{"id":154,"date":"2021-10-10T18:22:26","date_gmt":"2021-10-10T18:22:26","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=154"},"modified":"2022-02-18T17:26:32","modified_gmt":"2022-02-18T17:26:32","slug":"3c-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/3c-coreq\/","title":{"raw":"Corequisite Support Activity for Visualizing Quantitative Data: 3C - 7","rendered":"Corequisite Support Activity for Visualizing Quantitative Data: 3C &#8211; 7"},"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=\"#FreqData\">Create a frequency table from a dataset by hand.<\/a><\/li>\r\n \t<li><a href=\"#dotplottable\">Create a dotplot from a frequency table using technology.<\/a><\/li>\r\n \t<li><a href=\"#histogramtable\">Create a histogram from a frequency table using technology.<\/a><\/li>\r\n \t<li><a href=\"#barhist\">Understand the difference between a bar graph and a histogram.\u00a0<\/a><\/li>\r\n \t<li><a href=\"#histogramtech\">Create a histogram from a dataset using technology.<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\n<a title=\"Andrian Valeanu freephotocc, CC0, via Wikimedia Commons\" href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Andrian_Valeanu_2016-04-11_(Unsplash).jpg\"><img class=\"aligncenter\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/a\/ae\/Andrian_Valeanu_2016-04-11_%28Unsplash%29.jpg\/512px-Andrian_Valeanu_2016-04-11_%28Unsplash%29.jpg\" alt=\"Used paint brushes and opened yellow, blue, red, and black paint tubes on a wooden floor with paint splattered on it.\" width=\"512\" height=\"342\" \/><\/a>\r\nIn the next section of the course material and in the following activity, you will need to be able to use technology to make plots to visualize the distribution of quantitative variables and then use the plots to identify features of the distribution.\r\n\r\nLet's practice creating, reading, and interpreting quantitative distributions using a dataset of information about a beloved painter and art instructor whose work aired on public television in the late 20th century.\r\n<h2><strong>Analyzing Bob Ross Paintings<\/strong><\/h2>\r\nBob Ross was a famous painter and star of the TV show <em>The Joy of Painting<\/em>, during which viewers followed along as he painted. He (and occasionally a guest host) created a single painting in each of the 403 episodes of his show. He was particularly known for painting trees and clouds, which he famously called \u201chappy little trees\u201d and \u201chappy little clouds,\u201d respectively.\r\n\r\nThe objective of this analysis is to explore how many paintings included clouds in a given season. To answer this question, you\u2019ll use technology to make plots to visualize the number of paintings that included clouds in a given season. You may use the <em>Describing and Exploring Quantitative Variables <\/em>tool or comparable technology for this assignment.\r\n\r\nThe dataset \u201cClouds\u201d [footnote] Hickey, W. (2014, April 14). A statistical analysis of the work of Bob Ross. FiveThirtyEight. https:\/\/fivethirtyeight.com\/features\/a-statistical-analysis-of-the-work-of-bob-ross\/\r\n[\/footnote] contains the following variables for each season of <em>The Joy of Painting<\/em>:\r\n<ul>\r\n \t<li><em style=\"font-size: 1em;\">season<\/em><span style=\"font-size: 1em;\">: Season number (1\u201313)<\/span><\/li>\r\n \t<li><em>num_clouds<\/em>: Number of paintings that included clouds in the season<\/li>\r\n<\/ul>\r\nThe following data table includes the number of paintings that included clouds, represented by the variable <em>num_clouds<\/em>, for each of the first 13 seasons.\r\n<div align=\"center\">\r\n<table style=\"width: 326px;\">\r\n<tbody>\r\n<tr>\r\n<td style=\"text-align: center; width: 402.5px;\" colspan=\"2\"><strong>Clouds in Bob Ross' Paintings<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 193.812px;\"><em><strong>season<\/strong><\/em><\/td>\r\n<td style=\"text-align: center; width: 196.188px;\"><em><strong>num_clouds<\/strong><\/em><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 193.812px;\"><strong>1<\/strong><\/td>\r\n<td style=\"text-align: center; width: 196.188px;\">4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 193.812px;\"><strong>2<\/strong><\/td>\r\n<td style=\"text-align: center; width: 196.188px;\">7<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 193.812px;\"><strong>3<\/strong><\/td>\r\n<td style=\"text-align: center; width: 196.188px;\">5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 193.812px;\"><strong>4<\/strong><\/td>\r\n<td style=\"text-align: center; width: 196.188px;\">5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 193.812px;\"><strong>5<\/strong><\/td>\r\n<td style=\"text-align: center; width: 196.188px;\">6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 193.812px;\"><strong>6<\/strong><\/td>\r\n<td style=\"text-align: center; width: 196.188px;\">9<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 193.812px;\"><strong>7<\/strong><\/td>\r\n<td style=\"text-align: center; width: 196.188px;\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 193.812px;\"><strong>8<\/strong><\/td>\r\n<td style=\"text-align: center; width: 196.188px;\">7<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 193.812px;\"><strong>9<\/strong><\/td>\r\n<td style=\"text-align: center; width: 196.188px;\">9<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 193.812px;\"><strong>10<\/strong><\/td>\r\n<td style=\"text-align: center; width: 196.188px;\">9<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 193.812px;\"><strong>11<\/strong><\/td>\r\n<td style=\"text-align: center; width: 196.188px;\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 193.812px;\"><strong>12<\/strong><\/td>\r\n<td style=\"text-align: center; width: 196.188px;\">8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 193.812px;\"><strong>13<\/strong><\/td>\r\n<td style=\"text-align: center; width: 196.188px;\">8<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div align=\"center\">\r\n\r\nWe will use this data to write a frequency table. Then we'll use the frequency table to create a dotplot and a histogram.\r\n<h3 id=\"FreqData\">Create a frequency table from a dataset<\/h3>\r\nBelow, you'll see a partially created frequency table for the dataset. Your goal is to complete the frequency table using information from the above data table.\r\n\r\nCharacteristics of the frequency table:\r\n<ul>\r\n \t<li style=\"text-align: left;\">The column on the left should contain, in numerical order, each number that appears in the dataset\u00a0<em>num_clouds<\/em> column. You'll need to complete this column with the missing numbers. Each number is listed only once.<\/li>\r\n \t<li style=\"text-align: left;\">The column on the right in the frequency table should contain the number of seasons in which that many paintings with clouds were created. We can see that there was only one season in which 4 paintings with clouds were created, so we say the frequency of 4 clouds in a painting is 1.<\/li>\r\n<\/ul>\r\n<div align=\"center\">\r\n<table class=\"lines\" style=\"width: 286px; height: 154px;\" border=\"1\">\r\n<tbody>\r\n<tr style=\"height: 28px;\">\r\n<td style=\"width: 402.5px; text-align: center; height: 14px;\" colspan=\"2\"><strong>Frequency Table<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 28px;\">\r\n<td style=\"width: 192.469px; text-align: center; height: 28px;\"><strong>Number of Paintings with Clouds in a Season<\/strong><\/td>\r\n<td style=\"width: 197.531px; text-align: center; height: 28px;\"><strong>Frequency<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 192.469px; text-align: center; height: 14px;\"><strong>4<\/strong><\/td>\r\n<td style=\"width: 197.531px; height: 14px; text-align: center;\">1<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 192.469px; text-align: center; height: 14px;\"><strong>5<\/strong><\/td>\r\n<td style=\"width: 197.531px; height: 14px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 192.469px; text-align: center; height: 14px;\"><strong>6<\/strong><\/td>\r\n<td style=\"width: 197.531px; height: 14px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 192.469px; text-align: center; height: 14px;\"><strong>7<\/strong><\/td>\r\n<td style=\"width: 197.531px; height: 14px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 192.469px; text-align: center; height: 14px;\"><strong>8<\/strong><\/td>\r\n<td style=\"width: 197.531px; height: 14px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"width: 192.469px; height: 22px;\"><\/td>\r\n<td style=\"width: 197.531px; height: 22px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 20px;\">\r\n<td style=\"width: 192.469px; height: 20px;\"><\/td>\r\n<td style=\"width: 197.531px; height: 20px;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nUse the interactive example below to get started then finish the table on your own in Question 1.\r\n<div class=\"textbox exercises\">\r\n<h3>Interactive Example<\/h3>\r\nLooking back on the data table at the start of this page, we see that there were no seasons in which fewer than 4 paintings with clouds were created. And we can see that only one season included exactly that many.\r\n\r\n<em>The frequency of 4 paintings with clouds is 1. <\/em>\r\n<ol>\r\n \t<li>How many seasons included 5 paintings of clouds? That is, what is the frequency of 5 paintings in the dataset?\r\n[reveal-answer q=\"692359\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"692359\"]The data table shows 5 paintings with clouds were created in both season 4 and season 5. Therefore,\u00a0the\u00a0<em>frequency of 5 paintings with clouds in a season is 2<\/em>.\u00a0[\/hidden-answer]<\/li>\r\n \t<li>\u00a0What is the\u00a0frequency of 6 paintings with clouds in a season?[reveal-answer q=\"782444\"]Show Answer[\/reveal-answer][hidden-answer a=\"782444\"]The frequency is 1 since 6 paintings with clouds were created in only 1 season.[\/hidden-answer]<\/li>\r\n \t<li>What is the frequency of 7 paintings with clouds in a season?[reveal-answer q=\"547624\"]Show Answer[\/reveal-answer][hidden-answer a=\"547624\"]The frequency is 2 since 7 paintings with clouds were created in 2 seasons.[\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/div>\r\nUse the answers from the interactive example above to begin filling in the frequency table in Question 1, then complete the missing information on your own. Don't forget to look for seasons in which more than 8 paintings with clouds were created.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\nCreate a frequency table that summarizes the number of paintings that include clouds by filling in the missing values.\r\n<div align=\"center\">\r\n<table class=\"lines\" style=\"width: 363px;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 392.656px; text-align: center;\" colspan=\"2\"><strong>Frequency Table<\/strong><strong>\r\n<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 189.078px; text-align: center;\"><strong>Number of Paintings with Clouds in a Season<\/strong><\/td>\r\n<td style=\"width: 192.234px; text-align: center;\"><strong>Frequency<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 189.078px; text-align: center;\"><strong>4<\/strong><\/td>\r\n<td style=\"width: 192.234px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 189.078px; text-align: center;\"><strong>5<\/strong><\/td>\r\n<td style=\"width: 192.234px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 189.078px; text-align: center;\"><strong>6<\/strong><\/td>\r\n<td style=\"width: 192.234px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 189.078px; text-align: center;\"><strong>7<\/strong><\/td>\r\n<td style=\"width: 192.234px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 189.078px; text-align: center;\"><strong>8<\/strong><\/td>\r\n<td style=\"width: 192.234px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 189.078px; text-align: center;\"><\/td>\r\n<td style=\"width: 192.234px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 189.078px; text-align: center;\"><\/td>\r\n<td style=\"width: 192.234px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[reveal-answer q=\"474589\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"474589\"]Were there seasons that included more than 8 paintings with clouds and what were the associated frequencies?[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<h3 id=\"dotplottable\">Create a dotplot from a frequency table.<\/h3>\r\nIn a previous activity you learned about <strong>dotplots<\/strong>, graphical displays for quantitative data where each dot represents an observation. Dotplots are useful for visualizing distributions when the dataset is small.\r\n\r\nCreate a dotplot for the number of paintings with clouds using the data analysis tool. Follow these steps to create a dotplot with raw observations or a frequency table:\r\n<div class=\"textbox\">\r\n\r\nGo to the\u00a0<em>Describing and Exploring Quantitative Variables <\/em>tool at\u00a0\u00a0<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 dropdown under <strong>Enter Data<\/strong> and select <strong>Your Own<\/strong>.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 3) Locate the options under <strong>Do you have<\/strong>, and select <strong>Individual Observations<\/strong>.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 4): For <strong>Name of Variable<\/strong>, enter \u201cNumber of Paintings with Clouds.\u201d<\/p>\r\n<p style=\"padding-left: 30px;\">Step 5) Locate the box under the variable name and enter the observations\u00a0<em><strong>num_clouds<\/strong>\u00a0<\/em>from the data set.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 6) For <strong>Choose Type of Plot<\/strong> Select <strong>Dotplot<\/strong>. Unselect any other choices that were already selected.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 7) Under <strong>Dotplot Options<\/strong>,\u00a0<strong>Select<\/strong>\u00a0<strong>Dotsize for Dotplot:<\/strong> 0.5\u00a0and <strong>Select Binwidth for Dotplot<\/strong>:\u00a00.5.<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\n[ohm_question]240648[\/ohm_question]\r\n\r\n<\/div>\r\n<h3 id=\"histogramtable\">Create a histogram from a frequency table<\/h3>\r\nTypically, a histogram is more useful for large datasets. If there are a large number of observations, a histogram is easier to read, since it groups observations into bins (see this defined below) rather than having a single dot for each observation.\r\n\r\nUse the same data analysis tool to make a histogram to visualize the distribution of the number of paintings that included clouds in a season.\r\n\r\nWith the same tool still open, (or after following Steps 1 - 5 above),\r\n<div class=\"textbox\">Step 7) For <strong>Choose Type of Plot<\/strong> select <strong>Histogram<\/strong> option. <strong>Select Binwidth for Histogram<\/strong>: 1.<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 3<\/h3>\r\n[ohm_question]240603[\/ohm_question]\r\n\r\n<\/div>\r\n<h3 id=\"barhist\">Understand the difference between a bar graph and a histogram<\/h3>\r\nA histogram looks somewhat like a bar graph. But, while a\u00a0bar graph displays categorical data, showing counts of observations within categories, a histogram displays quantitative data by showing frequencies of a quantitative variable. You'll be able to tell a bar graph from a histogram by observing whether the horizontal axis appears to be a list of categories (e.g. eye color, zip code, etc...) or a number line.\r\n\r\n&nbsp;\r\n\r\n<img class=\"alignnone size-full wp-image-2831\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/05173345\/Bar_Hist_Compare.jpg\" alt=\"A bar chart displaying &quot;Eye Color&quot; adjacent to a histogram displaying &quot;Sleep Hours.&quot;The bars of the bar chart are separated and labeled Blue, Hazel, Brown, Grey, and Green. The bars of the histogram are adjacent and cover equals intervals of width 0.5 over a horizontal number line ranging from 4 to 11.\" width=\"872\" height=\"238\" \/>\r\n\r\nThe bars of a histogram are each of the same width and meet smoothly together over the horizontal axis.\u00a0In a histogram, we call the bars\u00a0<em>bins.\u00a0<\/em>\r\n<ul>\r\n \t<li style=\"text-align: left;\"><span style=\"font-size: 1em;\">A <\/span><strong style=\"font-size: 1em;\">bin <\/strong><span style=\"font-size: 1em;\">is a range of values that the quantitative variable can take.<\/span><\/li>\r\n \t<li style=\"text-align: left;\">A bin can be defined by its <strong>end points<\/strong>, the smallest and largest values of the quantitative variable represented in the bin. For the first bin [latex]\\left[4 , 5\\right)[\/latex], the end points are 4 and 5. The notation [latex]\\left[4 , 5\\right)[\/latex] means this bin includes observations of the numbers of paintings with clouds that include 4 but not 5. We knew from the frequency table that the frequency of 4 paintings in a season is 1, and there is a single dot above the 4 on the horizontal axis to indicate this.<\/li>\r\n \t<li style=\"text-align: left;\">The <strong>width<\/strong> of the bin, called <strong>binwidth<\/strong>,\u00a0is calculated by taking the difference of the values of the end points. For the first bin, the width is [latex]5 - 4 = 1[\/latex]. The width of the bins should remain the same for each graph. You can verify visually that each bin is exactly 1 wide.<\/li>\r\n<\/ul>\r\nUse the histogram you created to answer the following questions.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\nWhich value of the variable (number of paintings with clouds) occurs most frequently in the dataset?\r\n\r\n[reveal-answer q=\"440732\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"440732\"]Hover over the bar in the histogram to reveal the frequency contain in each.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 5<\/h3>\r\nHow many seasons have 10 paintings with clouds?\r\n\r\n[reveal-answer q=\"794824\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"794824\"]Remember that the left end-point of each bin is included, but not the right end-point.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 6<\/h3>\r\nHow many seasons have at least 8 paintings with clouds?\r\n\r\n[reveal-answer q=\"167233\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"167233\"]Include <em>all<\/em> the seasons with at least 8.Hover over the bars to reveal the number in each bin. Remember that the left end-point of each bin is included, but not the right.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 7<\/h3>\r\nHow many seasons have 5 or fewer paintings with clouds?\r\n\r\n[reveal-answer q=\"753731\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"753731\"]Hover over the bars to reveal the number in each bin. Remember that the left end-point of each bin is included, but not the right.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 8<\/h3>\r\nThere are 13 seasons with 13 new paintings in each season. In how many seasons do at least half the paintings include clouds?\r\n\r\n[reveal-answer q=\"660433\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"660433\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 9<\/h3>\r\nMake a new histogram of the number of paintings with clouds using a bin width of 2 (bin width = 2) and then compare the new histogram to the one from Question 1. How are they similar? How are they different?\r\n\r\n[reveal-answer q=\"58603\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"58603\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"histogramtech\">Create a histogram from a dataset using technology.<\/h3>\r\nHopefully, you are feeling comfortable using histograms to answer questions about the dataset. Try creating a histogram from a new dataset, then use it to answer questions. This time, you won't need to enter the data by hand. We'll use an existing dataset in the tool.\r\n\r\nIf you don't still have the <em>Describing and Exploring Quantitative Variables <\/em>tool open, open it at\u00a0\u00a0 \u00a0<a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\" target=\"_blank\" rel=\"noopener\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>\u00a0and follow these steps:\r\n<div class=\"textbox\">\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 dropdown under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 3) Choose the <strong>Dataset<\/strong> \"Hours Watching TV (2018) to create a histogram.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 4) Under\u00a0<strong>Type of Plot<\/strong>, make sure the Histogram box is checked. You can uncheck any other boxes that are selected.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 5)\u00a0<strong>Select Binwidth<\/strong> = 2.<\/p>\r\n\r\n<\/div>\r\nThe dataset \u201cHours Watching TV (2018)\u201d in the <em>Describing and Exploring Quantitative Variables <\/em>tool has the weekly number of hours spent watching TV for 1,555 individuals. Create a histogram with binwidth = 2 to display the distribution of the variable. Use it to answer the questions below.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 10<\/h3>\r\n[ohm_question]240605[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 11<\/h3>\r\nLook at the histogram with bin widths of 2, 5, and 10. Which bin width is most useful for visualizing the distribution of weekly number of TV hours? Explain.\r\n\r\n[reveal-answer q=\"648646\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"648646\"]What do <em>you<\/em> think? Which helps you understand the characteristics of the distribution better?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 12<\/h3>\r\nUse the histogram to write 2 or 3 observations about the distribution of weekly number of hours watching TV.\r\n\r\n[reveal-answer q=\"367348\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"367348\"]Use the style of Questions 4 - 8 as a guide.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div style=\"text-align: left;\">You've had quite a bit of practice with the tool to create, read, and interpret histograms you created from a dataset and using technology. You'll see these skills again in the upcoming section and activity.<\/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=\"#FreqData\">Create a frequency table from a dataset by hand.<\/a><\/li>\n<li><a href=\"#dotplottable\">Create a dotplot from a frequency table using technology.<\/a><\/li>\n<li><a href=\"#histogramtable\">Create a histogram from a frequency table using technology.<\/a><\/li>\n<li><a href=\"#barhist\">Understand the difference between a bar graph and a histogram.\u00a0<\/a><\/li>\n<li><a href=\"#histogramtech\">Create a histogram from a dataset using technology.<\/a><\/li>\n<\/ul>\n<\/div>\n<p><a title=\"Andrian Valeanu freephotocc, CC0, via Wikimedia Commons\" href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Andrian_Valeanu_2016-04-11_(Unsplash).jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/a\/ae\/Andrian_Valeanu_2016-04-11_%28Unsplash%29.jpg\/512px-Andrian_Valeanu_2016-04-11_%28Unsplash%29.jpg\" alt=\"Used paint brushes and opened yellow, blue, red, and black paint tubes on a wooden floor with paint splattered on it.\" width=\"512\" height=\"342\" \/><\/a><br \/>\nIn the next section of the course material and in the following activity, you will need to be able to use technology to make plots to visualize the distribution of quantitative variables and then use the plots to identify features of the distribution.<\/p>\n<p>Let&#8217;s practice creating, reading, and interpreting quantitative distributions using a dataset of information about a beloved painter and art instructor whose work aired on public television in the late 20th century.<\/p>\n<h2><strong>Analyzing Bob Ross Paintings<\/strong><\/h2>\n<p>Bob Ross was a famous painter and star of the TV show <em>The Joy of Painting<\/em>, during which viewers followed along as he painted. He (and occasionally a guest host) created a single painting in each of the 403 episodes of his show. He was particularly known for painting trees and clouds, which he famously called \u201chappy little trees\u201d and \u201chappy little clouds,\u201d respectively.<\/p>\n<p>The objective of this analysis is to explore how many paintings included clouds in a given season. To answer this question, you\u2019ll use technology to make plots to visualize the number of paintings that included clouds in a given season. You may use the <em>Describing and Exploring Quantitative Variables <\/em>tool or comparable technology for this assignment.<\/p>\n<p>The dataset \u201cClouds\u201d <a class=\"footnote\" title=\"Hickey, W. (2014, April 14). A statistical analysis of the work of Bob Ross. FiveThirtyEight. https:\/\/fivethirtyeight.com\/features\/a-statistical-analysis-of-the-work-of-bob-ross\/\" id=\"return-footnote-154-1\" href=\"#footnote-154-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> contains the following variables for each season of <em>The Joy of Painting<\/em>:<\/p>\n<ul>\n<li><em style=\"font-size: 1em;\">season<\/em><span style=\"font-size: 1em;\">: Season number (1\u201313)<\/span><\/li>\n<li><em>num_clouds<\/em>: Number of paintings that included clouds in the season<\/li>\n<\/ul>\n<p>The following data table includes the number of paintings that included clouds, represented by the variable <em>num_clouds<\/em>, for each of the first 13 seasons.<\/p>\n<div style=\"margin: auto;\">\n<table style=\"width: 326px;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; width: 402.5px;\" colspan=\"2\"><strong>Clouds in Bob Ross&#8217; Paintings<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 193.812px;\"><em><strong>season<\/strong><\/em><\/td>\n<td style=\"text-align: center; width: 196.188px;\"><em><strong>num_clouds<\/strong><\/em><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 193.812px;\"><strong>1<\/strong><\/td>\n<td style=\"text-align: center; width: 196.188px;\">4<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 193.812px;\"><strong>2<\/strong><\/td>\n<td style=\"text-align: center; width: 196.188px;\">7<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 193.812px;\"><strong>3<\/strong><\/td>\n<td style=\"text-align: center; width: 196.188px;\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 193.812px;\"><strong>4<\/strong><\/td>\n<td style=\"text-align: center; width: 196.188px;\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 193.812px;\"><strong>5<\/strong><\/td>\n<td style=\"text-align: center; width: 196.188px;\">6<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 193.812px;\"><strong>6<\/strong><\/td>\n<td style=\"text-align: center; width: 196.188px;\">9<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 193.812px;\"><strong>7<\/strong><\/td>\n<td style=\"text-align: center; width: 196.188px;\">10<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 193.812px;\"><strong>8<\/strong><\/td>\n<td style=\"text-align: center; width: 196.188px;\">7<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 193.812px;\"><strong>9<\/strong><\/td>\n<td style=\"text-align: center; width: 196.188px;\">9<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 193.812px;\"><strong>10<\/strong><\/td>\n<td style=\"text-align: center; width: 196.188px;\">9<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 193.812px;\"><strong>11<\/strong><\/td>\n<td style=\"text-align: center; width: 196.188px;\">10<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 193.812px;\"><strong>12<\/strong><\/td>\n<td style=\"text-align: center; width: 196.188px;\">8<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 193.812px;\"><strong>13<\/strong><\/td>\n<td style=\"text-align: center; width: 196.188px;\">8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div style=\"margin: auto;\">\n<p>We will use this data to write a frequency table. Then we&#8217;ll use the frequency table to create a dotplot and a histogram.<\/p>\n<h3 id=\"FreqData\">Create a frequency table from a dataset<\/h3>\n<p>Below, you&#8217;ll see a partially created frequency table for the dataset. Your goal is to complete the frequency table using information from the above data table.<\/p>\n<p>Characteristics of the frequency table:<\/p>\n<ul>\n<li style=\"text-align: left;\">The column on the left should contain, in numerical order, each number that appears in the dataset\u00a0<em>num_clouds<\/em> column. You&#8217;ll need to complete this column with the missing numbers. Each number is listed only once.<\/li>\n<li style=\"text-align: left;\">The column on the right in the frequency table should contain the number of seasons in which that many paintings with clouds were created. We can see that there was only one season in which 4 paintings with clouds were created, so we say the frequency of 4 clouds in a painting is 1.<\/li>\n<\/ul>\n<div style=\"margin: auto;\">\n<table class=\"lines\" style=\"width: 286px; height: 154px;\">\n<tbody>\n<tr style=\"height: 28px;\">\n<td style=\"width: 402.5px; text-align: center; height: 14px;\" colspan=\"2\"><strong>Frequency Table<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 192.469px; text-align: center; height: 28px;\"><strong>Number of Paintings with Clouds in a Season<\/strong><\/td>\n<td style=\"width: 197.531px; text-align: center; height: 28px;\"><strong>Frequency<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 192.469px; text-align: center; height: 14px;\"><strong>4<\/strong><\/td>\n<td style=\"width: 197.531px; height: 14px; text-align: center;\">1<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 192.469px; text-align: center; height: 14px;\"><strong>5<\/strong><\/td>\n<td style=\"width: 197.531px; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 192.469px; text-align: center; height: 14px;\"><strong>6<\/strong><\/td>\n<td style=\"width: 197.531px; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 192.469px; text-align: center; height: 14px;\"><strong>7<\/strong><\/td>\n<td style=\"width: 197.531px; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 192.469px; text-align: center; height: 14px;\"><strong>8<\/strong><\/td>\n<td style=\"width: 197.531px; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"width: 192.469px; height: 22px;\"><\/td>\n<td style=\"width: 197.531px; height: 22px;\"><\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 192.469px; height: 20px;\"><\/td>\n<td style=\"width: 197.531px; height: 20px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Use the interactive example below to get started then finish the table on your own in Question 1.<\/p>\n<div class=\"textbox exercises\">\n<h3>Interactive Example<\/h3>\n<p>Looking back on the data table at the start of this page, we see that there were no seasons in which fewer than 4 paintings with clouds were created. And we can see that only one season included exactly that many.<\/p>\n<p><em>The frequency of 4 paintings with clouds is 1. <\/em><\/p>\n<ol>\n<li>How many seasons included 5 paintings of clouds? That is, what is the frequency of 5 paintings in the dataset?\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q692359\">Show Answer<\/span><\/p>\n<div id=\"q692359\" class=\"hidden-answer\" style=\"display: none\">The data table shows 5 paintings with clouds were created in both season 4 and season 5. Therefore,\u00a0the\u00a0<em>frequency of 5 paintings with clouds in a season is 2<\/em>.\u00a0<\/div>\n<\/div>\n<\/li>\n<li>\u00a0What is the\u00a0frequency of 6 paintings with clouds in a season?\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q782444\">Show Answer<\/span><\/p>\n<div id=\"q782444\" class=\"hidden-answer\" style=\"display: none\">The frequency is 1 since 6 paintings with clouds were created in only 1 season.<\/div>\n<\/div>\n<\/li>\n<li>What is the frequency of 7 paintings with clouds in a season?\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q547624\">Show Answer<\/span><\/p>\n<div id=\"q547624\" class=\"hidden-answer\" style=\"display: none\">The frequency is 2 since 7 paintings with clouds were created in 2 seasons.<\/div>\n<\/div>\n<\/li>\n<\/ol>\n<\/div>\n<p>Use the answers from the interactive example above to begin filling in the frequency table in Question 1, then complete the missing information on your own. Don&#8217;t forget to look for seasons in which more than 8 paintings with clouds were created.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p>Create a frequency table that summarizes the number of paintings that include clouds by filling in the missing values.<\/p>\n<div style=\"margin: auto;\">\n<table class=\"lines\" style=\"width: 363px;\">\n<tbody>\n<tr>\n<td style=\"width: 392.656px; text-align: center;\" colspan=\"2\"><strong>Frequency Table<\/strong><strong><br \/>\n<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 189.078px; text-align: center;\"><strong>Number of Paintings with Clouds in a Season<\/strong><\/td>\n<td style=\"width: 192.234px; text-align: center;\"><strong>Frequency<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 189.078px; text-align: center;\"><strong>4<\/strong><\/td>\n<td style=\"width: 192.234px; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 189.078px; text-align: center;\"><strong>5<\/strong><\/td>\n<td style=\"width: 192.234px; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 189.078px; text-align: center;\"><strong>6<\/strong><\/td>\n<td style=\"width: 192.234px; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 189.078px; text-align: center;\"><strong>7<\/strong><\/td>\n<td style=\"width: 192.234px; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 189.078px; text-align: center;\"><strong>8<\/strong><\/td>\n<td style=\"width: 192.234px; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 189.078px; text-align: center;\"><\/td>\n<td style=\"width: 192.234px; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 189.078px; text-align: center;\"><\/td>\n<td style=\"width: 192.234px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q474589\">Hint<\/span><\/p>\n<div id=\"q474589\" class=\"hidden-answer\" style=\"display: none\">Were there seasons that included more than 8 paintings with clouds and what were the associated frequencies?<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h3 id=\"dotplottable\">Create a dotplot from a frequency table.<\/h3>\n<p>In a previous activity you learned about <strong>dotplots<\/strong>, graphical displays for quantitative data where each dot represents an observation. Dotplots are useful for visualizing distributions when the dataset is small.<\/p>\n<p>Create a dotplot for the number of paintings with clouds using the data analysis tool. Follow these steps to create a dotplot with raw observations or a frequency table:<\/p>\n<div class=\"textbox\">\n<p>Go to the\u00a0<em>Describing and Exploring Quantitative Variables <\/em>tool at\u00a0\u00a0<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 dropdown under <strong>Enter Data<\/strong> and select <strong>Your Own<\/strong>.<\/p>\n<p style=\"padding-left: 30px;\">Step 3) Locate the options under <strong>Do you have<\/strong>, and select <strong>Individual Observations<\/strong>.<\/p>\n<p style=\"padding-left: 30px;\">Step 4): For <strong>Name of Variable<\/strong>, enter \u201cNumber of Paintings with Clouds.\u201d<\/p>\n<p style=\"padding-left: 30px;\">Step 5) Locate the box under the variable name and enter the observations\u00a0<em><strong>num_clouds<\/strong>\u00a0<\/em>from the data set.<\/p>\n<p style=\"padding-left: 30px;\">Step 6) For <strong>Choose Type of Plot<\/strong> Select <strong>Dotplot<\/strong>. Unselect any other choices that were already selected.<\/p>\n<p style=\"padding-left: 30px;\">Step 7) Under <strong>Dotplot Options<\/strong>,\u00a0<strong>Select<\/strong>\u00a0<strong>Dotsize for Dotplot:<\/strong> 0.5\u00a0and <strong>Select Binwidth for Dotplot<\/strong>:\u00a00.5.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240648\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240648&theme=oea&iframe_resize_id=ohm240648&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h3 id=\"histogramtable\">Create a histogram from a frequency table<\/h3>\n<p>Typically, a histogram is more useful for large datasets. If there are a large number of observations, a histogram is easier to read, since it groups observations into bins (see this defined below) rather than having a single dot for each observation.<\/p>\n<p>Use the same data analysis tool to make a histogram to visualize the distribution of the number of paintings that included clouds in a season.<\/p>\n<p>With the same tool still open, (or after following Steps 1 &#8211; 5 above),<\/p>\n<div class=\"textbox\">Step 7) For <strong>Choose Type of Plot<\/strong> select <strong>Histogram<\/strong> option. <strong>Select Binwidth for Histogram<\/strong>: 1.<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240603\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240603&theme=oea&iframe_resize_id=ohm240603&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h3 id=\"barhist\">Understand the difference between a bar graph and a histogram<\/h3>\n<p>A histogram looks somewhat like a bar graph. But, while a\u00a0bar graph displays categorical data, showing counts of observations within categories, a histogram displays quantitative data by showing frequencies of a quantitative variable. You&#8217;ll be able to tell a bar graph from a histogram by observing whether the horizontal axis appears to be a list of categories (e.g. eye color, zip code, etc&#8230;) or a number line.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2831\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/05173345\/Bar_Hist_Compare.jpg\" alt=\"A bar chart displaying &quot;Eye Color&quot; adjacent to a histogram displaying &quot;Sleep Hours.&quot;The bars of the bar chart are separated and labeled Blue, Hazel, Brown, Grey, and Green. The bars of the histogram are adjacent and cover equals intervals of width 0.5 over a horizontal number line ranging from 4 to 11.\" width=\"872\" height=\"238\" \/><\/p>\n<p>The bars of a histogram are each of the same width and meet smoothly together over the horizontal axis.\u00a0In a histogram, we call the bars\u00a0<em>bins.\u00a0<\/em><\/p>\n<ul>\n<li style=\"text-align: left;\"><span style=\"font-size: 1em;\">A <\/span><strong style=\"font-size: 1em;\">bin <\/strong><span style=\"font-size: 1em;\">is a range of values that the quantitative variable can take.<\/span><\/li>\n<li style=\"text-align: left;\">A bin can be defined by its <strong>end points<\/strong>, the smallest and largest values of the quantitative variable represented in the bin. For the first bin [latex]\\left[4 , 5\\right)[\/latex], the end points are 4 and 5. The notation [latex]\\left[4 , 5\\right)[\/latex] means this bin includes observations of the numbers of paintings with clouds that include 4 but not 5. We knew from the frequency table that the frequency of 4 paintings in a season is 1, and there is a single dot above the 4 on the horizontal axis to indicate this.<\/li>\n<li style=\"text-align: left;\">The <strong>width<\/strong> of the bin, called <strong>binwidth<\/strong>,\u00a0is calculated by taking the difference of the values of the end points. For the first bin, the width is [latex]5 - 4 = 1[\/latex]. The width of the bins should remain the same for each graph. You can verify visually that each bin is exactly 1 wide.<\/li>\n<\/ul>\n<p>Use the histogram you created to answer the following questions.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p>Which value of the variable (number of paintings with clouds) occurs most frequently in the dataset?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q440732\">Hint<\/span><\/p>\n<div id=\"q440732\" class=\"hidden-answer\" style=\"display: none\">Hover over the bar in the histogram to reveal the frequency contain in each.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 5<\/h3>\n<p>How many seasons have 10 paintings with clouds?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q794824\">Hint<\/span><\/p>\n<div id=\"q794824\" class=\"hidden-answer\" style=\"display: none\">Remember that the left end-point of each bin is included, but not the right end-point.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 6<\/h3>\n<p>How many seasons have at least 8 paintings with clouds?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q167233\">Hint<\/span><\/p>\n<div id=\"q167233\" class=\"hidden-answer\" style=\"display: none\">Include <em>all<\/em> the seasons with at least 8.Hover over the bars to reveal the number in each bin. Remember that the left end-point of each bin is included, but not the right.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 7<\/h3>\n<p>How many seasons have 5 or fewer paintings with clouds?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q753731\">Hint<\/span><\/p>\n<div id=\"q753731\" class=\"hidden-answer\" style=\"display: none\">Hover over the bars to reveal the number in each bin. Remember that the left end-point of each bin is included, but not the right.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 8<\/h3>\n<p>There are 13 seasons with 13 new paintings in each season. In how many seasons do at least half the paintings include clouds?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q660433\">Hint<\/span><\/p>\n<div id=\"q660433\" 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 9<\/h3>\n<p>Make a new histogram of the number of paintings with clouds using a bin width of 2 (bin width = 2) and then compare the new histogram to the one from Question 1. How are they similar? How are they different?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q58603\">Hint<\/span><\/p>\n<div id=\"q58603\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<h3 id=\"histogramtech\">Create a histogram from a dataset using technology.<\/h3>\n<p>Hopefully, you are feeling comfortable using histograms to answer questions about the dataset. Try creating a histogram from a new dataset, then use it to answer questions. This time, you won&#8217;t need to enter the data by hand. We&#8217;ll use an existing dataset in the tool.<\/p>\n<p>If you don&#8217;t still have the <em>Describing and Exploring Quantitative Variables <\/em>tool open, open it at\u00a0\u00a0 \u00a0<a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\" target=\"_blank\" rel=\"noopener\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>\u00a0and follow these steps:<\/p>\n<div class=\"textbox\">\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 dropdown under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.<\/p>\n<p style=\"padding-left: 30px;\">Step 3) Choose the <strong>Dataset<\/strong> &#8220;Hours Watching TV (2018) to create a histogram.<\/p>\n<p style=\"padding-left: 30px;\">Step 4) Under\u00a0<strong>Type of Plot<\/strong>, make sure the Histogram box is checked. You can uncheck any other boxes that are selected.<\/p>\n<p style=\"padding-left: 30px;\">Step 5)\u00a0<strong>Select Binwidth<\/strong> = 2.<\/p>\n<\/div>\n<p>The dataset \u201cHours Watching TV (2018)\u201d in the <em>Describing and Exploring Quantitative Variables <\/em>tool has the weekly number of hours spent watching TV for 1,555 individuals. Create a histogram with binwidth = 2 to display the distribution of the variable. Use it to answer the questions below.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 10<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240605\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240605&theme=oea&iframe_resize_id=ohm240605&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 11<\/h3>\n<p>Look at the histogram with bin widths of 2, 5, and 10. Which bin width is most useful for visualizing the distribution of weekly number of TV hours? Explain.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q648646\">Hint<\/span><\/p>\n<div id=\"q648646\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think? Which helps you understand the characteristics of the distribution better?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 12<\/h3>\n<p>Use the histogram to write 2 or 3 observations about the distribution of weekly number of hours watching TV.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q367348\">Hint<\/span><\/p>\n<div id=\"q367348\" class=\"hidden-answer\" style=\"display: none\">Use the style of Questions 4 &#8211; 8 as a guide.<\/div>\n<\/div>\n<\/div>\n<div style=\"text-align: left;\">You&#8217;ve had quite a bit of practice with the tool to create, read, and interpret histograms you created from a dataset and using technology. You&#8217;ll see these skills again in the upcoming section and activity.<\/div>\n<\/div>\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-154\">\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>Used paint brushes and opened yellow, blue, red, and black paint tubes on a wooden floor with paint splattered on it.. <strong>Authored by<\/strong>: Andrian Valeanu. <strong>Provided by<\/strong>: Wikimedia Commons. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Andrian_Valeanu_2016-04-11_(Unsplash).jpg\">https:\/\/commons.wikimedia.org\/wiki\/File:Andrian_Valeanu_2016-04-11_(Unsplash).jpg<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section><hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-154-1\"> Hickey, W. (2014, April 14). A statistical analysis of the work of Bob Ross. FiveThirtyEight. https:\/\/fivethirtyeight.com\/features\/a-statistical-analysis-of-the-work-of-bob-ross\/\r\n <a href=\"#return-footnote-154-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":428269,"menu_order":17,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Used paint brushes and opened yellow, blue, red, and black paint tubes on a wooden floor with paint splattered on it.\",\"author\":\"Andrian Valeanu\",\"organization\":\"Wikimedia Commons\",\"url\":\"https:\/\/commons.wikimedia.org\/wiki\/File:Andrian_Valeanu_2016-04-11_(Unsplash).jpg\",\"project\":\"\",\"license\":\"cc0\",\"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-154","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/154","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/428269"}],"version-history":[{"count":50,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/154\/revisions"}],"predecessor-version":[{"id":3362,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/154\/revisions\/3362"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/154\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=154"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=154"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=154"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}