>Core Skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q130155\">Write a proportion then convert to a percent.<\/span><\/p>\n<div id=\"q130155\" class=\"hidden-answer\" style=\"display: none\">\n<p>Ex: A class of\u00a0[latex]30[\/latex] students has\u00a0[latex]13[\/latex] student athletes enrolled.\u00a0[latex]6[\/latex] play soccer,\u00a0[latex]3[\/latex] play football, and\u00a0[latex]3[\/latex] are swimmers, and\u00a0[latex]1[\/latex] plays baseball. What proportion of the students in the class play soccer?<\/p>\n<p>[latex]6[\/latex] of the\u00a0[latex]30[\/latex] play soccer.<\/p>\n<p style=\"padding-left: 30px;\">[latex]\\dfrac{6}{30} \\Rightarrow \\dfrac{1}{5}[\/latex], reduce the ratio by dividing the common factor of\u00a0[latex]6[\/latex] from the numerator and denominator.<\/p>\n<p style=\"padding-left: 30px;\">[latex]1\\div 5 = 0.2[\/latex] perform the division to obtain the proportion.<\/p>\n<p style=\"padding-left: 30px;\">[latex]0.2\\Rightarrow 20\\%[\/latex] move the decimal two places to the right and append the percent symbol to write the proportion as a percentage.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>interactive example<\/h3>\n<p>In Questions 4 &#8211; 7, you&#8217;ll use the histogram you created for the variable\u00a0<em>age<\/em> to answer questions about the data. Let&#8217;s answer a few practice questions to warm up.<\/p>\n<p>Here is an image of the histogram you created. You can hover over the bars of the graph in the tool to get information about count and endpoints for the bins. Use the histogram in your tool to answer the following questions.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1170\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/16143201\/TeachingEval_Age.png\" alt=\"A histogram of the variable Age from the Teaching Evaluations dataset.\" width=\"700\" height=\"310\" \/><\/p>\n<ol>\n<li>About what proportion of courses are taught by a professor older than 60? Remember to hover over the bars of the graph in the tool to get the counts. The sample size is given in Descriptive Statistics.<\/li>\n<li>What does the graph suggest for the median age, and what does the median imply for the data?<\/li>\n<li>Which would be more likely: that a course is taught by a professor close to 32 years old or 62 years old?<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q643249\">Show Answer<\/span><\/p>\n<div id=\"q643249\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]16.7\\%[\/latex]. You can hover over the bars in the tool to find the counts of ages over [latex]60[\/latex]. Remember the left endpoint is included in the bin. There are two bins to count, [latex]60-64[\/latex] and [latex]70-74[\/latex]. These total [latex]77[\/latex] out of the sample size of [latex]463[\/latex]. See the recall box above if you need to refresh how to change a proportion to a percent.<\/li>\n<li>To answer this question, the idea is to use the graph, not the descriptive statistics. Where does the center of data appear to lie in the graph? That is, since we are looking for a median and not mean, what age appears to split the data in half?\u00a0 It looks like about half the ages are under 50 and half over. If you refer to the descriptive statistics, you&#8217;ll see that&#8217;s a close approximation for the actual median.<\/li>\n<li>It appears that more data is located in the bin containing 62 than the one containing 32. It would be more likely that a professor is closer to 62.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<p>Now it&#8217;s your turn to try answering questions about the data using a histogram.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240863\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240863&theme=oea&iframe_resize_id=ohm240863\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q978862\">Hint<\/span><\/p>\n<div id=\"q978862\" class=\"hidden-answer\" style=\"display: none\">The number of observations in each group can be easily seen by hovering over the bar on the histogram. Recall that a proportion is a part out of a whole, often expressed as a percentage. There were\u00a0[latex]463[\/latex] courses in total.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 5<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240864\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240864&theme=oea&iframe_resize_id=ohm240864\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q152137\">Hint<\/span><\/p>\n<div id=\"q152137\" class=\"hidden-answer\" style=\"display: none\">Where do about half the observations of the distribution appear to lie?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 6<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240865\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240865&theme=oea&iframe_resize_id=ohm240865\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q807097\">Hint<\/span><\/p>\n<div id=\"q807097\" class=\"hidden-answer\" style=\"display: none\">The minimum and maximum values can estimated from the graph.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 7<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240866\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240866&theme=oea&iframe_resize_id=ohm240866\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q221296\">Hint<\/span><\/p>\n<div id=\"q221296\" class=\"hidden-answer\" style=\"display: none\">Which age is associated with more observations?<\/div>\n<\/div>\n<\/div>\n<p>Now that you&#8217;ve gained some valuable practice creating and interpreting a histogram, it&#8217;s time to move on to the next section and activity.<\/p>\n<div>\n<div><\/div>\n<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-259-1\"> Professor evaluations and beauty. (n.d.). OpenIntro. Retrieved from https:\/\/www.openintro.org\/data\/index.php?data=evals <a href=\"#return-footnote-259-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":175116,"menu_order":18,"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-259","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/259","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":18,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/259\/revisions"}],"predecessor-version":[{"id":1198,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/259\/revisions\/1198"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/259\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/media?parent=259"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapter-type?post=259"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/contributor?post=259"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/license?post=259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}