{"id":3487,"date":"2022-03-02T15:46:47","date_gmt":"2022-03-02T15:46:47","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=3487"},"modified":"2022-04-07T22:37:26","modified_gmt":"2022-04-07T22:37:26","slug":"corequisite-support-activity-for-2a","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/corequisite-support-activity-for-2a\/","title":{"raw":"Corequisite Support Activity for 2A: Random Sampling","rendered":"Corequisite Support Activity for 2A: Random Sampling"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>What you'll need to know:<\/h3>\r\nIn this support activity you\u2019ll become familiar with the following:\r\n<ul>\r\n \t<li>Use technology to create a dotplot from a dataset.<\/li>\r\n \t<li>Answer questions about a variable using a dotplot.<\/li>\r\n \t<li>Use a random number generator to select a random sample.<\/li>\r\n \t<li>Anticipate sample-to-sample variability.<\/li>\r\n<\/ul>\r\nYou will also have an opportunity to refresh the following skills:\r\n<ul>\r\n \t<li>Calculate a sample mean by hand<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the next preview assignment and in the next class, you will need to interpret features of a dotplot, use a random number generator to select a random sample from a finite population, and calculate the arithmetic mean. In this activity, you will become familiar with the data analysis tools that will be used throughout this course. You can access these tools on any smart device, including a phone.\r\n\r\nSome new vocabulary will appear in this section of course material. These are terms you'll discuss in greater terms later, that you'll use throughout the course, and that you may have seen before. As you work through this assignment, try to draw the statistical meaning of the words\u00a0<em>random<\/em> and\u00a0<em>sample<\/em> as they are used in context.\r\n\r\nThe two tools in this activity are the\u00a0<em>Describing and Exploring Quantitative Data<\/em> tool at\u00a0 <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a> and the\u00a0Generate Random Numbers tool at\r\n<a href=\"https:\/\/dcmathpathways.shinyapps.io\/RandomNumbers\/\">https:\/\/dcmathpathways.shinyapps.io\/RandomNumbers\/<\/a>. They'll also be linked below as you need them.\r\n\r\nWork in pairs during this activity if possible, in close proximity so that you can share and compare the outputs from the tool. If more than one of you share a device to complete the activity, switch roles halfway through so everyone gets practice using the tools.\r\n<h2>Interpreting Dotplots<\/h2>\r\n<span style=\"background-color: #ffff99;\">[insert image of a generic dotplot with labels, arrows pointing to individual observations, horizontal axis]<\/span>\r\n\r\nA <strong>dotplot<\/strong> is a graphical display of the distribution of a quantitative variable. It shows the variable\u2019s possible values and the frequency of each value. In this corequisite support activity, you will use technology to generate a dotplot and then use the dotplot to describe the features of the distribution. You will explore other ways of visualizing a quantitative variable in <em>Forming Connections [3C]<\/em>.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\nGo to the Describing and Exploring Quantitative Data tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>.\r\n\r\nStep 1) Select the Single Group tab.\r\n\r\nStep 2) Locate the drop-down menu under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.\r\n\r\nStep 3) Locate the drop-down menu under <strong>Dataset<\/strong> and select <strong>Cereal Sodium Content<\/strong>.\r\n\r\nStep 4) Under <strong>Choose Type of Plot<\/strong>, uncheck <strong>Histogram<\/strong> and <strong>Boxplot<\/strong> and check <strong>Dotplot<\/strong>. Then adjust the Dot size to 0.5 and the Bin width to 10.\r\n\r\nUse the dotplot displayed in the tool to answer the following questions.\r\n\r\n&nbsp;\r\n\r\nPart A: Which type of variable is cereal sodium content?\r\n\r\n[reveal-answer q=\"182576\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"182576\"]Is it categorical or quantitative?[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nPart B: Describe the typical value of cereal sodium content.\r\n\r\n[reveal-answer q=\"907818\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"907818\"]Look for a clump of dots on the graph clustered near a value.[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nPart C: How many observations of cereal sodium content are less than 100 milligrams (mg)? Approximately what are the values of these observations?\r\n\r\n[reveal-answer q=\"109637\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"109637\"]Look for dots on the graph that are to the left of [latex]100[\/latex] on the horizontal axis.[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nPart D: How many observations of cereal sodium content are between 200 and 300 mg (including 200 and 300)?\r\n\r\n[reveal-answer q=\"164496\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"164496\"]Locate 200 and 300 on the graph.\u00a0What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\nYou'll be using the tools frequently throughout this course, and detailed instructions will be provided for each of the first few times you do, so don't worry if it doesn't yet feel comfortable.\r\n\r\nLet's turn our focus now to another tool you'll need to use soon, the random number generator.\r\n<h2>Calculating a Sample Mean<\/h2>\r\nIn the upcoming course activity, you'll need to take a sample from a population and ensure that the sampling method you use is unbiased. We'll learn more about what that really means later. For now, we'll focus on using the random number generator to select a random sample, then calculate the mean of that sample.\r\n<h3>Random Sample<\/h3>\r\nThe following table (continued on the next page) displays the number of drivers involved in fatal collisions per billion miles for each of the 50 states.\r\n<div align=\"left\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Ordered Number<\/td>\r\n<td>State<\/td>\r\n<td>Number of Drivers<\/td>\r\n<td><\/td>\r\n<td>Ordered Number<\/td>\r\n<td>State<\/td>\r\n<td>Number of Drivers<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>Alabama<\/td>\r\n<td>18.8<\/td>\r\n<td><\/td>\r\n<td>26<\/td>\r\n<td>Montana<\/td>\r\n<td>21.4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>Alaska<\/td>\r\n<td>18.1<\/td>\r\n<td><\/td>\r\n<td>27<\/td>\r\n<td>Nebraska<\/td>\r\n<td>14.9<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>Arizona<\/td>\r\n<td>18.6<\/td>\r\n<td><\/td>\r\n<td>28<\/td>\r\n<td>Nevada<\/td>\r\n<td>14.7<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td>Arkansas<\/td>\r\n<td>22.4<\/td>\r\n<td><\/td>\r\n<td>29<\/td>\r\n<td>New\u00a0Hampshire<\/td>\r\n<td>11.6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td>California<\/td>\r\n<td>12.0<\/td>\r\n<td><\/td>\r\n<td>30<\/td>\r\n<td>New\u00a0Jersey<\/td>\r\n<td>11.2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>6<\/td>\r\n<td>Colorado<\/td>\r\n<td>13.6<\/td>\r\n<td><\/td>\r\n<td>31<\/td>\r\n<td>New\u00a0Mexico<\/td>\r\n<td>18.4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>7<\/td>\r\n<td>Connecticut<\/td>\r\n<td>10.8<\/td>\r\n<td><\/td>\r\n<td>32<\/td>\r\n<td>New\u00a0York<\/td>\r\n<td>12.3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>8<\/td>\r\n<td>Delaware<\/td>\r\n<td>16.2<\/td>\r\n<td><\/td>\r\n<td>33<\/td>\r\n<td>North\u00a0Carolina<\/td>\r\n<td>16.8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>9<\/td>\r\n<td>Florida<\/td>\r\n<td>17.9<\/td>\r\n<td><\/td>\r\n<td>34<\/td>\r\n<td>North\u00a0Dakota<\/td>\r\n<td>23.9<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>10<\/td>\r\n<td>Georgia<\/td>\r\n<td>15.6<\/td>\r\n<td><\/td>\r\n<td>35<\/td>\r\n<td>Ohio<\/td>\r\n<td>14.1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>11<\/td>\r\n<td>Hawaii<\/td>\r\n<td>17.5<\/td>\r\n<td><\/td>\r\n<td>36<\/td>\r\n<td>Oklahoma<\/td>\r\n<td>19.9<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>12<\/td>\r\n<td>Idaho<\/td>\r\n<td>15.3<\/td>\r\n<td><\/td>\r\n<td>37<\/td>\r\n<td>Oregon<\/td>\r\n<td>12.8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>13<\/td>\r\n<td>Illinois<\/td>\r\n<td>12.8<\/td>\r\n<td><\/td>\r\n<td>38<\/td>\r\n<td>Pennsylvania<\/td>\r\n<td>18.2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>14<\/td>\r\n<td>Indiana<\/td>\r\n<td>14.5<\/td>\r\n<td><\/td>\r\n<td>39<\/td>\r\n<td>Rhode\u00a0Island<\/td>\r\n<td>11.1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>15<\/td>\r\n<td>Iowa<\/td>\r\n<td>15.7<\/td>\r\n<td><\/td>\r\n<td>40<\/td>\r\n<td>South\u00a0Carolina<\/td>\r\n<td>23.9<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>16<\/td>\r\n<td>Kansas<\/td>\r\n<td>17.8<\/td>\r\n<td><\/td>\r\n<td>41<\/td>\r\n<td>South\u00a0Dakota<\/td>\r\n<td>19.4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>17<\/td>\r\n<td>Kentucky<\/td>\r\n<td>21.4<\/td>\r\n<td><\/td>\r\n<td>42<\/td>\r\n<td>Tennessee<\/td>\r\n<td>19.5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>18<\/td>\r\n<td>Louisiana<\/td>\r\n<td>20.5<\/td>\r\n<td><\/td>\r\n<td>43<\/td>\r\n<td>Texas<\/td>\r\n<td>19.4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>19<\/td>\r\n<td>Maine<\/td>\r\n<td>15.1<\/td>\r\n<td><\/td>\r\n<td>44<\/td>\r\n<td>Utah<\/td>\r\n<td>11.3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>20<\/td>\r\n<td>Maryland<\/td>\r\n<td>12.5<\/td>\r\n<td><\/td>\r\n<td>45<\/td>\r\n<td>Vermont<\/td>\r\n<td>13.6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>21<\/td>\r\n<td>Massachusetts<\/td>\r\n<td>8.2<\/td>\r\n<td><\/td>\r\n<td>46<\/td>\r\n<td>Virginia<\/td>\r\n<td>12.7<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>22<\/td>\r\n<td>Michigan<\/td>\r\n<td>14.1<\/td>\r\n<td><\/td>\r\n<td>47<\/td>\r\n<td>Washington<\/td>\r\n<td>10.6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>23<\/td>\r\n<td>Minnesota<\/td>\r\n<td>9.6<\/td>\r\n<td><\/td>\r\n<td>48<\/td>\r\n<td>West\u00a0Virginia<\/td>\r\n<td>23.8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>24<\/td>\r\n<td>Mississippi<\/td>\r\n<td>17.6<\/td>\r\n<td><\/td>\r\n<td>49<\/td>\r\n<td>Wisconsin<\/td>\r\n<td>13.8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>25<\/td>\r\n<td>Missouri<\/td>\r\n<td>16.1<\/td>\r\n<td><\/td>\r\n<td>50<\/td>\r\n<td>Wyoming<\/td>\r\n<td>17.4<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nWe would like to select a random sample of six states from this list. We will select this sample \u201cwithout replacement,\u201d meaning that we cannot select the same state twice. The word\u00a0<em>random<\/em>, used statistically, means that each individual in the population has the same chance of being selected in the sample.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 2<\/h3>\r\nDescribe how you could use cards to select a random sample of six states, without replacement. In your description, include the number of cards you would need, what you would write on each card, and how you would select your sample.\r\n\r\n[reveal-answer q=\"416399\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"416399\"]What do <em>you<\/em> think? You can discuss this with a partner.[\/hidden-answer]\r\n\r\n<\/div>\r\nNow, instead of using cards, you are going to use a random number generator to select a random sample of six states. You'll use the tool to do this. If you work with a partner, use the sample you generate together in Question 3 to answer Question 4.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 3<\/h3>\r\nGo to the Generate Random Numbers tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/RandomNumbers\/\">https:\/\/dcmathpathways.shinyapps.io\/RandomNumbers\/<\/a>.\r\n\r\nStep 1) Select the Random Numbers tab.\r\n\r\nStep 2) Under \u201cChoose Minimum,\u201d select \u201c1.\u201d\r\n\r\nStep 3) Under \u201cChoose Maximum,\u201d select \u201c50.\u201d\r\n\r\nStep 4) Under \u201cHow many numbers do you want to generate,\u201d select \u201c6.\u201d\r\n\r\nStep 5) Under \u201cSample with Replacement,\u201d select \u201cNo.\u201d\r\n\r\nStep 6) Click \u201cGenerate.\u201d This will generate six random numbers between 1 and 50. These six numbers correspond to the states chosen for your sample (locate the number next to its corresponding state name in the data list above). Fill in the following table with the corresponding state and number of drivers involved in fatal collisions per billion miles for each of your randomly-generated numbers.\r\n<div align=\"left\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Randomly\r\n\r\nGenerated Number<\/td>\r\n<td>State<\/td>\r\n<td>Number of Drivers\r\n\r\nInvolved in Fatal Collisions\r\n\r\nper Billion Miles<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[reveal-answer q=\"594746\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"594746\"]Since this method generates a random sample, there is no exact answer for this question.[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<h3>Sample Mean<\/h3>\r\nTo understand what the typical number of drivers involved in fatal collisions might be, we can calculate the <strong>mean<\/strong> or <strong>average<\/strong> of the values. The mean is calculated by adding the values and then dividing the total by the number of values in the dataset.\u00a0When we calculate the mean of a random sample, we call this the\u00a0<strong>sample mean.<\/strong>\r\n<div class=\"textbox examples\">\r\n<h3>Recall<\/h3>\r\nCore skill:\r\n[reveal-answer q=\"253359\"]Calculate the mean of a list of values[\/reveal-answer]\r\n[hidden-answer a=\"253359\"]\r\n\r\nTo calculate the mean of a list of numbers, divide the sum of the numbers by the number of values in the list.\r\n\r\nEx. Suppose a sample of the costs of five lunch orders was taken from all the lunch orders at a sandwich shop near a college campus. These were $14, $17, $22, $27, and $32, rounded to the nearest dollar. Let's find the sample mean.\r\n<p style=\"padding-left: 30px;\">There are five values in the list. We'll add them up, then divide by 5.<\/p>\r\n<p style=\"padding-left: 30px;\">[latex]\\dfrac}{14+17+22+27+32}{5}=22.4[\/latex]<\/p>\r\nThe sample mean lunch cost is $22.40.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nSee the example below, then answer Question 4 using the random sample you generated from the data table during Question 3.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSuppose a random sample of states was taken from the list above:\u00a0Minnesota, Nevada, West Virginia, Tennessee, Alaska, Indiana.\r\n\r\nTo calculate the mean number of drivers involved in fatal collisions per billion miles for this sample, we take the sum of the number of drivers per state in the sample, then divide by the total number of states in sample.\r\n<ol>\r\n \t<li>What are the number of drivers involved in fatal collisions per billions associated with each state in the sample? Look these up in the data table.[reveal-answer q=\"57762\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"57762\"]Minnesota: 9.6\r\n\r\nNevada: 14.7\r\n\r\nWest Virginia: 23.8\r\n\r\nTennessee: 19.5\r\n\r\nAlaska: 18.1\r\n\r\nIndiana: 14.5\r\n\r\n[\/hidden-answer]<\/li>\r\n \t<li>Calculate the sample mean.\r\n[reveal-answer q=\"560790\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"560790\"] [latex]\\dfrac{9.6+14.7+23.8+19.5+18.1+14.5}{6}=16.7[\/latex] drivers per billion miles[\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/div>\r\nNow you try it.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\nCalculate the sample mean (i.e., average) number of drivers involved in fatal collisions per billion miles for the six states in your randomly-selected sample.\r\n\r\n[reveal-answer q=\"668049\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"668049\"]Use the number of drivers in the random sample of six states you generated in Question 3.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 5<\/h3>\r\nIf you were to use the random number generator to generate another simple random sample of six states, would you get the same six numbers you found in Question 3? Would you get the same value for the sample mean number of drivers involved in fatal collisions per billion miles you found in Question 4? Explain.\r\n\r\n[reveal-answer q=\"89659\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"89659\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\nYou've had an introduction to the analysis tool, learned about dotplots, had a chance to refresh your skills at computing the mean, and learned how to use the random number generator in order to choose a random sample from a dataset. Hopefully, you are feeling secure with these new abilities and are ready to move on to the next section and activity.","rendered":"<div class=\"textbox learning-objectives\">\n<h3>What you&#8217;ll need to know:<\/h3>\n<p>In this support activity you\u2019ll become familiar with the following:<\/p>\n<ul>\n<li>Use technology to create a dotplot from a dataset.<\/li>\n<li>Answer questions about a variable using a dotplot.<\/li>\n<li>Use a random number generator to select a random sample.<\/li>\n<li>Anticipate sample-to-sample variability.<\/li>\n<\/ul>\n<p>You will also have an opportunity to refresh the following skills:<\/p>\n<ul>\n<li>Calculate a sample mean by hand<\/li>\n<\/ul>\n<\/div>\n<p>In the next preview assignment and in the next class, you will need to interpret features of a dotplot, use a random number generator to select a random sample from a finite population, and calculate the arithmetic mean. In this activity, you will become familiar with the data analysis tools that will be used throughout this course. You can access these tools on any smart device, including a phone.<\/p>\n<p>Some new vocabulary will appear in this section of course material. These are terms you&#8217;ll discuss in greater terms later, that you&#8217;ll use throughout the course, and that you may have seen before. As you work through this assignment, try to draw the statistical meaning of the words\u00a0<em>random<\/em> and\u00a0<em>sample<\/em> as they are used in context.<\/p>\n<p>The two tools in this activity are the\u00a0<em>Describing and Exploring Quantitative Data<\/em> tool at\u00a0 <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a> and the\u00a0Generate Random Numbers tool at<br \/>\n<a href=\"https:\/\/dcmathpathways.shinyapps.io\/RandomNumbers\/\">https:\/\/dcmathpathways.shinyapps.io\/RandomNumbers\/<\/a>. They&#8217;ll also be linked below as you need them.<\/p>\n<p>Work in pairs during this activity if possible, in close proximity so that you can share and compare the outputs from the tool. If more than one of you share a device to complete the activity, switch roles halfway through so everyone gets practice using the tools.<\/p>\n<h2>Interpreting Dotplots<\/h2>\n<p><span style=\"background-color: #ffff99;\">[insert image of a generic dotplot with labels, arrows pointing to individual observations, horizontal axis]<\/span><\/p>\n<p>A <strong>dotplot<\/strong> is a graphical display of the distribution of a quantitative variable. It shows the variable\u2019s possible values and the frequency of each value. In this corequisite support activity, you will use technology to generate a dotplot and then use the dotplot to describe the features of the distribution. You will explore other ways of visualizing a quantitative variable in <em>Forming Connections [3C]<\/em>.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p>Go to the Describing and Exploring Quantitative Data tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>.<\/p>\n<p>Step 1) Select the Single Group tab.<\/p>\n<p>Step 2) Locate the drop-down menu under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.<\/p>\n<p>Step 3) Locate the drop-down menu under <strong>Dataset<\/strong> and select <strong>Cereal Sodium Content<\/strong>.<\/p>\n<p>Step 4) Under <strong>Choose Type of Plot<\/strong>, uncheck <strong>Histogram<\/strong> and <strong>Boxplot<\/strong> and check <strong>Dotplot<\/strong>. Then adjust the Dot size to 0.5 and the Bin width to 10.<\/p>\n<p>Use the dotplot displayed in the tool to answer the following questions.<\/p>\n<p>&nbsp;<\/p>\n<p>Part A: Which type of variable is cereal sodium content?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q182576\">Hint<\/span><\/p>\n<div id=\"q182576\" class=\"hidden-answer\" style=\"display: none\">Is it categorical or quantitative?<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part B: Describe the typical value of cereal sodium content.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q907818\">Hint<\/span><\/p>\n<div id=\"q907818\" class=\"hidden-answer\" style=\"display: none\">Look for a clump of dots on the graph clustered near a value.<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part C: How many observations of cereal sodium content are less than 100 milligrams (mg)? Approximately what are the values of these observations?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q109637\">Hint<\/span><\/p>\n<div id=\"q109637\" class=\"hidden-answer\" style=\"display: none\">Look for dots on the graph that are to the left of [latex]100[\/latex] on the horizontal axis.<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part D: How many observations of cereal sodium content are between 200 and 300 mg (including 200 and 300)?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q164496\">Hint<\/span><\/p>\n<div id=\"q164496\" class=\"hidden-answer\" style=\"display: none\">Locate 200 and 300 on the graph.\u00a0What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<p>You&#8217;ll be using the tools frequently throughout this course, and detailed instructions will be provided for each of the first few times you do, so don&#8217;t worry if it doesn&#8217;t yet feel comfortable.<\/p>\n<p>Let&#8217;s turn our focus now to another tool you&#8217;ll need to use soon, the random number generator.<\/p>\n<h2>Calculating a Sample Mean<\/h2>\n<p>In the upcoming course activity, you&#8217;ll need to take a sample from a population and ensure that the sampling method you use is unbiased. We&#8217;ll learn more about what that really means later. For now, we&#8217;ll focus on using the random number generator to select a random sample, then calculate the mean of that sample.<\/p>\n<h3>Random Sample<\/h3>\n<p>The following table (continued on the next page) displays the number of drivers involved in fatal collisions per billion miles for each of the 50 states.<\/p>\n<div style=\"text-align: left;\">\n<table>\n<tbody>\n<tr>\n<td>Ordered Number<\/td>\n<td>State<\/td>\n<td>Number of Drivers<\/td>\n<td><\/td>\n<td>Ordered Number<\/td>\n<td>State<\/td>\n<td>Number of Drivers<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>Alabama<\/td>\n<td>18.8<\/td>\n<td><\/td>\n<td>26<\/td>\n<td>Montana<\/td>\n<td>21.4<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>Alaska<\/td>\n<td>18.1<\/td>\n<td><\/td>\n<td>27<\/td>\n<td>Nebraska<\/td>\n<td>14.9<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>Arizona<\/td>\n<td>18.6<\/td>\n<td><\/td>\n<td>28<\/td>\n<td>Nevada<\/td>\n<td>14.7<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>Arkansas<\/td>\n<td>22.4<\/td>\n<td><\/td>\n<td>29<\/td>\n<td>New\u00a0Hampshire<\/td>\n<td>11.6<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>California<\/td>\n<td>12.0<\/td>\n<td><\/td>\n<td>30<\/td>\n<td>New\u00a0Jersey<\/td>\n<td>11.2<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>Colorado<\/td>\n<td>13.6<\/td>\n<td><\/td>\n<td>31<\/td>\n<td>New\u00a0Mexico<\/td>\n<td>18.4<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>Connecticut<\/td>\n<td>10.8<\/td>\n<td><\/td>\n<td>32<\/td>\n<td>New\u00a0York<\/td>\n<td>12.3<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>Delaware<\/td>\n<td>16.2<\/td>\n<td><\/td>\n<td>33<\/td>\n<td>North\u00a0Carolina<\/td>\n<td>16.8<\/td>\n<\/tr>\n<tr>\n<td>9<\/td>\n<td>Florida<\/td>\n<td>17.9<\/td>\n<td><\/td>\n<td>34<\/td>\n<td>North\u00a0Dakota<\/td>\n<td>23.9<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>Georgia<\/td>\n<td>15.6<\/td>\n<td><\/td>\n<td>35<\/td>\n<td>Ohio<\/td>\n<td>14.1<\/td>\n<\/tr>\n<tr>\n<td>11<\/td>\n<td>Hawaii<\/td>\n<td>17.5<\/td>\n<td><\/td>\n<td>36<\/td>\n<td>Oklahoma<\/td>\n<td>19.9<\/td>\n<\/tr>\n<tr>\n<td>12<\/td>\n<td>Idaho<\/td>\n<td>15.3<\/td>\n<td><\/td>\n<td>37<\/td>\n<td>Oregon<\/td>\n<td>12.8<\/td>\n<\/tr>\n<tr>\n<td>13<\/td>\n<td>Illinois<\/td>\n<td>12.8<\/td>\n<td><\/td>\n<td>38<\/td>\n<td>Pennsylvania<\/td>\n<td>18.2<\/td>\n<\/tr>\n<tr>\n<td>14<\/td>\n<td>Indiana<\/td>\n<td>14.5<\/td>\n<td><\/td>\n<td>39<\/td>\n<td>Rhode\u00a0Island<\/td>\n<td>11.1<\/td>\n<\/tr>\n<tr>\n<td>15<\/td>\n<td>Iowa<\/td>\n<td>15.7<\/td>\n<td><\/td>\n<td>40<\/td>\n<td>South\u00a0Carolina<\/td>\n<td>23.9<\/td>\n<\/tr>\n<tr>\n<td>16<\/td>\n<td>Kansas<\/td>\n<td>17.8<\/td>\n<td><\/td>\n<td>41<\/td>\n<td>South\u00a0Dakota<\/td>\n<td>19.4<\/td>\n<\/tr>\n<tr>\n<td>17<\/td>\n<td>Kentucky<\/td>\n<td>21.4<\/td>\n<td><\/td>\n<td>42<\/td>\n<td>Tennessee<\/td>\n<td>19.5<\/td>\n<\/tr>\n<tr>\n<td>18<\/td>\n<td>Louisiana<\/td>\n<td>20.5<\/td>\n<td><\/td>\n<td>43<\/td>\n<td>Texas<\/td>\n<td>19.4<\/td>\n<\/tr>\n<tr>\n<td>19<\/td>\n<td>Maine<\/td>\n<td>15.1<\/td>\n<td><\/td>\n<td>44<\/td>\n<td>Utah<\/td>\n<td>11.3<\/td>\n<\/tr>\n<tr>\n<td>20<\/td>\n<td>Maryland<\/td>\n<td>12.5<\/td>\n<td><\/td>\n<td>45<\/td>\n<td>Vermont<\/td>\n<td>13.6<\/td>\n<\/tr>\n<tr>\n<td>21<\/td>\n<td>Massachusetts<\/td>\n<td>8.2<\/td>\n<td><\/td>\n<td>46<\/td>\n<td>Virginia<\/td>\n<td>12.7<\/td>\n<\/tr>\n<tr>\n<td>22<\/td>\n<td>Michigan<\/td>\n<td>14.1<\/td>\n<td><\/td>\n<td>47<\/td>\n<td>Washington<\/td>\n<td>10.6<\/td>\n<\/tr>\n<tr>\n<td>23<\/td>\n<td>Minnesota<\/td>\n<td>9.6<\/td>\n<td><\/td>\n<td>48<\/td>\n<td>West\u00a0Virginia<\/td>\n<td>23.8<\/td>\n<\/tr>\n<tr>\n<td>24<\/td>\n<td>Mississippi<\/td>\n<td>17.6<\/td>\n<td><\/td>\n<td>49<\/td>\n<td>Wisconsin<\/td>\n<td>13.8<\/td>\n<\/tr>\n<tr>\n<td>25<\/td>\n<td>Missouri<\/td>\n<td>16.1<\/td>\n<td><\/td>\n<td>50<\/td>\n<td>Wyoming<\/td>\n<td>17.4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>We would like to select a random sample of six states from this list. We will select this sample \u201cwithout replacement,\u201d meaning that we cannot select the same state twice. The word\u00a0<em>random<\/em>, used statistically, means that each individual in the population has the same chance of being selected in the sample.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Question 2<\/h3>\n<p>Describe how you could use cards to select a random sample of six states, without replacement. In your description, include the number of cards you would need, what you would write on each card, and how you would select your sample.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q416399\">Hint<\/span><\/p>\n<div id=\"q416399\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think? You can discuss this with a partner.<\/div>\n<\/div>\n<\/div>\n<p>Now, instead of using cards, you are going to use a random number generator to select a random sample of six states. You&#8217;ll use the tool to do this. If you work with a partner, use the sample you generate together in Question 3 to answer Question 4.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p>Go to the Generate Random Numbers tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/RandomNumbers\/\">https:\/\/dcmathpathways.shinyapps.io\/RandomNumbers\/<\/a>.<\/p>\n<p>Step 1) Select the Random Numbers tab.<\/p>\n<p>Step 2) Under \u201cChoose Minimum,\u201d select \u201c1.\u201d<\/p>\n<p>Step 3) Under \u201cChoose Maximum,\u201d select \u201c50.\u201d<\/p>\n<p>Step 4) Under \u201cHow many numbers do you want to generate,\u201d select \u201c6.\u201d<\/p>\n<p>Step 5) Under \u201cSample with Replacement,\u201d select \u201cNo.\u201d<\/p>\n<p>Step 6) Click \u201cGenerate.\u201d This will generate six random numbers between 1 and 50. These six numbers correspond to the states chosen for your sample (locate the number next to its corresponding state name in the data list above). Fill in the following table with the corresponding state and number of drivers involved in fatal collisions per billion miles for each of your randomly-generated numbers.<\/p>\n<div style=\"text-align: left;\">\n<table>\n<tbody>\n<tr>\n<td>Randomly<\/p>\n<p>Generated Number<\/td>\n<td>State<\/td>\n<td>Number of Drivers<\/p>\n<p>Involved in Fatal Collisions<\/p>\n<p>per Billion Miles<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/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=\"q594746\">Hint<\/span><\/p>\n<div id=\"q594746\" class=\"hidden-answer\" style=\"display: none\">Since this method generates a random sample, there is no exact answer for this question.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h3>Sample Mean<\/h3>\n<p>To understand what the typical number of drivers involved in fatal collisions might be, we can calculate the <strong>mean<\/strong> or <strong>average<\/strong> of the values. The mean is calculated by adding the values and then dividing the total by the number of values in the dataset.\u00a0When we calculate the mean of a random sample, we call this the\u00a0<strong>sample mean.<\/strong><\/p>\n<div class=\"textbox examples\">\n<h3>Recall<\/h3>\n<p>Core skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q253359\">Calculate the mean of a list of values<\/span><\/p>\n<div id=\"q253359\" class=\"hidden-answer\" style=\"display: none\">\n<p>To calculate the mean of a list of numbers, divide the sum of the numbers by the number of values in the list.<\/p>\n<p>Ex. Suppose a sample of the costs of five lunch orders was taken from all the lunch orders at a sandwich shop near a college campus. These were $14, $17, $22, $27, and $32, rounded to the nearest dollar. Let&#8217;s find the sample mean.<\/p>\n<p style=\"padding-left: 30px;\">There are five values in the list. We&#8217;ll add them up, then divide by 5.<\/p>\n<p style=\"padding-left: 30px;\">[latex]\\dfrac}{14+17+22+27+32}{5}=22.4[\/latex]<\/p>\n<p>The sample mean lunch cost is $22.40.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>See the example below, then answer Question 4 using the random sample you generated from the data table during Question 3.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Suppose a random sample of states was taken from the list above:\u00a0Minnesota, Nevada, West Virginia, Tennessee, Alaska, Indiana.<\/p>\n<p>To calculate the mean number of drivers involved in fatal collisions per billion miles for this sample, we take the sum of the number of drivers per state in the sample, then divide by the total number of states in sample.<\/p>\n<ol>\n<li>What are the number of drivers involved in fatal collisions per billions associated with each state in the sample? Look these up in the data table.\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q57762\">Show Answer<\/span><\/p>\n<div id=\"q57762\" class=\"hidden-answer\" style=\"display: none\">Minnesota: 9.6<\/p>\n<p>Nevada: 14.7<\/p>\n<p>West Virginia: 23.8<\/p>\n<p>Tennessee: 19.5<\/p>\n<p>Alaska: 18.1<\/p>\n<p>Indiana: 14.5<\/p>\n<\/div>\n<\/div>\n<\/li>\n<li>Calculate the sample mean.\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q560790\">Show Answer<\/span><\/p>\n<div id=\"q560790\" class=\"hidden-answer\" style=\"display: none\"> [latex]\\dfrac{9.6+14.7+23.8+19.5+18.1+14.5}{6}=16.7[\/latex] drivers per billion miles<\/div>\n<\/div>\n<\/li>\n<\/ol>\n<\/div>\n<p>Now you try it.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p>Calculate the sample mean (i.e., average) number of drivers involved in fatal collisions per billion miles for the six states in your randomly-selected sample.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q668049\">Hint<\/span><\/p>\n<div id=\"q668049\" class=\"hidden-answer\" style=\"display: none\">Use the number of drivers in the random sample of six states you generated in Question 3.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 5<\/h3>\n<p>If you were to use the random number generator to generate another simple random sample of six states, would you get the same six numbers you found in Question 3? Would you get the same value for the sample mean number of drivers involved in fatal collisions per billion miles you found in Question 4? Explain.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q89659\">Hint<\/span><\/p>\n<div id=\"q89659\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<p>You&#8217;ve had an introduction to the analysis tool, learned about dotplots, had a chance to refresh your skills at computing the mean, and learned how to use the random number generator in order to choose a random sample from a dataset. Hopefully, you are feeling secure with these new abilities and are ready to move on to the next section and activity.<\/p>\n","protected":false},"author":493460,"menu_order":33,"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-3487","chapter","type-chapter","status-publish","hentry"],"part":3418,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3487","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\/493460"}],"version-history":[{"count":12,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3487\/revisions"}],"predecessor-version":[{"id":4290,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3487\/revisions\/4290"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/3418"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3487\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=3487"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=3487"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=3487"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=3487"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}