{"id":3658,"date":"2022-03-09T14:20:30","date_gmt":"2022-03-09T14:20:30","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=3658"},"modified":"2022-03-16T17:44:03","modified_gmt":"2022-03-16T17:44:03","slug":"4b-comparing-variability-model-page-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/4b-comparing-variability-model-page-coreq\/","title":{"raw":"For UTC Testing -- Comparing Variability of Datasets: Corequisite Support Activity","rendered":"For UTC Testing &#8212; Comparing Variability of Datasets: Corequisite Support Activity"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>What you'll need to know<\/h3>\r\nIn this support activity you'll become familiar with the following:\r\n<ul>\r\n \t<li><a href=\"#DevMean\">Calculate the deviation from the mean of an observation in a dataset.<\/a><\/li>\r\n<\/ul>\r\nYou will also have an opportunity to refresh the following skills:\r\n<ul>\r\n \t<li><a href=\"#MeanMedian\">Understand the difference between mean and median.<\/a><\/li>\r\n \t<li><a href=\"#SampleSizeMean\">Use technology to calculate the sample size and mean of a distribution.<\/a><\/li>\r\n \t<li><a href=\"#LargeNumbers\">Interpret large numbers.<\/a><\/li>\r\n \t<li><a href=\"#name\">Compare differently signed numbers.<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the next section of the course material and in the following activity, you will need to understand and calculate the deviation from the mean. You will be extending this knowledge in the course section to understanding what the spread of a dataset is and how it is calculated. For now, let's concentrate on refreshing necessary skills and learning about\u00a0<strong>deviation from the mean<\/strong>.\r\n<h2>Deviation from the Mean<\/h2>\r\nConsider the following dotplot of the exam scores for two different math classes on their midterm. The class average was\u00a0[latex]70[\/latex] points for both Class 1 and Class 2.\r\n\r\n<strong><img class=\"alignnone wp-image-999\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11192200\/Picture32-300x139.png\" alt=\"Two dot plots of exam scores. One shows dots clustered primarily between 60 and 80, while the other shows dots spread out between 40 and 100.\" width=\"900\" height=\"417\" \/><\/strong>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\n[ohm_question]241043[\/ohm_question]\r\n\r\n[reveal-answer q=\"282689\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"282689\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the next activity, we will be measuring the variability of a dataset. We do this by measuring the distance, known as <strong>deviation<\/strong>, of an observed value from the mean. Let\u2019s look at an example from the real world.\r\n\r\n<img class=\"gnt_em_img_i aligncenter\" style=\"height: 339px;\" src=\"https:\/\/www.gannett-cdn.com\/media\/2018\/07\/08\/USATODAY\/usatsports\/hurricane-sandy-damage1.jpg?width=660&amp;height=372&amp;fit=crop&amp;format=pjpg&amp;auto=webp\" srcset=\"https:\/\/www.gannett-cdn.com\/media\/2018\/07\/08\/USATODAY\/usatsports\/hurricane-sandy-damage1.jpg?width=1320&amp;height=744&amp;fit=crop&amp;format=pjpg&amp;auto=webp 2x\" alt=\"The 2018 extreme weather season continues to unfold. A city is shown in the aftermath of a hurricane.\" width=\"601\" height=\"372\" \/>\r\n\r\nHurricanes cause extensive amounts of damage. In this corequisite support activity, we will consider the amount of damage in dollars of the\u00a0[latex]30[\/latex] most expensive hurricanes to have hit the U.S. mainland between 1990 and 2010. In order to explore this dataset, you will need to recall what you have learned about measures of center. We'll concentrate on the mean of a quantitative distribution in this activity.\r\n<h3>Mean vs. median<\/h3>\r\n<span id=\"MeanMedian\">Before we move on, take a moment to recall the difference between mean and median.<\/span>\r\n<div class=\"textbox examples\">\r\n<h3>recall<\/h3>\r\nDo you recall the two measures of center you learned about in the previous section of the course: mean and median?\r\n\r\nCore skill: [reveal-answer q=\"127055\"]Define the mean and the median of a dataset[\/reveal-answer]\r\n[hidden-answer a=\"127055\"]\r\n\r\nThe\u00a0<strong>mean<\/strong> of a dataset is the \"balancing weight\" of the data values, what is commonly called the \"average.\"\r\n<ul>\r\n \t<li>To calculate the mean, divide the sum of all the data values by the number of them.<\/li>\r\n<\/ul>\r\nThe\u00a0<strong>median<\/strong> of a dataset is the \"middle-most\" of the data values, the\u00a0[latex]50[\/latex]<sup>th<\/sup> percentile, and splits the data in half.\r\n<ul>\r\n \t<li>To identify the median, order the numbers then locate the middle number. Half the data will be above the median and half will be below it. If the dataset contains an even amount of values, take the mean of the middle two values.<\/li>\r\n<\/ul>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nLet's go to the technology to analyze the dataset \"Hurricane Damage.\"\r\n<h3 id=\"SampleSizeMean\">Sample size and mean<\/h3>\r\n<div class=\"textbox\">\r\n\r\nGo to the Describing and Exploring Quantitative Variables tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\" target=\"_blank\" rel=\"noopener\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>.\r\n<p style=\"padding-left: 30px;\">Step 1) Select the <strong>Single Group<\/strong> tab.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 2) Locate the drop-down menu under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 3) Locate the drop-down menu under <strong>Dataset<\/strong> and select <strong>Hurricane Damage<\/strong>.<\/p>\r\n\r\n<\/div>\r\nIn the descriptive statistics at the top of the applet, you will see the sample size [latex]\\left(n\\right)[\/latex] and the mean [latex]\\left(\\bar{x}\\right)[\/latex] of the dataset.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\n[ohm_question]241044[\/ohm_question]\r\n\r\n[reveal-answer q=\"943053\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"943053\"]Make sure the Dataset \"Hurricane Damage\" is selected then locate the Sample Size in Descriptive Statistics.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 3<\/h3>\r\n[ohm_question]241045[\/ohm_question]\r\n\r\n[reveal-answer q=\"77790\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"77790\"]What is the name of the variable of interest? Use units when expressing your answer to put it in context.[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"DevMean\">Deviation from the mean<\/h3>\r\nA <strong>deviation from the mean<\/strong> is the distance between an observation, [latex]x[\/latex], in a dataset and the mean, [latex]\\bar{x}[\/latex], of the dataset. To calculate the deviation from the mean, subtract the sample mean from each observation in the dataset [latex]\\left(x-\\bar{x}\\right)[\/latex].\r\n\r\nPractice calculating the deviation from the mean in the following interactive example. Then, for the data table that follows, calculate the deviation from the mean to answer Question 4.\r\n<div class=\"textbox exercises\">\r\n<h3>Interactive Example<\/h3>\r\nSeven of\u00a0[latex]50[\/latex] observations a student made about her commute time by bicycle from her apartment to school are listed in the following table. Her mean commute time was\u00a0[latex]10[\/latex] minutes,\u00a0[latex]\\bar{x}=10[\/latex]. Use this information to calculate the deviation from the mean [latex]\\left(x-\\bar{x}\\right)[\/latex] for each of the seven observations given.\r\n\r\nExample: See the first entry in the table: an observed 8 minute commute time.\u00a0 Given a mean commute time of 10 minutes, the deviation from the mean for the observation of 8 minutes is [latex]8-10=-2[\/latex].\r\n\r\nComplete the table then check your answers below.\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\">\r\n<p style=\"text-align: center;\"><strong><strong>Bike Ride to School (in minutes)<\/strong><\/strong><\/p>\r\n<p style=\"text-align: center;\"><strong>[latex]x[\/latex]<\/strong><\/p>\r\n<\/td>\r\n<td style=\"width: 50%; text-align: center;\">\r\n<p style=\"text-align: center;\"><strong>Deviation from the Mean (in minutes)<\/strong><\/p>\r\n<p style=\"text-align: center;\"><strong>[latex]x-\\bar{x}[\/latex]<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\"><strong><strong>8<\/strong><\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center;\">[latex]8 - 10 = -2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\"><strong>10<\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\"><strong>12<\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\"><strong>14<\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\"><strong>5<\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\"><strong>15<\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\"><strong>9<\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[reveal-answer q=\"129517\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"129517\"]\r\n<table style=\"border-collapse: collapse; width: 100%; height: 151px;\" border=\"1\">\r\n<tbody>\r\n<tr style=\"height: 67px;\">\r\n<td style=\"width: 50%; height: 67px;\">\r\n<p style=\"text-align: center;\"><strong>Bike Ride to School (in minutes)<\/strong><\/p>\r\n<p style=\"text-align: center;\"><strong>[latex]x[\/latex]<\/strong><\/p>\r\n<\/td>\r\n<td style=\"width: 50%; height: 67px;\">\r\n<p style=\"text-align: center;\"><strong>Deviation from the Mean (in minutes)<\/strong><\/p>\r\n<p style=\"text-align: center;\"><strong>[latex]x-\\bar{x}[\/latex]<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 50%; text-align: center; height: 12px;\"><strong>8<\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center; height: 12px;\">[latex]8 - 10 = -2[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 50%; text-align: center; height: 12px;\"><strong>10<\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center; height: 12px;\">[latex]10 - 10 = 0[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 50%; text-align: center; height: 12px;\"><strong>12<\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center; height: 12px;\">[latex]12 - 10 = 2[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 50%; text-align: center; height: 12px;\"><strong>14<\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center; height: 12px;\">[latex]14 - 10 = 4[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 50%; text-align: center; height: 12px;\"><strong>5<\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center; height: 12px;\">[latex]5 - 10 = -5[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 50%; text-align: center; height: 12px;\"><strong>15<\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center; height: 12px;\">[latex]15 - 10 = 5[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 50%; text-align: center; height: 12px;\"><strong>9<\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center; height: 12px;\">[latex]9 - 10 = -1[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nEach value listed in the first column is identified as an observation. Subtract the given mean, [latex]\\bar{x}=10[\/latex] from each observation to obtain the deviation from the mean. For example, the observation of\u00a0[latex]12[\/latex] minutes results in that ride to school being\u00a0[latex]2[\/latex] minutes above the mean (or a longer ride), while the observation of\u00a0[latex]5[\/latex] results in that ride to school being\u00a0[latex]5[\/latex] minutes below the mean (or a shorter ride).\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow it's your turn to calculate the deviation from the mean for ten of the 30 hurricane damage observations from the dataset \"Hurricane Damage.\" Follow the instructions above to reopen the dataset if you have closed it.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\n[ohm_question]241046[\/ohm_question]\r\n<div align=\"left\">\r\n\r\n[reveal-answer q=\"719277\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"719277\"]Locate the value for [latex]\\bar{x}[\/latex] in Descriptive Statistics.[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<h3>Representations of large numbers<\/h3>\r\n<span id=\"LargeNumbers\">Before answering Question 5 below, take a moment to consider the ways in which large numbers can be represented. In the table above, we see hurricane damage in millions of dollars in the column on the left. Look at the the bottom number in the column:\u00a0[latex]11,227[\/latex]. Presumably, that means\u00a0[latex]11,227[\/latex] millions of dollars. But what does that mean in terms of a pure number?\u00a0The hurricanes contributing to this data were catastrophic, causing billions of dollars of damage. Use the recall box below to see how to write a number like [latex]11,227[\/latex]\u00a0<em>million dollars\u00a0<\/em>as $[latex]11.227[\/latex]\u00a0<em>billion<\/em>.<\/span><span id=\"LargeNumbers\">\u00a0You may also see the Student Resource: <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Number-Word+Combinations.pdf\"><em>Number-Word Combinations<\/em><\/a>.<\/span>\r\n<div class=\"textbox examples\">\r\n<h3>recall<\/h3>\r\nIt can be helpful to communicate large numbers using a combination of numbers and words.\r\n\r\nWhen reading text containing a large value, we generally comprehend a number written as a combination of numbers and words more quickly than we do the pure number form. For example, it may take a moment to make sense of $[latex]1,250,000[\/latex] but we understand immediately what $[latex]1.25[\/latex] million represents.\r\n\r\nTake a moment to refresh your understanding of combining numbers and words to express large numbers.\r\n\r\nCore Skill:\r\n[reveal-answer q=\"301175\"]Express and interpret large numbers[\/reveal-answer]\r\n[hidden-answer a=\"301175\"]\r\n\r\nWhen a number is so large that it would be unwieldy to list all of its digits on a page, we often use a power of ten to represent some of the digits.\r\n\r\nFor example, one million is written\u00a0[latex]1,000,000[\/latex]: a one followed by six zeros: [latex]10^{6}[\/latex].\r\n\r\nA billion is a thousand million. It's written\u00a0[latex]1,000,000,000[\/latex]: a one followed by nine zeros; [latex]10^{9}[\/latex].\r\n<p style=\"padding-left: 30px;\">Or,\u00a0[latex]1,000[\/latex] followed by six zeros, since a thousand million is\u00a0[latex]1,000[\/latex] times [latex]1,000,000[\/latex].<\/p>\r\n<p style=\"padding-left: 30px;\">[latex]10^{3}\\times10^{6}=10^{3+6}=10^{9}[\/latex]<\/p>\r\nRecall, when we multiply by a million, we move the decimal point six places to the right in the number we are multiplying. That is, we multiply by [latex]10^{6}[\/latex]\r\n\r\nWe can express multiples of millions or billions using a combination of digits and words.\r\n\r\nEx. Write\u00a0[latex]35[\/latex] million as a number.\r\n<p style=\"padding-left: 30px;\">[latex]35\\times1,000,000=35,000,000[\/latex]<\/p>\r\nEx. Write\u00a0[latex]350[\/latex] million as a number.\r\n<p style=\"padding-left: 30px;\">[latex]350\\times1,000,000=350,000,000[\/latex]<\/p>\r\nEx. Write\u00a0[latex]3500[\/latex] million as a number.\r\n<p style=\"padding-left: 30px;\">[latex]3500\\times1,000,000=3,500,000,000[\/latex], which is 3 billion, 500 million.<\/p>\r\nNote that the final row of the table above gives\u00a0[latex]11,227[\/latex] millions of dollars in hurricane damage. How much is that in billions?\r\n\r\nEx. Write\u00a0[latex]11,227[\/latex] million as a number.\r\n<p style=\"padding-left: 30px;\">[latex]11,227\\times1,000,000=11,227,000,000[\/latex], which is\u00a0[latex]11[\/latex] billion,\u00a0[latex]227[\/latex] million.<\/p>\r\nWe can also write this as\u00a0[latex]11.227[\/latex] billion.\r\n\r\nEx. [latex]11.227\\times1,000,000,000=11.227\\times10^{9}=11,227,000,000[\/latex] by moving the decimal\u00a0[latex]9[\/latex] places to the right.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow, try Question 5.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 5<\/h3>\r\n[ohm_question]241050[\/ohm_question]\r\n\r\n[reveal-answer q=\"101343\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"101343\"]What do <em>you<\/em> think? Use the recall box above as a guide.[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3>Signed numbers as proximities<\/h3>\r\nBefore answering Question 6 and 7, you may wish to refresh your understanding of distance as an absolute value.\r\n<div class=\"textbox examples\">\r\n<h3>recall<\/h3>\r\nWhen discussing the difference between two numbers as a distance, use the concept of absolute value to help make sense of the result. For example, we would say the difference between\u00a0[latex]-1[\/latex] and\u00a0[latex]3[\/latex] is four units even though taking their difference may result in a negative or a positive depending upon which we subtract from which.\r\n<p style=\"text-align: center;\">[latex]-1-3=-4\\qquad\\text{ and }\\qquad3 - \\left(-1\\right)=4[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]|-1-3|=4\\qquad\\text{ and }\\qquad|3 - \\left(-1\\right)|=4[\/latex]<\/p>\r\nSee the skill below if needed for an example of how absolute value can be applied in Questions 6 and 7 and how to interpret positive and negative results when calculating deviation from the mean.\r\n\r\nCore skill:\r\n[reveal-answer q=\"761688\"]Express a distance as an absolute value.[\/reveal-answer]\r\n[hidden-answer a=\"761688\"]\r\n\r\nSay the mean of a sample is given as [latex]\\bar{x}=12[\/latex] and the observations\u00a0[latex]7[\/latex] and\u00a0[latex]15[\/latex] are contained in the sample. Which value is closer to the mean?\r\n<p style=\"padding-left: 30px;\">For the value of\u00a0[latex]7[\/latex], [latex]x-\\bar{x} = 7-12=-5[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">For the value of\u00a0[latex]15[\/latex], [latex]x-\\bar{x} = 15-12=3[\/latex]<\/p>\r\nWe might be tempted to conclude that\u00a0[latex]7[\/latex] is closer since\u00a0[latex]-5[\/latex] is a smaller number than\u00a0[latex]3[\/latex]. But distance is calculated using absolute value. The value of\u00a0[latex]7[\/latex] is\u00a0[latex]5[\/latex] units away from the mean (to the left) while the value of\u00a0[latex]15[\/latex] is only\u00a0[latex]3[\/latex] units away from the mean (to the right). To calculate which is closer, use absolute value.\r\n<p style=\"padding-left: 30px;\">For the value of\u00a0[latex]7[\/latex], [latex]|7-12|=|-5|=5[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">For the value of\u00a0[latex]15[\/latex], [latex]|15-12|=|3|=3[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 6<\/h3>\r\n[ohm_question]241051[\/ohm_question]\r\n\r\n[reveal-answer q=\"282551\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"282551\"]For each calculation, you subtracted the mean from the observed value. Why would some result in a negative deviation? See the interactive example above for an explanation.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 7<\/h3>\r\n[ohm_question]241052[\/ohm_question]\r\n\r\n[reveal-answer q=\"421294\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"421294\"]Think of <em>closer<\/em> as being a distance (i.e., absolute value).[\/hidden-answer]\r\n\r\n<\/div>\r\nYou've learned how to calculate the deviation from the mean in this activity, which you'll be using in the upcoming section and following activity. You've also refreshed several mathematical skills and statistical definitions. Hopefully, you are feeling comfortable enough with these concepts to move on to the next section.","rendered":"<div class=\"textbox learning-objectives\">\n<h3>What you&#8217;ll need to know<\/h3>\n<p>In this support activity you&#8217;ll become familiar with the following:<\/p>\n<ul>\n<li><a href=\"#DevMean\">Calculate the deviation from the mean of an observation in a dataset.<\/a><\/li>\n<\/ul>\n<p>You will also have an opportunity to refresh the following skills:<\/p>\n<ul>\n<li><a href=\"#MeanMedian\">Understand the difference between mean and median.<\/a><\/li>\n<li><a href=\"#SampleSizeMean\">Use technology to calculate the sample size and mean of a distribution.<\/a><\/li>\n<li><a href=\"#LargeNumbers\">Interpret large numbers.<\/a><\/li>\n<li><a href=\"#name\">Compare differently signed numbers.<\/a><\/li>\n<\/ul>\n<\/div>\n<p>In the next section of the course material and in the following activity, you will need to understand and calculate the deviation from the mean. You will be extending this knowledge in the course section to understanding what the spread of a dataset is and how it is calculated. For now, let&#8217;s concentrate on refreshing necessary skills and learning about\u00a0<strong>deviation from the mean<\/strong>.<\/p>\n<h2>Deviation from the Mean<\/h2>\n<p>Consider the following dotplot of the exam scores for two different math classes on their midterm. The class average was\u00a0[latex]70[\/latex] points for both Class 1 and Class 2.<\/p>\n<p><strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-999\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11192200\/Picture32-300x139.png\" alt=\"Two dot plots of exam scores. One shows dots clustered primarily between 60 and 80, while the other shows dots spread out between 40 and 100.\" width=\"900\" height=\"417\" \/><\/strong><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241043\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241043&theme=oea&iframe_resize_id=ohm241043&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q282689\">Hint<\/span><\/p>\n<div id=\"q282689\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<p>In the next activity, we will be measuring the variability of a dataset. We do this by measuring the distance, known as <strong>deviation<\/strong>, of an observed value from the mean. Let\u2019s look at an example from the real world.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"gnt_em_img_i aligncenter\" style=\"height: 339px;\" src=\"https:\/\/www.gannett-cdn.com\/media\/2018\/07\/08\/USATODAY\/usatsports\/hurricane-sandy-damage1.jpg?width=660&amp;height=372&amp;fit=crop&amp;format=pjpg&amp;auto=webp\" srcset=\"https:\/\/www.gannett-cdn.com\/media\/2018\/07\/08\/USATODAY\/usatsports\/hurricane-sandy-damage1.jpg?width=1320&amp;height=744&amp;fit=crop&amp;format=pjpg&amp;auto=webp 2x\" alt=\"The 2018 extreme weather season continues to unfold. A city is shown in the aftermath of a hurricane.\" width=\"601\" height=\"372\" \/><\/p>\n<p>Hurricanes cause extensive amounts of damage. In this corequisite support activity, we will consider the amount of damage in dollars of the\u00a0[latex]30[\/latex] most expensive hurricanes to have hit the U.S. mainland between 1990 and 2010. In order to explore this dataset, you will need to recall what you have learned about measures of center. We&#8217;ll concentrate on the mean of a quantitative distribution in this activity.<\/p>\n<h3>Mean vs. median<\/h3>\n<p><span id=\"MeanMedian\">Before we move on, take a moment to recall the difference between mean and median.<\/span><\/p>\n<div class=\"textbox examples\">\n<h3>recall<\/h3>\n<p>Do you recall the two measures of center you learned about in the previous section of the course: mean and median?<\/p>\n<p>Core skill: <\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q127055\">Define the mean and the median of a dataset<\/span><\/p>\n<div id=\"q127055\" class=\"hidden-answer\" style=\"display: none\">\n<p>The\u00a0<strong>mean<\/strong> of a dataset is the &#8220;balancing weight&#8221; of the data values, what is commonly called the &#8220;average.&#8221;<\/p>\n<ul>\n<li>To calculate the mean, divide the sum of all the data values by the number of them.<\/li>\n<\/ul>\n<p>The\u00a0<strong>median<\/strong> of a dataset is the &#8220;middle-most&#8221; of the data values, the\u00a0[latex]50[\/latex]<sup>th<\/sup> percentile, and splits the data in half.<\/p>\n<ul>\n<li>To identify the median, order the numbers then locate the middle number. Half the data will be above the median and half will be below it. If the dataset contains an even amount of values, take the mean of the middle two values.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<p>Let&#8217;s go to the technology to analyze the dataset &#8220;Hurricane Damage.&#8221;<\/p>\n<h3 id=\"SampleSizeMean\">Sample size and mean<\/h3>\n<div class=\"textbox\">\n<p>Go to the Describing and Exploring Quantitative Variables tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\" target=\"_blank\" rel=\"noopener\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>.<\/p>\n<p style=\"padding-left: 30px;\">Step 1) Select the <strong>Single Group<\/strong> tab.<\/p>\n<p style=\"padding-left: 30px;\">Step 2) Locate the drop-down menu under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.<\/p>\n<p style=\"padding-left: 30px;\">Step 3) Locate the drop-down menu under <strong>Dataset<\/strong> and select <strong>Hurricane Damage<\/strong>.<\/p>\n<\/div>\n<p>In the descriptive statistics at the top of the applet, you will see the sample size [latex]\\left(n\\right)[\/latex] and the mean [latex]\\left(\\bar{x}\\right)[\/latex] of the dataset.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241044\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241044&theme=oea&iframe_resize_id=ohm241044&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q943053\">Hint<\/span><\/p>\n<div id=\"q943053\" class=\"hidden-answer\" style=\"display: none\">Make sure the Dataset &#8220;Hurricane Damage&#8221; is selected then locate the Sample Size in Descriptive Statistics.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241045\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241045&theme=oea&iframe_resize_id=ohm241045&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q77790\">Hint<\/span><\/p>\n<div id=\"q77790\" class=\"hidden-answer\" style=\"display: none\">What is the name of the variable of interest? Use units when expressing your answer to put it in context.<\/div>\n<\/div>\n<\/div>\n<h3 id=\"DevMean\">Deviation from the mean<\/h3>\n<p>A <strong>deviation from the mean<\/strong> is the distance between an observation, [latex]x[\/latex], in a dataset and the mean, [latex]\\bar{x}[\/latex], of the dataset. To calculate the deviation from the mean, subtract the sample mean from each observation in the dataset [latex]\\left(x-\\bar{x}\\right)[\/latex].<\/p>\n<p>Practice calculating the deviation from the mean in the following interactive example. Then, for the data table that follows, calculate the deviation from the mean to answer Question 4.<\/p>\n<div class=\"textbox exercises\">\n<h3>Interactive Example<\/h3>\n<p>Seven of\u00a0[latex]50[\/latex] observations a student made about her commute time by bicycle from her apartment to school are listed in the following table. Her mean commute time was\u00a0[latex]10[\/latex] minutes,\u00a0[latex]\\bar{x}=10[\/latex]. Use this information to calculate the deviation from the mean [latex]\\left(x-\\bar{x}\\right)[\/latex] for each of the seven observations given.<\/p>\n<p>Example: See the first entry in the table: an observed 8 minute commute time.\u00a0 Given a mean commute time of 10 minutes, the deviation from the mean for the observation of 8 minutes is [latex]8-10=-2[\/latex].<\/p>\n<p>Complete the table then check your answers below.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%; text-align: center;\">\n<p style=\"text-align: center;\"><strong><strong>Bike Ride to School (in minutes)<\/strong><\/strong><\/p>\n<p style=\"text-align: center;\"><strong>[latex]x[\/latex]<\/strong><\/p>\n<\/td>\n<td style=\"width: 50%; text-align: center;\">\n<p style=\"text-align: center;\"><strong>Deviation from the Mean (in minutes)<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>[latex]x-\\bar{x}[\/latex]<\/strong><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\"><strong><strong>8<\/strong><\/strong><\/td>\n<td style=\"width: 50%; text-align: center;\">[latex]8 - 10 = -2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\"><strong>10<\/strong><\/td>\n<td style=\"width: 50%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\"><strong>12<\/strong><\/td>\n<td style=\"width: 50%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\"><strong>14<\/strong><\/td>\n<td style=\"width: 50%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\"><strong>5<\/strong><\/td>\n<td style=\"width: 50%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\"><strong>15<\/strong><\/td>\n<td style=\"width: 50%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\"><strong>9<\/strong><\/td>\n<td style=\"width: 50%; 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=\"q129517\">Show Answer<\/span><\/p>\n<div id=\"q129517\" class=\"hidden-answer\" style=\"display: none\">\n<table style=\"border-collapse: collapse; width: 100%; height: 151px;\">\n<tbody>\n<tr style=\"height: 67px;\">\n<td style=\"width: 50%; height: 67px;\">\n<p style=\"text-align: center;\"><strong>Bike Ride to School (in minutes)<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>[latex]x[\/latex]<\/strong><\/p>\n<\/td>\n<td style=\"width: 50%; height: 67px;\">\n<p style=\"text-align: center;\"><strong>Deviation from the Mean (in minutes)<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>[latex]x-\\bar{x}[\/latex]<\/strong><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 50%; text-align: center; height: 12px;\"><strong>8<\/strong><\/td>\n<td style=\"width: 50%; text-align: center; height: 12px;\">[latex]8 - 10 = -2[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 50%; text-align: center; height: 12px;\"><strong>10<\/strong><\/td>\n<td style=\"width: 50%; text-align: center; height: 12px;\">[latex]10 - 10 = 0[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 50%; text-align: center; height: 12px;\"><strong>12<\/strong><\/td>\n<td style=\"width: 50%; text-align: center; height: 12px;\">[latex]12 - 10 = 2[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 50%; text-align: center; height: 12px;\"><strong>14<\/strong><\/td>\n<td style=\"width: 50%; text-align: center; height: 12px;\">[latex]14 - 10 = 4[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 50%; text-align: center; height: 12px;\"><strong>5<\/strong><\/td>\n<td style=\"width: 50%; text-align: center; height: 12px;\">[latex]5 - 10 = -5[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 50%; text-align: center; height: 12px;\"><strong>15<\/strong><\/td>\n<td style=\"width: 50%; text-align: center; height: 12px;\">[latex]15 - 10 = 5[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 50%; text-align: center; height: 12px;\"><strong>9<\/strong><\/td>\n<td style=\"width: 50%; text-align: center; height: 12px;\">[latex]9 - 10 = -1[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Each value listed in the first column is identified as an observation. Subtract the given mean, [latex]\\bar{x}=10[\/latex] from each observation to obtain the deviation from the mean. For example, the observation of\u00a0[latex]12[\/latex] minutes results in that ride to school being\u00a0[latex]2[\/latex] minutes above the mean (or a longer ride), while the observation of\u00a0[latex]5[\/latex] results in that ride to school being\u00a0[latex]5[\/latex] minutes below the mean (or a shorter ride).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Now it&#8217;s your turn to calculate the deviation from the mean for ten of the 30 hurricane damage observations from the dataset &#8220;Hurricane Damage.&#8221; Follow the instructions above to reopen the dataset if you have closed it.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241046\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241046&theme=oea&iframe_resize_id=ohm241046&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div style=\"text-align: left;\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q719277\">Hint<\/span><\/p>\n<div id=\"q719277\" class=\"hidden-answer\" style=\"display: none\">Locate the value for [latex]\\bar{x}[\/latex] in Descriptive Statistics.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h3>Representations of large numbers<\/h3>\n<p><span id=\"LargeNumbers\">Before answering Question 5 below, take a moment to consider the ways in which large numbers can be represented. In the table above, we see hurricane damage in millions of dollars in the column on the left. Look at the the bottom number in the column:\u00a0[latex]11,227[\/latex]. Presumably, that means\u00a0[latex]11,227[\/latex] millions of dollars. But what does that mean in terms of a pure number?\u00a0The hurricanes contributing to this data were catastrophic, causing billions of dollars of damage. Use the recall box below to see how to write a number like [latex]11,227[\/latex]\u00a0<em>million dollars\u00a0<\/em>as $[latex]11.227[\/latex]\u00a0<em>billion<\/em>.<\/span><span id=\"LargeNumbers\">\u00a0You may also see the Student Resource: <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Number-Word+Combinations.pdf\"><em>Number-Word Combinations<\/em><\/a>.<\/span><\/p>\n<div class=\"textbox examples\">\n<h3>recall<\/h3>\n<p>It can be helpful to communicate large numbers using a combination of numbers and words.<\/p>\n<p>When reading text containing a large value, we generally comprehend a number written as a combination of numbers and words more quickly than we do the pure number form. For example, it may take a moment to make sense of $[latex]1,250,000[\/latex] but we understand immediately what $[latex]1.25[\/latex] million represents.<\/p>\n<p>Take a moment to refresh your understanding of combining numbers and words to express large numbers.<\/p>\n<p>Core Skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q301175\">Express and interpret large numbers<\/span><\/p>\n<div id=\"q301175\" class=\"hidden-answer\" style=\"display: none\">\n<p>When a number is so large that it would be unwieldy to list all of its digits on a page, we often use a power of ten to represent some of the digits.<\/p>\n<p>For example, one million is written\u00a0[latex]1,000,000[\/latex]: a one followed by six zeros: [latex]10^{6}[\/latex].<\/p>\n<p>A billion is a thousand million. It&#8217;s written\u00a0[latex]1,000,000,000[\/latex]: a one followed by nine zeros; [latex]10^{9}[\/latex].<\/p>\n<p style=\"padding-left: 30px;\">Or,\u00a0[latex]1,000[\/latex] followed by six zeros, since a thousand million is\u00a0[latex]1,000[\/latex] times [latex]1,000,000[\/latex].<\/p>\n<p style=\"padding-left: 30px;\">[latex]10^{3}\\times10^{6}=10^{3+6}=10^{9}[\/latex]<\/p>\n<p>Recall, when we multiply by a million, we move the decimal point six places to the right in the number we are multiplying. That is, we multiply by [latex]10^{6}[\/latex]<\/p>\n<p>We can express multiples of millions or billions using a combination of digits and words.<\/p>\n<p>Ex. Write\u00a0[latex]35[\/latex] million as a number.<\/p>\n<p style=\"padding-left: 30px;\">[latex]35\\times1,000,000=35,000,000[\/latex]<\/p>\n<p>Ex. Write\u00a0[latex]350[\/latex] million as a number.<\/p>\n<p style=\"padding-left: 30px;\">[latex]350\\times1,000,000=350,000,000[\/latex]<\/p>\n<p>Ex. Write\u00a0[latex]3500[\/latex] million as a number.<\/p>\n<p style=\"padding-left: 30px;\">[latex]3500\\times1,000,000=3,500,000,000[\/latex], which is 3 billion, 500 million.<\/p>\n<p>Note that the final row of the table above gives\u00a0[latex]11,227[\/latex] millions of dollars in hurricane damage. How much is that in billions?<\/p>\n<p>Ex. Write\u00a0[latex]11,227[\/latex] million as a number.<\/p>\n<p style=\"padding-left: 30px;\">[latex]11,227\\times1,000,000=11,227,000,000[\/latex], which is\u00a0[latex]11[\/latex] billion,\u00a0[latex]227[\/latex] million.<\/p>\n<p>We can also write this as\u00a0[latex]11.227[\/latex] billion.<\/p>\n<p>Ex. [latex]11.227\\times1,000,000,000=11.227\\times10^{9}=11,227,000,000[\/latex] by moving the decimal\u00a0[latex]9[\/latex] places to the right.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Now, try Question 5.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 5<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241050\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241050&theme=oea&iframe_resize_id=ohm241050&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q101343\">Hint<\/span><\/p>\n<div id=\"q101343\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think? Use the recall box above as a guide.<\/div>\n<\/div>\n<\/div>\n<h3>Signed numbers as proximities<\/h3>\n<p>Before answering Question 6 and 7, you may wish to refresh your understanding of distance as an absolute value.<\/p>\n<div class=\"textbox examples\">\n<h3>recall<\/h3>\n<p>When discussing the difference between two numbers as a distance, use the concept of absolute value to help make sense of the result. For example, we would say the difference between\u00a0[latex]-1[\/latex] and\u00a0[latex]3[\/latex] is four units even though taking their difference may result in a negative or a positive depending upon which we subtract from which.<\/p>\n<p style=\"text-align: center;\">[latex]-1-3=-4\\qquad\\text{ and }\\qquad3 - \\left(-1\\right)=4[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]|-1-3|=4\\qquad\\text{ and }\\qquad|3 - \\left(-1\\right)|=4[\/latex]<\/p>\n<p>See the skill below if needed for an example of how absolute value can be applied in Questions 6 and 7 and how to interpret positive and negative results when calculating deviation from the mean.<\/p>\n<p>Core skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q761688\">Express a distance as an absolute value.<\/span><\/p>\n<div id=\"q761688\" class=\"hidden-answer\" style=\"display: none\">\n<p>Say the mean of a sample is given as [latex]\\bar{x}=12[\/latex] and the observations\u00a0[latex]7[\/latex] and\u00a0[latex]15[\/latex] are contained in the sample. Which value is closer to the mean?<\/p>\n<p style=\"padding-left: 30px;\">For the value of\u00a0[latex]7[\/latex], [latex]x-\\bar{x} = 7-12=-5[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">For the value of\u00a0[latex]15[\/latex], [latex]x-\\bar{x} = 15-12=3[\/latex]<\/p>\n<p>We might be tempted to conclude that\u00a0[latex]7[\/latex] is closer since\u00a0[latex]-5[\/latex] is a smaller number than\u00a0[latex]3[\/latex]. But distance is calculated using absolute value. The value of\u00a0[latex]7[\/latex] is\u00a0[latex]5[\/latex] units away from the mean (to the left) while the value of\u00a0[latex]15[\/latex] is only\u00a0[latex]3[\/latex] units away from the mean (to the right). To calculate which is closer, use absolute value.<\/p>\n<p style=\"padding-left: 30px;\">For the value of\u00a0[latex]7[\/latex], [latex]|7-12|=|-5|=5[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">For the value of\u00a0[latex]15[\/latex], [latex]|15-12|=|3|=3[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 6<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241051\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241051&theme=oea&iframe_resize_id=ohm241051&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q282551\">Hint<\/span><\/p>\n<div id=\"q282551\" class=\"hidden-answer\" style=\"display: none\">For each calculation, you subtracted the mean from the observed value. Why would some result in a negative deviation? See the interactive example above for an explanation.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 7<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241052\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241052&theme=oea&iframe_resize_id=ohm241052&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q421294\">Hint<\/span><\/p>\n<div id=\"q421294\" class=\"hidden-answer\" style=\"display: none\">Think of <em>closer<\/em> as being a distance (i.e., absolute value).<\/div>\n<\/div>\n<\/div>\n<p>You&#8217;ve learned how to calculate the deviation from the mean in this activity, which you&#8217;ll be using in the upcoming section and following activity. You&#8217;ve also refreshed several mathematical skills and statistical definitions. Hopefully, you are feeling comfortable enough with these concepts to move on to the next section.<\/p>\n","protected":false},"author":25777,"menu_order":5,"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-3658","chapter","type-chapter","status-publish","hentry"],"part":3887,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3658","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":8,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3658\/revisions"}],"predecessor-version":[{"id":3675,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3658\/revisions\/3675"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/3887"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3658\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=3658"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=3658"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=3658"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=3658"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}