{"id":462,"date":"2021-12-20T14:35:59","date_gmt":"2021-12-20T14:35:59","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=462"},"modified":"2022-02-17T20:13:20","modified_gmt":"2022-02-17T20:13:20","slug":"what-to-know-about-4d","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/what-to-know-about-4d\/","title":{"raw":"What to Know About Five Number Summary in Box Plots and Datasets: 4D - 26","rendered":"What to Know About Five Number Summary in Box Plots and Datasets: 4D &#8211; 26"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>goals for this section<\/h3>\r\nAfter completing this section, you should feel comfortable performing these skills.\r\n<ul>\r\n \t<li><a href=\"#5NumberSummary\">Define the terms: first quartile, third quartile, interquartile range, and five-number summary.<\/a><\/li>\r\n \t<li><a href=\"#featboxplot\">Identify the features of a boxplot<\/a><\/li>\r\n \t<li><a href=\"#outlier\">Calculate interquartile range for a dataset.<\/a><\/li>\r\n \t<li><a href=\"#outlier\">Calculate the range of observations characterized as upper outliers or lower outliers.<\/a><\/li>\r\n \t<li><a href=\"#interpfeat_bxplt\">Interpret the features of a boxplot.<\/a><\/li>\r\n \t<li><a href=\"#identshape_bxplt\">Use a boxplot of a dataset to identify whether the shape of its distribution is left-skewed, symmetric, or right-skewed.<\/a><\/li>\r\n<\/ul>\r\nClick on a skill above to jump to its location in this section.\r\n\r\n<\/div>\r\nBoxplots are helpful for visualizing the distribution of a quantitative variable. A boxplot clearly shows the median of the data and provides a summary at a glance of the bulk of the data and the presence of outliers. In the next activity, you will need to be able to identity and interpret the features of a boxplot, identify outliers in a dataset, and relate a boxplot of a quantitative variable to its distribution. In this section, you'll learn to identify the key pieces of information needed to accomplish these tasks.\r\n<h2>Features of a Boxplot<\/h2>\r\nIn order to interpret boxplots, you will need to identify the minimum, maximum, and median of a quantitative variable. You've done this in previous activities. If you need a refresher, take a look at the video below. A boxplot captures only the median of the dataset, not the mean, as a measure of center.\r\n<div class=\"textbox examples\">\r\n<h3>recall<\/h3>\r\nCore skill:\r\n[reveal-answer q=\"952167\"]Identify the minimum value, maximum value, and median of a quantitative variable.[\/reveal-answer]\r\n[hidden-answer a=\"952167\"]\r\n\r\nPlace the observed values in order to identify the minimum and maximum values. The median will be the middle number in the list (or the mean of the middle two numbers in an even-numbered list).\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"5NumberSummary\">Five-Number Summary<\/h3>\r\nYou\u00a0will also need to know the following definitions:\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">the <strong>first quartile<\/strong> of a quantitative variable (sometimes denoted <strong>Q1<\/strong>) is the value below which one quarter of the data lies, and the first quartile is also equal to the 25th percentile;<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">the <strong>third quartile<\/strong> of a quantitative variable (sometimes denoted <strong>Q3<\/strong>) is the value below which three quarters of the data lay, and the third quartile is also equal to the 75th percentile; and<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">the<strong> interquartile range<\/strong> (sometimes denoted <strong>IQR<\/strong>) of a quantitative variable is the quantity Q3\u2013Q1.<\/li>\r\n<\/ul>\r\nThe collection of the minimum, first quartile, median, third quartile, and maximum form the <strong>five-number summary<\/strong> of the variable.\r\n<div class=\"textbox tryit\">\r\n<h3>first and third quartiles<\/h3>\r\n<span style=\"background-color: #ffff00;\"><span style=\"background-color: #99cc00;\">[Perspective video -- a 3 instructor video showing how to understand Q1 and Q3 as percentiles and\/or quarters of data. See below for the idea:]<\/span><\/span>\r\n<ul>\r\n \t<li><span style=\"background-color: #99cc00;\">the location of the Q1\/25th percentile and Q3\/75th percentile on a number line along with other percentile locations such as 10th and 98th along with three ways to think about it: <\/span>\r\n<ul>\r\n \t<li><span style=\"background-color: #99cc00;\">1)\u00a0 \"if a student scores in the 10th percentile of a test like the SAT, they have scored higher than only 10% of all the test takers but if they score in the 98th percentile, then their score is higher than 98% of all the test takers.\" and <\/span><\/li>\r\n \t<li><span style=\"background-color: #99cc00;\">2) \"percentiles divide data into two parts -- the lower part (she scored higher than 98% of the test takers) and the higher part (2% of the test takers scored higher than she did)\" and 3) \"the 25th percentile (first quartile) splits the data into the lower 25% and the 75% above that; the 50th percentile (2nd quartile) splits the data in half (marked by the median); the 75th percentile (3rd quartile)splits the data into the lower 75% and the 25% of the data above that.\" <\/span><\/li>\r\n \t<li><span style=\"background-color: #99cc00;\">3) Subtracting the value of Q1 from the value of Q3 gives the IQR (the distance between the 25th percentile and the 75th percentile)<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><span style=\"background-color: #99cc00;\">(critics may point out that students will have seen all of this before, which is true but doesn't acknowledge that students also need a brief refresher at this point.)<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3 id=\"featboxplot\">Identifying the Features of a Boxplot<\/h3>\r\nAs we explore the features of boxplots, we will work with part of a dataset that reports information about whether drivers involved in a fatal crash were impaired by alcohol.[footnote]Chalabi, M. (2014, October 24). <em>Dear Mona, which state has the worst driver?<\/em> FiveThirtyEight. https:\/\/fivethirtyeight.com\/features\/which-state-has-the-worst-drivers\/[\/footnote] The dataset contains 51 entries corresponding to all 50 states, as well as Washington, DC.\r\n\r\nThe following table gives the five-number summary for the percentage of drivers involved in fatal collisions who were alcohol-impaired in all 50 states and Washington, DC.\r\n<table class=\"aligncenter\" style=\"border-collapse: collapse; width: 50%;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\"><strong>Minimum<\/strong><\/td>\r\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\"><strong>First Quartile<\/strong><\/td>\r\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\"><strong>Median<\/strong><\/td>\r\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\"><strong>Third Quartile<\/strong><\/td>\r\n<td style=\"width: 155.938px; text-align: center; vertical-align: middle;\"><strong>Maximum<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\">16<\/td>\r\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\">28<\/td>\r\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\">30<\/td>\r\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\">33<\/td>\r\n<td style=\"width: 155.938px; text-align: center; vertical-align: middle;\">44<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nOne of the ways to visualize the data using the five-number summary is by creating a <strong>boxplot<\/strong>.\u00a0For questions 1 - 4, refer to the following boxplot, which depicts data about the percentage of drivers involved in fatal collisions who were alcohol-impaired in all 50 states and Washington, DC. The boxplot is superimposed with the letters A - G labeling different features of the plot.\r\n\r\n<strong><img class=\"alignnone wp-image-1029\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11223308\/Picture55-267x300.png\" alt=\"A vertical boxplot titled &quot;Percentage of drivers involved in fatal collisions who were alcohol-impaired.&quot; The vertical axis is numbered by increments of 5 from 15 to 50. On the graph, there are points at16, 41, 42, and 44. The point at 44 is labeled &quot;A.&quot; The high point of the box plot is at 38 and labeled &quot;B,&quot; while the low point is at 23 and labeled &quot;F.&quot; The high end of the box is at 33 and labeled &quot;C&quot; while the low end is at 28 and labeled &quot;E.&quot; The middle line is at 30 and labeled &quot;D.&quot;\" width=\"454\" height=\"510\" \/><\/strong>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\nMatch the labeled feature on the above boxplot to the term that describes it.\r\n<div align=\"center\">\r\n<table class=\"lines\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 206px; text-align: center;\"><strong>Term<\/strong><\/td>\r\n<td style=\"width: 180.812px; text-align: center;\"><strong>Boxplot Feature<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 206px; text-align: center;\"><strong>Minimum<\/strong><\/td>\r\n<td style=\"width: 180.812px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 206px; text-align: center;\"><strong>First quartile (Q1)<\/strong><\/td>\r\n<td style=\"width: 180.812px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 206px; text-align: center;\"><strong>Median<\/strong><\/td>\r\n<td style=\"width: 180.812px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 206px; text-align: center;\"><strong>Third quartile (Q3)<\/strong><\/td>\r\n<td style=\"width: 180.812px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 206px; text-align: center;\"><strong>Maximum<\/strong><\/td>\r\n<td style=\"width: 180.812px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n[reveal-answer q=\"102884\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"102884\"]Look back at the table showing the five-number summary, and enter the letter that corresponds to the indicated term.[\/hidden-answer]\r\n\r\n<\/div>\r\nFor questions 2 -4, complete each sentence using information from the boxplot above.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\nIn about half of the states, fewer than _______ of drivers involved in a fatal crash were impaired by alcohol.\r\n<p style=\"padding-left: 30px;\">a) 23%<\/p>\r\n<p style=\"padding-left: 30px;\">b) 28%<\/p>\r\n<p style=\"padding-left: 30px;\">c) 30%<\/p>\r\n<p style=\"padding-left: 30px;\">d) 33%<\/p>\r\n<p style=\"padding-left: 30px;\">e) 38%<\/p>\r\n<p style=\"padding-left: 30px;\">f) 44%<\/p>\r\n[reveal-answer q=\"519981\"]Hint[\/reveal-answer]\r\n\r\n[hidden-answer a=\"519981\"]This question involves about half of the states, so look for the median.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 3<\/h3>\r\nIn about one quarter of the states, fewer than _______ of drivers involved in a fatal crash were impaired by alcohol.\r\n<p style=\"padding-left: 30px;\">a) 23%<\/p>\r\n<p style=\"padding-left: 30px;\">b) 28%<\/p>\r\n<p style=\"padding-left: 30px;\">c) 30%<\/p>\r\n<p style=\"padding-left: 30px;\">d) 33%<\/p>\r\n<p style=\"padding-left: 30px;\">e) 38%<\/p>\r\n<p style=\"padding-left: 30px;\">f) 44%<\/p>\r\n[reveal-answer q=\"16620\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"16620\"]Which number in the five-number summary is related to a quarter of the states?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\n_______ of the states had alcohol involved in 33% or more of their fatal crashes.\r\n<p style=\"padding-left: 30px;\">a) One-fourth<\/p>\r\n<p style=\"padding-left: 30px;\">b) One half<\/p>\r\n<p style=\"padding-left: 30px;\">c) Three-fourths<\/p>\r\n[reveal-answer q=\"735025\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"735025\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"outlier\">Interquartile Range and Outliers<\/h3>\r\nNow, let\u2019s define the idea of an outlier more precisely. Previously, we've seen that an outlier is a value that is unusual, given the other values in a dataset. But what does \u201cunusual\u201d mean? To be more precise, for data with only one variable, let's define the define the following:\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><strong>upper outlier<\/strong> as an observation that is greater than Q3 + 1.5 \u00d7 (IQR); and<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><strong>lower outlier<\/strong> as an observation that is less than Q1 - 1.5 \u00d7 (IQR).<\/li>\r\n<\/ul>\r\nUse these definitions with the boxplot above question 1 to complete the sentences in questions 5 and 6.\r\n<div class=\"textbox tryit\">\r\n<h3>identifying features of a boxplot<\/h3>\r\n<span style=\"background-color: #99cc00;\">[Worked example - a 3-instructor video showing a worked example similar to Questions 5 - 7]<\/span>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 5<\/h3>\r\nThe interquartile range (IQR) of this dataset is ______.\r\n\r\n&nbsp;\r\n\r\n[reveal-answer q=\"587526\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"587526\"]IQR = Q3 \u2013 Q1; use the table in Question 1 to evaluate.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 6<\/h3>\r\nRecall that we say that upper outliers lie above Q3 + 1.5 \u00d7 (IQR), and lower outliers lie below Q1 - 1.5 \u00d7 (IQR). Because of this, states with more than ________% of fatal crashes involving alcohol impairment are considered upper outliers, and states with fewer than ________% of fatal crashes involving alcohol impairment are considered lower outliers.\r\n\r\n[reveal-answer q=\"206360\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"206360\"]Use the five-number summary and your answer to Question 3, Part A to evaluate. What is 1.5 \u00d7 (IQR)?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 7<\/h3>\r\nAgain, referring to the boxplot above Question 1, we saw previously how some of the boxplot\u2019s features relate to the five-number summary, but when outliers are present, the boxplot is modified as shown below. On the following table, match the labeled feature on the boxplot to the term that describes it.\r\n\r\n<strong><img class=\"alignnone wp-image-1030\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11223314\/Picture56-252x300.png\" alt=\"A vertical boxplot titled &quot;Percentage of drivers involved in fatal collisions who were alcohol-impaired.&quot; The vertical axis is numbered by increments of 5 from 15 to 50. On the graph, there is a point at 16 labeled &quot;D.&quot; There are also points at 41, 42, and 44 collectively labeled &quot;A.&quot; The high point of the box plot is at 38 and labeled &quot;B,&quot; while the low point is at 23 and labeled &quot;C.&quot; The high end of the box is at 33 while the low end is at 28. The middle line is at 30.\" width=\"463\" height=\"551\" \/><\/strong>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Term<\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong>Boxplot Feature<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Upper outlier(s)<\/strong><\/td>\r\n<td style=\"text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Lower outlier(s)<\/strong><\/td>\r\n<td style=\"text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Greatest value of an observation that is not an upper outlier<\/strong><\/td>\r\n<td style=\"text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Lowest value of an observation that is not a lower outlier<\/strong><\/td>\r\n<td style=\"text-align: center;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[reveal-answer q=\"496986\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"496986\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\nIt's important to note that there are several good methods to use for determining an observation to be an outlier in the distribution. The IQR method commonly uses a distance 1.5 times IQR from Q1 or Q3, but certain applications use larger distances. The IQR method does work for skewed distributions, though. In the next section, you'll learn about another method that doesn't involve the IQR, and which works well for symmetrical distributions. Depending upon the application, it may be desirable to set the distance 2 or even 3 times IQR, but 1.5 times is commonly used and works well for our application, so we use it here.\r\n<h3 id=\"interpfeat_bxplt\">Interpreting the Features of a Boxplot<\/h3>\r\nThe following table lists each state in the dataset, along with the corresponding percentages of drivers involved in fatal crashes who were impaired by alcohol, in order from lowest percentage to highest percentage. Use this table and the definition of <em>outlier<\/em> to answer questions 8 -9.\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td style=\"text-align: center;\" colspan=\"4\"><strong>Drivers Involved in Fatal Crashes by State<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>State<\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong>Percentage of Drivers Involved in Fatal Crashes and Impaired by Alcohol<\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong>State<\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong>Percentage of Drivers Involved in Fatal Crashes and Impaired by Alcohol<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Utah<\/strong><\/td>\r\n<td style=\"text-align: center;\">16<\/td>\r\n<td style=\"text-align: center;\"><strong>Maine<\/strong><\/td>\r\n<td style=\"text-align: center;\">30<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Kentucky<\/strong><\/td>\r\n<td style=\"text-align: center;\">23<\/td>\r\n<td style=\"text-align: center;\"><strong>New Hampshire<\/strong><\/td>\r\n<td style=\"text-align: center;\">30<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Kansas<\/strong><\/td>\r\n<td style=\"text-align: center;\">24<\/td>\r\n<td style=\"text-align: center;\"><strong>Vermont<\/strong><\/td>\r\n<td style=\"text-align: center;\">30<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Alaska<\/strong><\/td>\r\n<td style=\"text-align: center;\">25<\/td>\r\n<td style=\"text-align: center;\"><strong>Mississippi<\/strong><\/td>\r\n<td style=\"text-align: center;\">31<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Georgia<\/strong><\/td>\r\n<td style=\"text-align: center;\">25<\/td>\r\n<td style=\"text-align: center;\"><strong>North Carolina<\/strong><\/td>\r\n<td style=\"text-align: center;\">31<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Iowa<\/strong><\/td>\r\n<td style=\"text-align: center;\">25<\/td>\r\n<td style=\"text-align: center;\"><strong>Pennsylvania<\/strong><\/td>\r\n<td style=\"text-align: center;\">31<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Arkansas<\/strong><\/td>\r\n<td style=\"text-align: center;\">26<\/td>\r\n<td style=\"text-align: center;\"><strong>Maryland<\/strong><\/td>\r\n<td style=\"text-align: center;\">32<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Oregon<\/strong><\/td>\r\n<td style=\"text-align: center;\">26<\/td>\r\n<td style=\"text-align: center;\"><strong>Nevada<\/strong><\/td>\r\n<td style=\"text-align: center;\">32<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>District of Columbia<\/strong><\/td>\r\n<td style=\"text-align: center;\">27<\/td>\r\n<td style=\"text-align: center;\"><strong>Wyoming<\/strong><\/td>\r\n<td style=\"text-align: center;\">32<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>New Mexico<\/strong><\/td>\r\n<td style=\"text-align: center;\">27<\/td>\r\n<td style=\"text-align: center;\"><strong>Louisiana<\/strong><\/td>\r\n<td style=\"text-align: center;\">33<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Virginia<\/strong><\/td>\r\n<td style=\"text-align: center;\">27<\/td>\r\n<td style=\"text-align: center;\"><strong>South Dakota<\/strong><\/td>\r\n<td style=\"text-align: center;\">33<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Arizona<\/strong><\/td>\r\n<td style=\"text-align: center;\">28<\/td>\r\n<td style=\"text-align: center;\"><strong>Washington<\/strong><\/td>\r\n<td style=\"text-align: center;\">33<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>California<\/strong><\/td>\r\n<td style=\"text-align: center;\">28<\/td>\r\n<td style=\"text-align: center;\"><strong>Wisconsin<\/strong><\/td>\r\n<td style=\"text-align: center;\">33<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Colorado<\/strong><\/td>\r\n<td style=\"text-align: center;\">28<\/td>\r\n<td style=\"text-align: center;\"><strong>Illinois<\/strong><\/td>\r\n<td style=\"text-align: center;\">34<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Michigan<\/strong><\/td>\r\n<td style=\"text-align: center;\">28<\/td>\r\n<td style=\"text-align: center;\"><strong>Missouri<\/strong><\/td>\r\n<td style=\"text-align: center;\">34<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>New Jersey<\/strong><\/td>\r\n<td style=\"text-align: center;\">28<\/td>\r\n<td style=\"text-align: center;\"><strong>Ohio<\/strong><\/td>\r\n<td style=\"text-align: center;\">34<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>West Virginia<\/strong><\/td>\r\n<td style=\"text-align: center;\">28<\/td>\r\n<td style=\"text-align: center;\"><strong>Massachusetts<\/strong><\/td>\r\n<td style=\"text-align: center;\">35<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Florida<\/strong><\/td>\r\n<td style=\"text-align: center;\">29<\/td>\r\n<td style=\"text-align: center;\"><strong>Nebraska<\/strong><\/td>\r\n<td style=\"text-align: center;\">35<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Idaho<\/strong><\/td>\r\n<td style=\"text-align: center;\">29<\/td>\r\n<td style=\"text-align: center;\"><strong>Connecticut<\/strong><\/td>\r\n<td style=\"text-align: center;\">36<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Indiana<\/strong><\/td>\r\n<td style=\"text-align: center;\">29<\/td>\r\n<td style=\"text-align: center;\"><strong>Rhode Island<\/strong><\/td>\r\n<td style=\"text-align: center;\">38<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Minnesota<\/strong><\/td>\r\n<td style=\"text-align: center;\">29<\/td>\r\n<td style=\"text-align: center;\"><strong>Texas<\/strong><\/td>\r\n<td style=\"text-align: center;\">38<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>New York<\/strong><\/td>\r\n<td style=\"text-align: center;\">29<\/td>\r\n<td style=\"text-align: center;\"><strong>Hawaii<\/strong><\/td>\r\n<td style=\"text-align: center;\">41<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Oklahoma<\/strong><\/td>\r\n<td style=\"text-align: center;\">29<\/td>\r\n<td style=\"text-align: center;\"><strong>South Carolina<\/strong><\/td>\r\n<td style=\"text-align: center;\">41<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Tennessee<\/strong><\/td>\r\n<td style=\"text-align: center;\">29<\/td>\r\n<td style=\"text-align: center;\"><strong>North Dakota<\/strong><\/td>\r\n<td style=\"text-align: center;\">42<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Alabama<\/strong><\/td>\r\n<td style=\"text-align: center;\">30<\/td>\r\n<td style=\"text-align: center;\"><strong>Montana<\/strong><\/td>\r\n<td style=\"text-align: center;\">44<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Delaware<\/strong><\/td>\r\n<td style=\"text-align: center;\">30<\/td>\r\n<td style=\"text-align: center;\"><\/td>\r\n<td style=\"text-align: center;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 8<\/h3>\r\nWhich state(s) in the list below is a lower outlier? In other words, which has an unusually low percentage of drivers involved in fatal crashes who were impaired by alcohol? Choose all that apply.\r\n<p style=\"padding-left: 30px;\">a) Kentucky<\/p>\r\n<p style=\"padding-left: 30px;\">b) Kansas<\/p>\r\n<p style=\"padding-left: 30px;\">c) Utah<\/p>\r\n<p style=\"padding-left: 30px;\">d) Alaska<\/p>\r\n[reveal-answer q=\"609285\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"609285\"]Use the IQR and the definition of <em>outlier<\/em>.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 9<\/h3>\r\nWhich of the following states have unusually high percentages of drivers involved in fatal crashes who were impaired by alcohol?\r\n<p style=\"padding-left: 30px;\">a) Texas, South Carolina, Montana<\/p>\r\n<p style=\"padding-left: 30px;\">b) Montana, North Dakota, South Carolina, Hawaii<\/p>\r\n<p style=\"padding-left: 30px;\">c) Montana, North Dakota, South Carolina<\/p>\r\n<p style=\"padding-left: 30px;\">d) Texas, South Carolina, Montana, Rhode Island<\/p>\r\n[reveal-answer q=\"96884\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"96884\"]Make sure to include all states that are considered to be upper outliers.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 10<\/h3>\r\nWithout computing the mean of the percentage of drivers involved in fatal crashes who were impaired by alcohol, make a prediction about whether the mean and median will be very different or fairly similar.\r\n\r\n[reveal-answer q=\"633143\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"633143\"]Imagine how the outliers might appear as tails on a histogram or dotplot and the symmetry (or lack thereof) of the IQR about the median.[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\nNow, let's use technology to explore the dataset.\r\n<div class=\"textbox\">\r\n\r\nGo to the Describing and Exploring Quantitative Variables tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\" target=\"_blank\" rel=\"noopener\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>.\r\n<p style=\"padding-left: 30px;\">Step 1) Select the <strong>Single Group<\/strong> tab.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 2) Locate the dropdown under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 3) Locate the drop-down menu under <strong>Dataset<\/strong> and select <strong>Bad Drivers (alcohol)<\/strong>.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 4) Use the tool to compute the mean percentage of drivers involved in fatal collisions who were alcohol-impaired.<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 11<\/h3>\r\nWhich of the following describes your findings?\r\n<p style=\"padding-left: 30px;\">a) The mean is much higher than the median.<\/p>\r\n<p style=\"padding-left: 30px;\">b) The median is much higher than the mean.<\/p>\r\n<p style=\"padding-left: 30px;\">c) The mean and the median are about the same.<\/p>\r\n[reveal-answer q=\"363793\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"363793\"]The mean will appear in the Descriptive Statistics[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"identshape_bxplt\">Identifying the Shape of a Distribution from a Boxplot<\/h3>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 12<\/h3>\r\nJust as histograms and dotplots can tell us about the distribution of a quantitative variable, so can a boxplot. For each boxplot below, choose the description that matches the shape of the data\u2019s distribution. (Note that boxplots can be oriented vertically, as we saw previously, or horizontally, as we see below.)\r\n\r\n&nbsp;\r\n<div align=\"left\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Boxplot<\/td>\r\n<td>Distribution<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong><img class=\"alignnone wp-image-1022\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11223158\/ChartPicture4-300x36.png\" alt=\"A boxplot numbered in increments of 50 from 0 to 350. The low point of the plot is at 50 and the high point is at approximately 290. The low end of the box is at approximately 140, the high end is at approximately 210, and the middle line is at approximately 180. There is also a point at 0 and one at approximately 340.\" width=\"975\" height=\"117\" \/><\/strong><\/td>\r\n<td>a) left skewed\r\n\r\nb) symmetric\r\n\r\nc) right skewed\r\n\r\n<span style=\"background-color: #ffff00;\">include dropdown options similar to Question 10 in WTK 4C<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong><img class=\"alignnone wp-image-1023\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11223205\/ChartPicture5-300x35.png\" alt=\"A boxplot numbered in increments of 5 from 0 to 25. The low end of the plot is at 0 and the high end is at approximately 8. The low edge of the box is at approximately 1, while the high edge is at approximately 4 and the center line is at approximately 2. There are also points at approximately 9, 10, 12, 13, 14, 15, 16, 18, 20, 22, and 24.\" width=\"947\" height=\"111\" \/><\/strong><\/td>\r\n<td>a) left skewed\r\n\r\nb) symmetric\r\n\r\nc) right skewed\r\n\r\n<span style=\"background-color: #ffff00;\">include dropdown options similar to Question 10 in WTK 4C<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong><img class=\"alignnone wp-image-1024\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11223210\/ChartPicture6-300x37.png\" alt=\"A box plot labeled in increments of 5 from 35 to 60. The low point of the box plot is at 55 and the high point is at approximately 61. The low end of the box is at approximately 56, the high end is at approximately 60, and the middle line is at approximately 58. There are also points at approximately 35, 36, 37, and 38.\" width=\"1058\" height=\"129\" \/><\/strong><\/td>\r\n<td>a) left skewed\r\n\r\nb) symmetric\r\n\r\nc) right skewed\r\n\r\n<span style=\"background-color: #ffff00;\">include dropdown options similar to Question 10 in WTK 4C<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n[reveal-answer q=\"41394\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"41394\"]What effect do outliers have on the skew of data?[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Summary<\/h2>\r\nIn this section, you've learned about boxplots: how to calculate the five-number summary, how to read these numbers from a boxplot, and how to identify outliers in a dataset using the interquartile range. Let's summarize where these skills showed up in the material.\r\n<ul>\r\n \t<li>In Questions 1 and 7, you identified the features of a boxplot.<\/li>\r\n \t<li>In Questions 2 - 4, you interpreted the features of a boxplot.<\/li>\r\n \t<li>In Questions 5, 6, 8, and 9, you identified outliers in a dataset.<\/li>\r\n \t<li>In Questions 10 - 12, you related the boxplot of a quantitative variable to its distribution.<\/li>\r\n<\/ul>\r\nBeing able to calculate and identify features of a boxplot and relate the boxplot and distribution of a quantitative variable are necessary statistical skills and will be used in the next activity. If you feel comfortable with these skills, please move on!","rendered":"<div class=\"textbox learning-objectives\">\n<h3>goals for this section<\/h3>\n<p>After completing this section, you should feel comfortable performing these skills.<\/p>\n<ul>\n<li><a href=\"#5NumberSummary\">Define the terms: first quartile, third quartile, interquartile range, and five-number summary.<\/a><\/li>\n<li><a href=\"#featboxplot\">Identify the features of a boxplot<\/a><\/li>\n<li><a href=\"#outlier\">Calculate interquartile range for a dataset.<\/a><\/li>\n<li><a href=\"#outlier\">Calculate the range of observations characterized as upper outliers or lower outliers.<\/a><\/li>\n<li><a href=\"#interpfeat_bxplt\">Interpret the features of a boxplot.<\/a><\/li>\n<li><a href=\"#identshape_bxplt\">Use a boxplot of a dataset to identify whether the shape of its distribution is left-skewed, symmetric, or right-skewed.<\/a><\/li>\n<\/ul>\n<p>Click on a skill above to jump to its location in this section.<\/p>\n<\/div>\n<p>Boxplots are helpful for visualizing the distribution of a quantitative variable. A boxplot clearly shows the median of the data and provides a summary at a glance of the bulk of the data and the presence of outliers. In the next activity, you will need to be able to identity and interpret the features of a boxplot, identify outliers in a dataset, and relate a boxplot of a quantitative variable to its distribution. In this section, you&#8217;ll learn to identify the key pieces of information needed to accomplish these tasks.<\/p>\n<h2>Features of a Boxplot<\/h2>\n<p>In order to interpret boxplots, you will need to identify the minimum, maximum, and median of a quantitative variable. You&#8217;ve done this in previous activities. If you need a refresher, take a look at the video below. A boxplot captures only the median of the dataset, not the mean, as a measure of center.<\/p>\n<div class=\"textbox examples\">\n<h3>recall<\/h3>\n<p>Core skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q952167\">Identify the minimum value, maximum value, and median of a quantitative variable.<\/span><\/p>\n<div id=\"q952167\" class=\"hidden-answer\" style=\"display: none\">\n<p>Place the observed values in order to identify the minimum and maximum values. The median will be the middle number in the list (or the mean of the middle two numbers in an even-numbered list).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h3 id=\"5NumberSummary\">Five-Number Summary<\/h3>\n<p>You\u00a0will also need to know the following definitions:<\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">the <strong>first quartile<\/strong> of a quantitative variable (sometimes denoted <strong>Q1<\/strong>) is the value below which one quarter of the data lies, and the first quartile is also equal to the 25th percentile;<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">the <strong>third quartile<\/strong> of a quantitative variable (sometimes denoted <strong>Q3<\/strong>) is the value below which three quarters of the data lay, and the third quartile is also equal to the 75th percentile; and<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">the<strong> interquartile range<\/strong> (sometimes denoted <strong>IQR<\/strong>) of a quantitative variable is the quantity Q3\u2013Q1.<\/li>\n<\/ul>\n<p>The collection of the minimum, first quartile, median, third quartile, and maximum form the <strong>five-number summary<\/strong> of the variable.<\/p>\n<div class=\"textbox tryit\">\n<h3>first and third quartiles<\/h3>\n<p><span style=\"background-color: #ffff00;\"><span style=\"background-color: #99cc00;\">[Perspective video &#8212; a 3 instructor video showing how to understand Q1 and Q3 as percentiles and\/or quarters of data. See below for the idea:]<\/span><\/span><\/p>\n<ul>\n<li><span style=\"background-color: #99cc00;\">the location of the Q1\/25th percentile and Q3\/75th percentile on a number line along with other percentile locations such as 10th and 98th along with three ways to think about it: <\/span>\n<ul>\n<li><span style=\"background-color: #99cc00;\">1)\u00a0 &#8220;if a student scores in the 10th percentile of a test like the SAT, they have scored higher than only 10% of all the test takers but if they score in the 98th percentile, then their score is higher than 98% of all the test takers.&#8221; and <\/span><\/li>\n<li><span style=\"background-color: #99cc00;\">2) &#8220;percentiles divide data into two parts &#8212; the lower part (she scored higher than 98% of the test takers) and the higher part (2% of the test takers scored higher than she did)&#8221; and 3) &#8220;the 25th percentile (first quartile) splits the data into the lower 25% and the 75% above that; the 50th percentile (2nd quartile) splits the data in half (marked by the median); the 75th percentile (3rd quartile)splits the data into the lower 75% and the 25% of the data above that.&#8221; <\/span><\/li>\n<li><span style=\"background-color: #99cc00;\">3) Subtracting the value of Q1 from the value of Q3 gives the IQR (the distance between the 25th percentile and the 75th percentile)<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span style=\"background-color: #99cc00;\">(critics may point out that students will have seen all of this before, which is true but doesn&#8217;t acknowledge that students also need a brief refresher at this point.)<\/span><\/li>\n<\/ul>\n<\/div>\n<h3 id=\"featboxplot\">Identifying the Features of a Boxplot<\/h3>\n<p>As we explore the features of boxplots, we will work with part of a dataset that reports information about whether drivers involved in a fatal crash were impaired by alcohol.<a class=\"footnote\" title=\"Chalabi, M. (2014, October 24). Dear Mona, which state has the worst driver? FiveThirtyEight. https:\/\/fivethirtyeight.com\/features\/which-state-has-the-worst-drivers\/\" id=\"return-footnote-462-1\" href=\"#footnote-462-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> The dataset contains 51 entries corresponding to all 50 states, as well as Washington, DC.<\/p>\n<p>The following table gives the five-number summary for the percentage of drivers involved in fatal collisions who were alcohol-impaired in all 50 states and Washington, DC.<\/p>\n<table class=\"aligncenter\" style=\"border-collapse: collapse; width: 50%;\">\n<tbody>\n<tr>\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\"><strong>Minimum<\/strong><\/td>\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\"><strong>First Quartile<\/strong><\/td>\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\"><strong>Median<\/strong><\/td>\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\"><strong>Third Quartile<\/strong><\/td>\n<td style=\"width: 155.938px; text-align: center; vertical-align: middle;\"><strong>Maximum<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\">16<\/td>\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\">28<\/td>\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\">30<\/td>\n<td style=\"width: 155.891px; text-align: center; vertical-align: middle;\">33<\/td>\n<td style=\"width: 155.938px; text-align: center; vertical-align: middle;\">44<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>One of the ways to visualize the data using the five-number summary is by creating a <strong>boxplot<\/strong>.\u00a0For questions 1 &#8211; 4, refer to the following boxplot, which depicts data about the percentage of drivers involved in fatal collisions who were alcohol-impaired in all 50 states and Washington, DC. The boxplot is superimposed with the letters A &#8211; G labeling different features of the plot.<\/p>\n<p><strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1029\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11223308\/Picture55-267x300.png\" alt=\"A vertical boxplot titled &quot;Percentage of drivers involved in fatal collisions who were alcohol-impaired.&quot; The vertical axis is numbered by increments of 5 from 15 to 50. On the graph, there are points at16, 41, 42, and 44. The point at 44 is labeled &quot;A.&quot; The high point of the box plot is at 38 and labeled &quot;B,&quot; while the low point is at 23 and labeled &quot;F.&quot; The high end of the box is at 33 and labeled &quot;C&quot; while the low end is at 28 and labeled &quot;E.&quot; The middle line is at 30 and labeled &quot;D.&quot;\" width=\"454\" height=\"510\" \/><\/strong><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p>Match the labeled feature on the above boxplot to the term that describes it.<\/p>\n<div style=\"margin: auto;\">\n<table class=\"lines\">\n<tbody>\n<tr>\n<td style=\"width: 206px; text-align: center;\"><strong>Term<\/strong><\/td>\n<td style=\"width: 180.812px; text-align: center;\"><strong>Boxplot Feature<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 206px; text-align: center;\"><strong>Minimum<\/strong><\/td>\n<td style=\"width: 180.812px; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 206px; text-align: center;\"><strong>First quartile (Q1)<\/strong><\/td>\n<td style=\"width: 180.812px; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 206px; text-align: center;\"><strong>Median<\/strong><\/td>\n<td style=\"width: 180.812px; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 206px; text-align: center;\"><strong>Third quartile (Q3)<\/strong><\/td>\n<td style=\"width: 180.812px; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 206px; text-align: center;\"><strong>Maximum<\/strong><\/td>\n<td style=\"width: 180.812px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q102884\">Hint<\/span><\/p>\n<div id=\"q102884\" class=\"hidden-answer\" style=\"display: none\">Look back at the table showing the five-number summary, and enter the letter that corresponds to the indicated term.<\/div>\n<\/div>\n<\/div>\n<p>For questions 2 -4, complete each sentence using information from the boxplot above.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p>In about half of the states, fewer than _______ of drivers involved in a fatal crash were impaired by alcohol.<\/p>\n<p style=\"padding-left: 30px;\">a) 23%<\/p>\n<p style=\"padding-left: 30px;\">b) 28%<\/p>\n<p style=\"padding-left: 30px;\">c) 30%<\/p>\n<p style=\"padding-left: 30px;\">d) 33%<\/p>\n<p style=\"padding-left: 30px;\">e) 38%<\/p>\n<p style=\"padding-left: 30px;\">f) 44%<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q519981\">Hint<\/span><\/p>\n<div id=\"q519981\" class=\"hidden-answer\" style=\"display: none\">This question involves about half of the states, so look for the median.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p>In about one quarter of the states, fewer than _______ of drivers involved in a fatal crash were impaired by alcohol.<\/p>\n<p style=\"padding-left: 30px;\">a) 23%<\/p>\n<p style=\"padding-left: 30px;\">b) 28%<\/p>\n<p style=\"padding-left: 30px;\">c) 30%<\/p>\n<p style=\"padding-left: 30px;\">d) 33%<\/p>\n<p style=\"padding-left: 30px;\">e) 38%<\/p>\n<p style=\"padding-left: 30px;\">f) 44%<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q16620\">Hint<\/span><\/p>\n<div id=\"q16620\" class=\"hidden-answer\" style=\"display: none\">Which number in the five-number summary is related to a quarter of the states?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p>_______ of the states had alcohol involved in 33% or more of their fatal crashes.<\/p>\n<p style=\"padding-left: 30px;\">a) One-fourth<\/p>\n<p style=\"padding-left: 30px;\">b) One half<\/p>\n<p style=\"padding-left: 30px;\">c) Three-fourths<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q735025\">Hint<\/span><\/p>\n<div id=\"q735025\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<h3 id=\"outlier\">Interquartile Range and Outliers<\/h3>\n<p>Now, let\u2019s define the idea of an outlier more precisely. Previously, we&#8217;ve seen that an outlier is a value that is unusual, given the other values in a dataset. But what does \u201cunusual\u201d mean? To be more precise, for data with only one variable, let&#8217;s define the define the following:<\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><strong>upper outlier<\/strong> as an observation that is greater than Q3 + 1.5 \u00d7 (IQR); and<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><strong>lower outlier<\/strong> as an observation that is less than Q1 &#8211; 1.5 \u00d7 (IQR).<\/li>\n<\/ul>\n<p>Use these definitions with the boxplot above question 1 to complete the sentences in questions 5 and 6.<\/p>\n<div class=\"textbox tryit\">\n<h3>identifying features of a boxplot<\/h3>\n<p><span style=\"background-color: #99cc00;\">[Worked example &#8211; a 3-instructor video showing a worked example similar to Questions 5 &#8211; 7]<\/span><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 5<\/h3>\n<p>The interquartile range (IQR) of this dataset is ______.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q587526\">Hint<\/span><\/p>\n<div id=\"q587526\" class=\"hidden-answer\" style=\"display: none\">IQR = Q3 \u2013 Q1; use the table in Question 1 to evaluate.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 6<\/h3>\n<p>Recall that we say that upper outliers lie above Q3 + 1.5 \u00d7 (IQR), and lower outliers lie below Q1 &#8211; 1.5 \u00d7 (IQR). Because of this, states with more than ________% of fatal crashes involving alcohol impairment are considered upper outliers, and states with fewer than ________% of fatal crashes involving alcohol impairment are considered lower outliers.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q206360\">Hint<\/span><\/p>\n<div id=\"q206360\" class=\"hidden-answer\" style=\"display: none\">Use the five-number summary and your answer to Question 3, Part A to evaluate. What is 1.5 \u00d7 (IQR)?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 7<\/h3>\n<p>Again, referring to the boxplot above Question 1, we saw previously how some of the boxplot\u2019s features relate to the five-number summary, but when outliers are present, the boxplot is modified as shown below. On the following table, match the labeled feature on the boxplot to the term that describes it.<\/p>\n<p><strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1030\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11223314\/Picture56-252x300.png\" alt=\"A vertical boxplot titled &quot;Percentage of drivers involved in fatal collisions who were alcohol-impaired.&quot; The vertical axis is numbered by increments of 5 from 15 to 50. On the graph, there is a point at 16 labeled &quot;D.&quot; There are also points at 41, 42, and 44 collectively labeled &quot;A.&quot; The high point of the box plot is at 38 and labeled &quot;B,&quot; while the low point is at 23 and labeled &quot;C.&quot; The high end of the box is at 33 while the low end is at 28. The middle line is at 30.\" width=\"463\" height=\"551\" \/><\/strong><\/p>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><strong>Term<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Boxplot Feature<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Upper outlier(s)<\/strong><\/td>\n<td style=\"text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Lower outlier(s)<\/strong><\/td>\n<td style=\"text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Greatest value of an observation that is not an upper outlier<\/strong><\/td>\n<td style=\"text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Lowest value of an observation that is not a lower outlier<\/strong><\/td>\n<td style=\"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=\"q496986\">Hint<\/span><\/p>\n<div id=\"q496986\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>It&#8217;s important to note that there are several good methods to use for determining an observation to be an outlier in the distribution. The IQR method commonly uses a distance 1.5 times IQR from Q1 or Q3, but certain applications use larger distances. The IQR method does work for skewed distributions, though. In the next section, you&#8217;ll learn about another method that doesn&#8217;t involve the IQR, and which works well for symmetrical distributions. Depending upon the application, it may be desirable to set the distance 2 or even 3 times IQR, but 1.5 times is commonly used and works well for our application, so we use it here.<\/p>\n<h3 id=\"interpfeat_bxplt\">Interpreting the Features of a Boxplot<\/h3>\n<p>The following table lists each state in the dataset, along with the corresponding percentages of drivers involved in fatal crashes who were impaired by alcohol, in order from lowest percentage to highest percentage. Use this table and the definition of <em>outlier<\/em> to answer questions 8 -9.<\/p>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center;\" colspan=\"4\"><strong>Drivers Involved in Fatal Crashes by State<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>State<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Percentage of Drivers Involved in Fatal Crashes and Impaired by Alcohol<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>State<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Percentage of Drivers Involved in Fatal Crashes and Impaired by Alcohol<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Utah<\/strong><\/td>\n<td style=\"text-align: center;\">16<\/td>\n<td style=\"text-align: center;\"><strong>Maine<\/strong><\/td>\n<td style=\"text-align: center;\">30<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Kentucky<\/strong><\/td>\n<td style=\"text-align: center;\">23<\/td>\n<td style=\"text-align: center;\"><strong>New Hampshire<\/strong><\/td>\n<td style=\"text-align: center;\">30<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Kansas<\/strong><\/td>\n<td style=\"text-align: center;\">24<\/td>\n<td style=\"text-align: center;\"><strong>Vermont<\/strong><\/td>\n<td style=\"text-align: center;\">30<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Alaska<\/strong><\/td>\n<td style=\"text-align: center;\">25<\/td>\n<td style=\"text-align: center;\"><strong>Mississippi<\/strong><\/td>\n<td style=\"text-align: center;\">31<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Georgia<\/strong><\/td>\n<td style=\"text-align: center;\">25<\/td>\n<td style=\"text-align: center;\"><strong>North Carolina<\/strong><\/td>\n<td style=\"text-align: center;\">31<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Iowa<\/strong><\/td>\n<td style=\"text-align: center;\">25<\/td>\n<td style=\"text-align: center;\"><strong>Pennsylvania<\/strong><\/td>\n<td style=\"text-align: center;\">31<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Arkansas<\/strong><\/td>\n<td style=\"text-align: center;\">26<\/td>\n<td style=\"text-align: center;\"><strong>Maryland<\/strong><\/td>\n<td style=\"text-align: center;\">32<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Oregon<\/strong><\/td>\n<td style=\"text-align: center;\">26<\/td>\n<td style=\"text-align: center;\"><strong>Nevada<\/strong><\/td>\n<td style=\"text-align: center;\">32<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>District of Columbia<\/strong><\/td>\n<td style=\"text-align: center;\">27<\/td>\n<td style=\"text-align: center;\"><strong>Wyoming<\/strong><\/td>\n<td style=\"text-align: center;\">32<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>New Mexico<\/strong><\/td>\n<td style=\"text-align: center;\">27<\/td>\n<td style=\"text-align: center;\"><strong>Louisiana<\/strong><\/td>\n<td style=\"text-align: center;\">33<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Virginia<\/strong><\/td>\n<td style=\"text-align: center;\">27<\/td>\n<td style=\"text-align: center;\"><strong>South Dakota<\/strong><\/td>\n<td style=\"text-align: center;\">33<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Arizona<\/strong><\/td>\n<td style=\"text-align: center;\">28<\/td>\n<td style=\"text-align: center;\"><strong>Washington<\/strong><\/td>\n<td style=\"text-align: center;\">33<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>California<\/strong><\/td>\n<td style=\"text-align: center;\">28<\/td>\n<td style=\"text-align: center;\"><strong>Wisconsin<\/strong><\/td>\n<td style=\"text-align: center;\">33<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Colorado<\/strong><\/td>\n<td style=\"text-align: center;\">28<\/td>\n<td style=\"text-align: center;\"><strong>Illinois<\/strong><\/td>\n<td style=\"text-align: center;\">34<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Michigan<\/strong><\/td>\n<td style=\"text-align: center;\">28<\/td>\n<td style=\"text-align: center;\"><strong>Missouri<\/strong><\/td>\n<td style=\"text-align: center;\">34<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>New Jersey<\/strong><\/td>\n<td style=\"text-align: center;\">28<\/td>\n<td style=\"text-align: center;\"><strong>Ohio<\/strong><\/td>\n<td style=\"text-align: center;\">34<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>West Virginia<\/strong><\/td>\n<td style=\"text-align: center;\">28<\/td>\n<td style=\"text-align: center;\"><strong>Massachusetts<\/strong><\/td>\n<td style=\"text-align: center;\">35<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Florida<\/strong><\/td>\n<td style=\"text-align: center;\">29<\/td>\n<td style=\"text-align: center;\"><strong>Nebraska<\/strong><\/td>\n<td style=\"text-align: center;\">35<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Idaho<\/strong><\/td>\n<td style=\"text-align: center;\">29<\/td>\n<td style=\"text-align: center;\"><strong>Connecticut<\/strong><\/td>\n<td style=\"text-align: center;\">36<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Indiana<\/strong><\/td>\n<td style=\"text-align: center;\">29<\/td>\n<td style=\"text-align: center;\"><strong>Rhode Island<\/strong><\/td>\n<td style=\"text-align: center;\">38<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Minnesota<\/strong><\/td>\n<td style=\"text-align: center;\">29<\/td>\n<td style=\"text-align: center;\"><strong>Texas<\/strong><\/td>\n<td style=\"text-align: center;\">38<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>New York<\/strong><\/td>\n<td style=\"text-align: center;\">29<\/td>\n<td style=\"text-align: center;\"><strong>Hawaii<\/strong><\/td>\n<td style=\"text-align: center;\">41<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Oklahoma<\/strong><\/td>\n<td style=\"text-align: center;\">29<\/td>\n<td style=\"text-align: center;\"><strong>South Carolina<\/strong><\/td>\n<td style=\"text-align: center;\">41<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Tennessee<\/strong><\/td>\n<td style=\"text-align: center;\">29<\/td>\n<td style=\"text-align: center;\"><strong>North Dakota<\/strong><\/td>\n<td style=\"text-align: center;\">42<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Alabama<\/strong><\/td>\n<td style=\"text-align: center;\">30<\/td>\n<td style=\"text-align: center;\"><strong>Montana<\/strong><\/td>\n<td style=\"text-align: center;\">44<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Delaware<\/strong><\/td>\n<td style=\"text-align: center;\">30<\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 8<\/h3>\n<p>Which state(s) in the list below is a lower outlier? In other words, which has an unusually low percentage of drivers involved in fatal crashes who were impaired by alcohol? Choose all that apply.<\/p>\n<p style=\"padding-left: 30px;\">a) Kentucky<\/p>\n<p style=\"padding-left: 30px;\">b) Kansas<\/p>\n<p style=\"padding-left: 30px;\">c) Utah<\/p>\n<p style=\"padding-left: 30px;\">d) Alaska<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q609285\">Hint<\/span><\/p>\n<div id=\"q609285\" class=\"hidden-answer\" style=\"display: none\">Use the IQR and the definition of <em>outlier<\/em>.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 9<\/h3>\n<p>Which of the following states have unusually high percentages of drivers involved in fatal crashes who were impaired by alcohol?<\/p>\n<p style=\"padding-left: 30px;\">a) Texas, South Carolina, Montana<\/p>\n<p style=\"padding-left: 30px;\">b) Montana, North Dakota, South Carolina, Hawaii<\/p>\n<p style=\"padding-left: 30px;\">c) Montana, North Dakota, South Carolina<\/p>\n<p style=\"padding-left: 30px;\">d) Texas, South Carolina, Montana, Rhode Island<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q96884\">Hint<\/span><\/p>\n<div id=\"q96884\" class=\"hidden-answer\" style=\"display: none\">Make sure to include all states that are considered to be upper outliers.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 10<\/h3>\n<p>Without computing the mean of the percentage of drivers involved in fatal crashes who were impaired by alcohol, make a prediction about whether the mean and median will be very different or fairly similar.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q633143\">Hint<\/span><\/p>\n<div id=\"q633143\" class=\"hidden-answer\" style=\"display: none\">Imagine how the outliers might appear as tails on a histogram or dotplot and the symmetry (or lack thereof) of the IQR about the median.<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<p>Now, let&#8217;s use technology to explore the dataset.<\/p>\n<div class=\"textbox\">\n<p>Go to the Describing and Exploring Quantitative Variables tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\" target=\"_blank\" rel=\"noopener\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>.<\/p>\n<p style=\"padding-left: 30px;\">Step 1) Select the <strong>Single Group<\/strong> tab.<\/p>\n<p style=\"padding-left: 30px;\">Step 2) Locate the dropdown under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.<\/p>\n<p style=\"padding-left: 30px;\">Step 3) Locate the drop-down menu under <strong>Dataset<\/strong> and select <strong>Bad Drivers (alcohol)<\/strong>.<\/p>\n<p style=\"padding-left: 30px;\">Step 4) Use the tool to compute the mean percentage of drivers involved in fatal collisions who were alcohol-impaired.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 11<\/h3>\n<p>Which of the following describes your findings?<\/p>\n<p style=\"padding-left: 30px;\">a) The mean is much higher than the median.<\/p>\n<p style=\"padding-left: 30px;\">b) The median is much higher than the mean.<\/p>\n<p style=\"padding-left: 30px;\">c) The mean and the median are about the same.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q363793\">Hint<\/span><\/p>\n<div id=\"q363793\" class=\"hidden-answer\" style=\"display: none\">The mean will appear in the Descriptive Statistics<\/div>\n<\/div>\n<\/div>\n<h3 id=\"identshape_bxplt\">Identifying the Shape of a Distribution from a Boxplot<\/h3>\n<div class=\"textbox key-takeaways\">\n<h3>question 12<\/h3>\n<p>Just as histograms and dotplots can tell us about the distribution of a quantitative variable, so can a boxplot. For each boxplot below, choose the description that matches the shape of the data\u2019s distribution. (Note that boxplots can be oriented vertically, as we saw previously, or horizontally, as we see below.)<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: left;\">\n<table>\n<tbody>\n<tr>\n<td>Boxplot<\/td>\n<td>Distribution<\/td>\n<\/tr>\n<tr>\n<td><strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1022\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11223158\/ChartPicture4-300x36.png\" alt=\"A boxplot numbered in increments of 50 from 0 to 350. The low point of the plot is at 50 and the high point is at approximately 290. The low end of the box is at approximately 140, the high end is at approximately 210, and the middle line is at approximately 180. There is also a point at 0 and one at approximately 340.\" width=\"975\" height=\"117\" \/><\/strong><\/td>\n<td>a) left skewed<\/p>\n<p>b) symmetric<\/p>\n<p>c) right skewed<\/p>\n<p><span style=\"background-color: #ffff00;\">include dropdown options similar to Question 10 in WTK 4C<\/span><\/td>\n<\/tr>\n<tr>\n<td><strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1023\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11223205\/ChartPicture5-300x35.png\" alt=\"A boxplot numbered in increments of 5 from 0 to 25. The low end of the plot is at 0 and the high end is at approximately 8. The low edge of the box is at approximately 1, while the high edge is at approximately 4 and the center line is at approximately 2. There are also points at approximately 9, 10, 12, 13, 14, 15, 16, 18, 20, 22, and 24.\" width=\"947\" height=\"111\" \/><\/strong><\/td>\n<td>a) left skewed<\/p>\n<p>b) symmetric<\/p>\n<p>c) right skewed<\/p>\n<p><span style=\"background-color: #ffff00;\">include dropdown options similar to Question 10 in WTK 4C<\/span><\/td>\n<\/tr>\n<tr>\n<td><strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1024\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11223210\/ChartPicture6-300x37.png\" alt=\"A box plot labeled in increments of 5 from 35 to 60. The low point of the box plot is at 55 and the high point is at approximately 61. The low end of the box is at approximately 56, the high end is at approximately 60, and the middle line is at approximately 58. There are also points at approximately 35, 36, 37, and 38.\" width=\"1058\" height=\"129\" \/><\/strong><\/td>\n<td>a) left skewed<\/p>\n<p>b) symmetric<\/p>\n<p>c) right skewed<\/p>\n<p><span style=\"background-color: #ffff00;\">include dropdown options similar to Question 10 in WTK 4C<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q41394\">Hint<\/span><\/p>\n<div id=\"q41394\" class=\"hidden-answer\" style=\"display: none\">What effect do outliers have on the skew of data?<\/div>\n<\/div>\n<\/div>\n<h2>Summary<\/h2>\n<p>In this section, you&#8217;ve learned about boxplots: how to calculate the five-number summary, how to read these numbers from a boxplot, and how to identify outliers in a dataset using the interquartile range. Let&#8217;s summarize where these skills showed up in the material.<\/p>\n<ul>\n<li>In Questions 1 and 7, you identified the features of a boxplot.<\/li>\n<li>In Questions 2 &#8211; 4, you interpreted the features of a boxplot.<\/li>\n<li>In Questions 5, 6, 8, and 9, you identified outliers in a dataset.<\/li>\n<li>In Questions 10 &#8211; 12, you related the boxplot of a quantitative variable to its distribution.<\/li>\n<\/ul>\n<p>Being able to calculate and identify features of a boxplot and relate the boxplot and distribution of a quantitative variable are necessary statistical skills and will be used in the next activity. If you feel comfortable with these skills, please move on!<\/p>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-462-1\">Chalabi, M. (2014, October 24). <em>Dear Mona, which state has the worst driver?<\/em> FiveThirtyEight. https:\/\/fivethirtyeight.com\/features\/which-state-has-the-worst-drivers\/ <a href=\"#return-footnote-462-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":25777,"menu_order":24,"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-462","chapter","type-chapter","status-publish","hentry"],"part":621,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/462","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\/25777"}],"version-history":[{"count":37,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/462\/revisions"}],"predecessor-version":[{"id":562,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/462\/revisions\/562"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/621"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/462\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=462"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=462"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=462"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=462"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}