{"id":476,"date":"2023-02-27T17:10:44","date_gmt":"2023-02-27T17:10:44","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/?post_type=chapter&#038;p=476"},"modified":"2026-03-02T17:19:19","modified_gmt":"2026-03-02T17:19:19","slug":"statistical-questions-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/statistical-questions-learn-it-2\/","title":{"raw":"Statistical Questions: Learn It 3","rendered":"Statistical Questions: Learn It 3"},"content":{"raw":"<h2>Variables<\/h2>\r\n<p>The next step in a statistical investigation is to decide what you're measuring and how you're going to collect the data. Data are often shown as a long list of information about a group of individuals, animals, or objects. What you choose to measure is called the\u00a0<strong>variable<\/strong>. Some examples can include favorite color, height, cost, age, heart rate, state, and more.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>variable<\/h3>\r\n<p>A characteristic that can be measured and has different values.<\/p>\r\n<\/div>\r\n<\/section>\r\n<h2>Qualitative and Quantitative Data<\/h2>\r\n<p>Data are the actual values of the variable. They may be numbers or they may be words. As such, data can be categorized as <strong>qualitative<\/strong> or <strong>quantitative data<\/strong>.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>qualitative\/categorical data<\/h3>\r\n<p><strong>Qualitative data<\/strong> are the result of categorizing or describing attributes of a population. <br \/>\r\n<br \/>\r\nHair color, blood type, ethnic group, the car a person drives, and the street a person lives on are examples of qualitative data. <br \/>\r\n<br \/>\r\nQualitative data are generally described by words or letters. For instance, hair color might be black, dark brown, light brown, blonde, gray, or red. Blood type might be AB+, O-, or B+. <br \/>\r\n<br \/>\r\nQualitative data are also often called <strong>categorical data<\/strong>.<\/p>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>quantitative data (discrete and continuous)<\/h3>\r\n<p><strong>Quantitative data<\/strong> are the result of counting or measuring attributes of a population. Amount of money, pulse rate, weight, number of people living in your town, and number of students who take statistics courses are examples of quantitative data.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>Quantitative data\u00a0are always numbers.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>Quantitative <strong>discrete<\/strong> data are the result of counting. If you count the number of phone calls you receive for each day of the week, you might get values such as [latex]0, 1, 2, \\mathrm{or} \\ 3[\/latex].\u00a0<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>Quantitative <strong>continuous<\/strong> data refers to a type of numerical data that can take on an infinite number of values within a given range. Continuous data are often the results of measurements like lengths, weights, or times like a list of the lengths in minutes for all the phone calls that you make in a week.<\/p>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox example\">Determine the the variable(s) and the type of data in the following study.<br \/>\r\n<br \/>\r\nWe want to know the average amount of money first year college students spend at ABC College on school supplies that do not include books. We randomly survey [latex]100[\/latex] first year students at the college. Three of those students spent [latex]$152.75[\/latex], [latex]$211.10[\/latex], and [latex]$225.50[\/latex], respectively.[reveal-answer q=\"315469\"]Show Solution[\/reveal-answer][hidden-answer a=\"315469\"]The <strong>variable <\/strong>is the amount of money spent on school supplies (excluding books) by one first year student.<br \/>\r\n<br \/>\r\nThe <strong>data <\/strong>are the dollar amounts spent by the first year students. Examples of the data are $[latex]152.75[\/latex], $[latex]211.10[\/latex], and $[latex]225.50[\/latex]. These are <strong>quantitative discrete data <\/strong>because the variable is numerical and can take on only specific possible values. Although money is conceptually continuous, in practice it is measured in fixed increments (to the nearest cent), so the amounts can only occur in multiples of $[latex]0.01[\/latex]. Since there are gaps between possible values (for example, $[latex]152.751[\/latex] is not possible), the data are discrete.[\/hidden-answer]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3161[\/ohm2_question]<\/section>\r\n<section><\/section>\r\n<section>\r\n<section class=\"textbox proTip\">\r\n<ol>\r\n\t<li>While quantitative variables <em>always\u00a0<\/em>have numerical data, not all numerical data is quantitative. Qualitative data can be numerical if the numbers don't help us compare the values. For example, zip code has a numerical response, but we don't compare zip codes numerically (think about how there is no such thing as an average zip code, and having a higher\/lower zip code doesn't really communicate information about where you live). Zip code is a categorical variable, not a quantitative one.<\/li>\r\n\t<li>Discrete data can include fractions or decimals. The key is to recognize whether\u00a0<em>any <\/em>fraction or decimal would be accepted. Shoe size is a great example of quantitative discrete data that includes decimals since your shoe size can be 9, 9.5, 10, 10.5, but could not be any decimal between 9 and 9.5.<\/li>\r\n<\/ol>\r\n<\/section>\r\n<\/section>\r\n<section class=\"textbox youChoose\"><img class=\"wp-image-4578 aligncenter\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/10\/13214944\/ChooseDatasetImage.png\" alt=\"\" width=\"610\" height=\"105\" \/><br \/>\r\n[choosedataset divId=\"tnh-choose-dataset\" title=\"Classify Variables\" label=\"For this problem, you'll identify and classify the variables using a data set of your choosing.\" default=\"Choose a Dataset\"][datasetoption]<br \/>\r\n[displayname]Unsolved Murders[\/displayname]<br \/>\r\n[ohmid]2642[\/ohmid]<br \/>\r\n[\/datasetoption][datasetoption]<br \/>\r\n[displayname]Rent Prices in the U.S.[\/displayname]<br \/>\r\n[ohmid]2643[\/ohmid]<br \/>\r\n[\/datasetoption][datasetoption]<br \/>\r\n[displayname]WNBA Players[\/displayname]<br \/>\r\n[ohmid]2644[\/ohmid]<br \/>\r\n[\/datasetoption][\/choosedataset]<\/section>","rendered":"<h2>Variables<\/h2>\n<p>The next step in a statistical investigation is to decide what you&#8217;re measuring and how you&#8217;re going to collect the data. Data are often shown as a long list of information about a group of individuals, animals, or objects. What you choose to measure is called the\u00a0<strong>variable<\/strong>. Some examples can include favorite color, height, cost, age, heart rate, state, and more.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>variable<\/h3>\n<p>A characteristic that can be measured and has different values.<\/p>\n<\/div>\n<\/section>\n<h2>Qualitative and Quantitative Data<\/h2>\n<p>Data are the actual values of the variable. They may be numbers or they may be words. As such, data can be categorized as <strong>qualitative<\/strong> or <strong>quantitative data<\/strong>.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>qualitative\/categorical data<\/h3>\n<p><strong>Qualitative data<\/strong> are the result of categorizing or describing attributes of a population. <\/p>\n<p>Hair color, blood type, ethnic group, the car a person drives, and the street a person lives on are examples of qualitative data. <\/p>\n<p>Qualitative data are generally described by words or letters. For instance, hair color might be black, dark brown, light brown, blonde, gray, or red. Blood type might be AB+, O-, or B+. <\/p>\n<p>Qualitative data are also often called <strong>categorical data<\/strong>.<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>quantitative data (discrete and continuous)<\/h3>\n<p><strong>Quantitative data<\/strong> are the result of counting or measuring attributes of a population. Amount of money, pulse rate, weight, number of people living in your town, and number of students who take statistics courses are examples of quantitative data.<\/p>\n<p>&nbsp;<\/p>\n<p>Quantitative data\u00a0are always numbers.<\/p>\n<p>&nbsp;<\/p>\n<p>Quantitative <strong>discrete<\/strong> data are the result of counting. If you count the number of phone calls you receive for each day of the week, you might get values such as [latex]0, 1, 2, \\mathrm{or} \\ 3[\/latex].\u00a0<\/p>\n<p>&nbsp;<\/p>\n<p>Quantitative <strong>continuous<\/strong> data refers to a type of numerical data that can take on an infinite number of values within a given range. Continuous data are often the results of measurements like lengths, weights, or times like a list of the lengths in minutes for all the phone calls that you make in a week.<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox example\">Determine the the variable(s) and the type of data in the following study.<\/p>\n<p>We want to know the average amount of money first year college students spend at ABC College on school supplies that do not include books. We randomly survey [latex]100[\/latex] first year students at the college. Three of those students spent [latex]$152.75[\/latex], [latex]$211.10[\/latex], and [latex]$225.50[\/latex], respectively.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q315469\">Show Solution<\/button><\/p>\n<div id=\"q315469\" class=\"hidden-answer\" style=\"display: none\">The <strong>variable <\/strong>is the amount of money spent on school supplies (excluding books) by one first year student.<\/p>\n<p>The <strong>data <\/strong>are the dollar amounts spent by the first year students. Examples of the data are $[latex]152.75[\/latex], $[latex]211.10[\/latex], and $[latex]225.50[\/latex]. These are <strong>quantitative discrete data <\/strong>because the variable is numerical and can take on only specific possible values. Although money is conceptually continuous, in practice it is measured in fixed increments (to the nearest cent), so the amounts can only occur in multiples of $[latex]0.01[\/latex]. Since there are gaps between possible values (for example, $[latex]152.751[\/latex] is not possible), the data are discrete.<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3161\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3161&theme=lumen&iframe_resize_id=ohm3161&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section><\/section>\n<section>\n<section class=\"textbox proTip\">\n<ol>\n<li>While quantitative variables <em>always\u00a0<\/em>have numerical data, not all numerical data is quantitative. Qualitative data can be numerical if the numbers don&#8217;t help us compare the values. For example, zip code has a numerical response, but we don&#8217;t compare zip codes numerically (think about how there is no such thing as an average zip code, and having a higher\/lower zip code doesn&#8217;t really communicate information about where you live). Zip code is a categorical variable, not a quantitative one.<\/li>\n<li>Discrete data can include fractions or decimals. The key is to recognize whether\u00a0<em>any <\/em>fraction or decimal would be accepted. Shoe size is a great example of quantitative discrete data that includes decimals since your shoe size can be 9, 9.5, 10, 10.5, but could not be any decimal between 9 and 9.5.<\/li>\n<\/ol>\n<\/section>\n<\/section>\n<section class=\"textbox youChoose\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4578 aligncenter\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/10\/13214944\/ChooseDatasetImage.png\" alt=\"\" width=\"610\" height=\"105\" \/><\/p>\n<div id=\"tnh-choose-dataset\" class=\"chooseDataset\">\n<h3>Classify Variables<\/h3>\n<h4>For this problem, you'll identify and classify the variables using a data set of your choosing.<\/h4>\n<form><select name=\"dataset\"><option value=\"\">Choose a Dataset<\/option><option value=\"2642\">Unsolved Murders<\/option><option value=\"2643\">Rent Prices in the U.S.<\/option><option value=\"2644\">WNBA Players<\/option><\/select><\/form>\n<div class=\"ohmContainer\"><\/div>\n<\/p><\/div>\n<\/section>\n","protected":false},"author":13,"menu_order":11,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":375,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":[{"divId":"tnh-choose-dataset","title":"Classify Variables","label":"For this problem, you'll identify and classify the variables using a data set of your choosing.","default":"Choose a Dataset","try_it_collection":[{"displayName":"Unsolved Murders","value":"2642"},{"displayName":"Rent Prices in the U.S.","value":"2643"},{"displayName":"WNBA Players","value":"2644"}]}],"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/476"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/13"}],"version-history":[{"count":32,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/476\/revisions"}],"predecessor-version":[{"id":7143,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/476\/revisions\/7143"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/375"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/476\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=476"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=476"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=476"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=476"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}