{"id":486,"date":"2021-12-20T14:49:15","date_gmt":"2021-12-20T14:49:15","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=486"},"modified":"2022-02-17T20:09:50","modified_gmt":"2022-02-17T20:09:50","slug":"corequisite-support-activity-4b","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/corequisite-support-activity-4b\/","title":{"raw":"Corequisite Support Activity for Comparing Variability of Datasets: 4B - 19","rendered":"Corequisite Support Activity for Comparing Variability of Datasets: 4B &#8211; 19"},"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 to understanding what the spread of a dataset is and how it is calculated.\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 70 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\nThe mean for both classes was 70 points. Does this tell the whole story? How are the two classes different?\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>, from the mean. Let\u2019s look at a more important example.\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. We are going to explore the amount of damage in dollars of the 30 most expensive hurricanes that have hit the U.S. mainland between 1990 and 2010 in this corequisite support activity. 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\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 50th 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\">Use technology to calculate the sample size and mean of a distribution<\/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\nWhat is the sample size of the dataset?\r\n\r\n[reveal-answer q=\"943053\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"943053\"]Make sure the Single Group tab 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\nWhat is the mean of the dataset in the context of the given situation?\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\">Calculate the deviation from the mean of an observation in a dataset<\/h3>\r\nA <strong>deviation from the mean<\/strong> is the distance between an observation [latex]\\left(x\\right)[\/latex] in a dataset and the mean of the dataset. To calculate the deviation from the mean, subtract the sample mean [latex]\\left(\\bar{x}\\right)[\/latex] 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 50 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 10 minutes,\u00a0[latex]\\left(\\bar{x}\\right)=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<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]\\left(x-\\bar{x}\\right)[\/latex]<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\">8<\/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;\">10<\/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;\">12<\/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;\">14<\/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;\">5<\/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;\">15<\/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;\">9<\/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%;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%;\">\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%;\">\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]\\left(x-\\bar{x}\\right)[\/latex]<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\">8<\/td>\r\n<td style=\"width: 50%; text-align: center;\">8 - 10 = -2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\">10<\/td>\r\n<td style=\"width: 50%; text-align: center;\">10 - 10 = 0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\">12<\/td>\r\n<td style=\"width: 50%; text-align: center;\">12 - 10 = 2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\">14<\/td>\r\n<td style=\"width: 50%; text-align: center;\">14 - 10 = 4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\">5<\/td>\r\n<td style=\"width: 50%; text-align: center;\">5 - 10 = -5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\">15<\/td>\r\n<td style=\"width: 50%; text-align: center;\">15 - 10 = 5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\">9<\/td>\r\n<td style=\"width: 50%; text-align: center;\">9 - 10 = -1<\/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 12 minutes results in that ride to school being 2 minutes above the mean (or a longer ride), while the observation of 5 results in that ride to school being 5 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.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\nTen of the 30 observations are listed in the following table. Calculate the deviation from the mean [latex]\\left(x-\\bar{x}\\right)[\/latex] for each of the 10 observations given.\r\n<div align=\"left\">\r\n<table style=\"height: 187px;\">\r\n<tbody>\r\n<tr style=\"height: 67px;\">\r\n<td style=\"width: 289px; height: 67px;\">\r\n<p style=\"text-align: center;\"><strong>Hurricane Damage (in millions of dollars)<\/strong><\/p>\r\n<p style=\"text-align: center;\"><strong>[latex]({x})[\/latex]<\/strong><\/p>\r\n<\/td>\r\n<td style=\"width: 329.016px; height: 67px;\">\r\n<p style=\"text-align: center;\"><strong>Deviation from the Mean (in millions of dollars)<\/strong><\/p>\r\n<p style=\"text-align: center;\"><strong>[latex]\\left(x-\\bar{x}\\right)[\/latex]<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 289px; height: 12px; text-align: center;\">105,840<\/td>\r\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 289px; height: 12px; text-align: center;\">45,561<\/td>\r\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 289px; height: 12px; text-align: center;\">27,790<\/td>\r\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 289px; height: 12px; text-align: center;\">20,587<\/td>\r\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 289px; height: 12px; text-align: center;\">19,832<\/td>\r\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 289px; height: 12px; text-align: center;\">15,820<\/td>\r\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 289px; height: 12px; text-align: center;\">12,775<\/td>\r\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 289px; height: 12px; text-align: center;\">11,797<\/td>\r\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 289px; height: 12px; text-align: center;\">11,760<\/td>\r\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 289px; height: 12px; text-align: center;\">11,227<\/td>\r\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\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<span id=\"LargeNumbers\">Before answering Question 5, 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: 11,227. Presumably, that means 11,227 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\u00a0<em>11,227 million dollars<\/em> as $<em>11.227 billion<\/em>. You 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 $1,250,000 but we understand immediately what $1.25 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 1,000,000: a one followed by six zeros: [latex]10^{6}[\/latex].\r\n\r\nA billion is a thousand million. It's written 1,000,000,000: a one followed by nine zeros; [latex]10^{9}[\/latex].\r\n<p style=\"padding-left: 30px;\">Or, 1,000 followed by six zeros, since a thousand million is 1,000 times 1,000,000.<\/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 35 million as a number.\r\n<p style=\"padding-left: 30px;\">[latex]35\\times1,000,000=35,000,000[\/latex]<\/p>\r\nEx. Write 350 million as a number.\r\n<p style=\"padding-left: 30px;\">[latex]350\\times1,000,000=350,000,000[\/latex]<\/p>\r\nEx. Write 3500 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 11,227 millions of dollars in hurricane damage. How much is that in billions?\r\n\r\nEx. Write 11,227 million as a number.\r\n<p style=\"padding-left: 30px;\">[latex]11,227\\times1,000,000=11,227,000,000[\/latex], which is 11 billion, 227 million.<\/p>\r\nWe can also write this as 11.227 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 9 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\nIn the second row of the table, what does 105,840 represent?\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\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 -1 and 3 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 7 and 15 are contained in the sample. Which value is closer to the mean?\r\n<p style=\"padding-left: 30px;\">For the value of 7, [latex]x-\\bar{x} = 7-12=-5[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">For the value of 15, [latex]x-\\bar{x} = 15-12=3[\/latex]<\/p>\r\nWe might be tempted to conclude that 7 is closer since -5 is a smaller number than 3. But distance is calculated using absolute value. The value of 7 is 5 units away from the mean (to the left) while the value of 15 is only 3 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 7, [latex]|7-12|=|-5|=5[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">For the value of 15, [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\nLook at the deviations from the mean you calculated in the previous table.\u00a0 Why are some of the values positive and some of the values negative?\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?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 7<\/h3>\r\nCompare the deviation for the value 12,775 million dollars to the deviation for the value 27,790 million dollars. Which one is closer to the mean?\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 to understanding what the spread of a dataset is and how it is calculated.<\/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 70 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>The mean for both classes was 70 points. Does this tell the whole story? How are the two classes different?<\/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>, from the mean. Let\u2019s look at a more important example.<\/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. We are going to explore the amount of damage in dollars of the 30 most expensive hurricanes that have hit the U.S. mainland between 1990 and 2010 in this corequisite support activity. 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<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 50th 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\">Use technology to calculate the sample size and mean of a distribution<\/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>What is the sample size of the dataset?<\/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 Single Group tab 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>What is the mean of the dataset in the context of the given situation?<\/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\">Calculate the deviation from the mean of an observation in a dataset<\/h3>\n<p>A <strong>deviation from the mean<\/strong> is the distance between an observation [latex]\\left(x\\right)[\/latex] in a dataset and the mean of the dataset. To calculate the deviation from the mean, subtract the sample mean [latex]\\left(\\bar{x}\\right)[\/latex] 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 50 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 10 minutes,\u00a0[latex]\\left(\\bar{x}\\right)=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<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]\\left(x-\\bar{x}\\right)[\/latex]<\/strong><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">8<\/td>\n<td style=\"width: 50%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">10<\/td>\n<td style=\"width: 50%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">12<\/td>\n<td style=\"width: 50%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">14<\/td>\n<td style=\"width: 50%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">5<\/td>\n<td style=\"width: 50%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">15<\/td>\n<td style=\"width: 50%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">9<\/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%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\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%;\">\n<p style=\"text-align: center;\"><strong>Deviation from the Mean (in minutes)<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>[latex]\\left(x-\\bar{x}\\right)[\/latex]<\/strong><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">8<\/td>\n<td style=\"width: 50%; text-align: center;\">8 &#8211; 10 = -2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">10<\/td>\n<td style=\"width: 50%; text-align: center;\">10 &#8211; 10 = 0<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">12<\/td>\n<td style=\"width: 50%; text-align: center;\">12 &#8211; 10 = 2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">14<\/td>\n<td style=\"width: 50%; text-align: center;\">14 &#8211; 10 = 4<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">5<\/td>\n<td style=\"width: 50%; text-align: center;\">5 &#8211; 10 = -5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">15<\/td>\n<td style=\"width: 50%; text-align: center;\">15 &#8211; 10 = 5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">9<\/td>\n<td style=\"width: 50%; text-align: center;\">9 &#8211; 10 = -1<\/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 12 minutes results in that ride to school being 2 minutes above the mean (or a longer ride), while the observation of 5 results in that ride to school being 5 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.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p>Ten of the 30 observations are listed in the following table. Calculate the deviation from the mean [latex]\\left(x-\\bar{x}\\right)[\/latex] for each of the 10 observations given.<\/p>\n<div style=\"text-align: left;\">\n<table style=\"height: 187px;\">\n<tbody>\n<tr style=\"height: 67px;\">\n<td style=\"width: 289px; height: 67px;\">\n<p style=\"text-align: center;\"><strong>Hurricane Damage (in millions of dollars)<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>[latex]({x})[\/latex]<\/strong><\/p>\n<\/td>\n<td style=\"width: 329.016px; height: 67px;\">\n<p style=\"text-align: center;\"><strong>Deviation from the Mean (in millions of dollars)<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>[latex]\\left(x-\\bar{x}\\right)[\/latex]<\/strong><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 289px; height: 12px; text-align: center;\">105,840<\/td>\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 289px; height: 12px; text-align: center;\">45,561<\/td>\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 289px; height: 12px; text-align: center;\">27,790<\/td>\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 289px; height: 12px; text-align: center;\">20,587<\/td>\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 289px; height: 12px; text-align: center;\">19,832<\/td>\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 289px; height: 12px; text-align: center;\">15,820<\/td>\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 289px; height: 12px; text-align: center;\">12,775<\/td>\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 289px; height: 12px; text-align: center;\">11,797<\/td>\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 289px; height: 12px; text-align: center;\">11,760<\/td>\n<td style=\"width: 329.016px; height: 12px;\"><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 289px; height: 12px; text-align: center;\">11,227<\/td>\n<td style=\"width: 329.016px; height: 12px;\"><\/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=\"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<p><span id=\"LargeNumbers\">Before answering Question 5, 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: 11,227. Presumably, that means 11,227 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\u00a0<em>11,227 million dollars<\/em> as $<em>11.227 billion<\/em>. You 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 $1,250,000 but we understand immediately what $1.25 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 1,000,000: a one followed by six zeros: [latex]10^{6}[\/latex].<\/p>\n<p>A billion is a thousand million. It&#8217;s written 1,000,000,000: a one followed by nine zeros; [latex]10^{9}[\/latex].<\/p>\n<p style=\"padding-left: 30px;\">Or, 1,000 followed by six zeros, since a thousand million is 1,000 times 1,000,000.<\/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 35 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 350 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 3500 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 11,227 millions of dollars in hurricane damage. How much is that in billions?<\/p>\n<p>Ex. Write 11,227 million as a number.<\/p>\n<p style=\"padding-left: 30px;\">[latex]11,227\\times1,000,000=11,227,000,000[\/latex], which is 11 billion, 227 million.<\/p>\n<p>We can also write this as 11.227 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 9 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>In the second row of the table, what does 105,840 represent?<\/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<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 -1 and 3 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 7 and 15 are contained in the sample. Which value is closer to the mean?<\/p>\n<p style=\"padding-left: 30px;\">For the value of 7, [latex]x-\\bar{x} = 7-12=-5[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">For the value of 15, [latex]x-\\bar{x} = 15-12=3[\/latex]<\/p>\n<p>We might be tempted to conclude that 7 is closer since -5 is a smaller number than 3. But distance is calculated using absolute value. The value of 7 is 5 units away from the mean (to the left) while the value of 15 is only 3 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 7, [latex]|7-12|=|-5|=5[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">For the value of 15, [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>Look at the deviations from the mean you calculated in the previous table.\u00a0 Why are some of the values positive and some of the values negative?<\/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?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 7<\/h3>\n<p>Compare the deviation for the value 12,775 million dollars to the deviation for the value 27,790 million dollars. Which one is closer to the mean?<\/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\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-486\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Damage shown from 2018 extreme weather season. <strong>Authored by<\/strong>: Spencer Platt \/ Getty Images. <strong>Provided by<\/strong>: USA Today. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.usatoday.com\/story\/money\/2018\/09\/12\/most-destructive-hurricanes-of-all-time\/36697269\/\">https:\/\/www.usatoday.com\/story\/money\/2018\/09\/12\/most-destructive-hurricanes-of-all-time\/36697269\/<\/a>. <strong>License<\/strong>: <em>All Rights Reserved<\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":25777,"menu_order":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Damage shown from 2018 extreme weather season\",\"author\":\"Spencer Platt \/ Getty Images\",\"organization\":\"USA Today\",\"url\":\"https:\/\/www.usatoday.com\/story\/money\/2018\/09\/12\/most-destructive-hurricanes-of-all-time\/36697269\/\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-486","chapter","type-chapter","status-publish","hentry"],"part":621,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/486","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":55,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/486\/revisions"}],"predecessor-version":[{"id":3310,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/486\/revisions\/3310"}],"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\/486\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=486"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=486"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=486"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=486"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}