{"id":303,"date":"2016-10-10T19:52:16","date_gmt":"2016-10-10T19:52:16","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/math4libarts\/?post_type=chapter&#038;p=303"},"modified":"2019-05-30T16:57:58","modified_gmt":"2019-05-30T16:57:58","slug":"categorizing-data","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/chapter\/categorizing-data\/","title":{"raw":"Categorizing Data","rendered":"Categorizing Data"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Determine whether a value calculated from a group\u00a0is a statistic or a parameter<\/li>\r\n \t<li>Identify the difference between a census and a sample<\/li>\r\n \t<li>Identify the population of a study<\/li>\r\n \t<li>Determine whether a measurement\u00a0is categorical or qualitative<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Quantitative or Categorical<\/h2>\r\nOnce we have gathered data, we might wish to classify it.\u00a0 Roughly speaking, data can be classified as categorical data or quantitative data.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/29214357\/12210424505_2da556e2df_z.jpg\"><img class=\"aligncenter size-full wp-image-1021\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/29214357\/12210424505_2da556e2df_z.jpg\" alt=\"vertical lines of colored circles\" width=\"640\" height=\"321\" \/><\/a>\r\n<div>\r\n<div class=\"textbox\">\r\n<div>\r\n<h3>Quantitative and categorical data<\/h3>\r\n<\/div>\r\n<div>\r\n\r\n<strong>Categorical (qualitative) data<\/strong> are pieces of information that allow us to classify the objects under investigation into various categories.\r\n\r\n<strong>Quantitative data<\/strong> are responses that are numerical in nature and with which we can perform meaningful arithmetic calculations.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWe might conduct a survey to determine the name of the favorite movie that each person in a math class saw in a movie theater.\r\n\r\nWhen we conduct such a survey, the responses would look like: <em>Finding Nemo<\/em>, <em>The Hulk<\/em>, or <em>Terminator 3: Rise of the Machines<\/em>. We might count the number of people who give each answer, but the answers themselves do not have any numerical values: we cannot perform computations with an answer like \"<em>Finding Nemo<\/em>.\" Is this categorical or quantitative data?\r\n[reveal-answer q=\"914414\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"914414\"]This would be categorical data.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nA survey could ask the number of movies you have seen in a movie theater in the past 12 months (0, 1, 2, 3, 4, . . .).\u00a0Is this categorical or quantitative data?\r\n[reveal-answer q=\"798578\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"798578\"]This would be quantitative data.Other examples of quantitative data would be the running time of the movie you saw most recently (104 minutes, 137 minutes, 104 minutes, . . .) or the amount of money you paid for a movie ticket the last time you went to a movie theater ($5.50, $7.75, $9, . . .).[\/hidden-answer]\r\n\r\n<\/div>\r\nSometimes, determining whether or not data is categorical or quantitative can be a bit trickier. \u00a0In the next example, teh data collected is in numerical form, but it is not quantitative data. \u00a0Read on to find out why.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\n[caption id=\"attachment_1453\" align=\"alignleft\" width=\"244\"]<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/09002155\/Screen-Shot-2017-02-08-at-4.21.15-PM.png\"><img class=\" wp-image-1453\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/09002155\/Screen-Shot-2017-02-08-at-4.21.15-PM-300x230.png\" alt=\"Map of Portland, OR with zip codes.\" width=\"244\" height=\"187\" \/><\/a> Zip Codes for Portland, OR[\/caption]\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\nSuppose we gather respondents' ZIP codes in a survey to track their geographical location. Is this categorical or quantitative?\r\n[reveal-answer q=\"103310\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"103310\"]ZIP codes are numbers, but we can't do any meaningful mathematical calculations with them (it doesn't make sense to say that 98036 is \"twice\" 49018\u00a0\u2014 that's like saying that Lynnwood, WA is \"twice\" Battle Creek, MI, which doesn't make sense at all), so ZIP codes are really categorical data.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nA survey about the movie you most recently attended includes the question \"How would you rate the movie you just saw?\" with these possible answers:\r\n\r\n1 - it was awful\r\n2 - it was just OK\r\n3 - I liked it\r\n4 - it was great\r\n5 - best movie ever!\r\n\r\nIs this categorical or quantitative?\r\n[reveal-answer q=\"286755\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"286755\"]\r\n<div>\r\n\r\nAgain, there are numbers associated with the responses, but we can't really do any calculations with them: a movie that rates a 4 is not necessarily twice as good as a movie that rates a 2, whatever that means; if two people see the movie and one of them thinks it stinks and the other thinks it's the best ever it doesn't necessarily make sense to say that \"on average they liked it.\"\r\n\r\n<\/div>\r\nAs we study movie-going habits and preferences, we shouldn't forget to specify the population under consideration. If we survey 3-7 year-olds the runaway favorite might be <em>Finding Nemo<\/em>. 13-17 year-olds might prefer <em>Terminator 3<\/em>. And 33-37 year-olds might prefer . . . well, <em>Finding Nemo<\/em>.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nThe examples in this page are discussed further in the following video:\r\n\r\nhttps:\/\/youtu.be\/mxZqyB01qPY\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nClassify each measurement as categorical or quantitative.\r\n<ol>\r\n \t<li>Eye color of a group of people<\/li>\r\n \t<li>Daily high temperature of a city over several weeks<\/li>\r\n \t<li>Annual income<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"122772\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"122772\"]1. Categorical. \u00a02. Quantitative 3. Quantitative[\/hidden-answer]\r\n\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=6743&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe>\r\n\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Determine whether a value calculated from a group\u00a0is a statistic or a parameter<\/li>\n<li>Identify the difference between a census and a sample<\/li>\n<li>Identify the population of a study<\/li>\n<li>Determine whether a measurement\u00a0is categorical or qualitative<\/li>\n<\/ul>\n<\/div>\n<h2>Quantitative or Categorical<\/h2>\n<p>Once we have gathered data, we might wish to classify it.\u00a0 Roughly speaking, data can be classified as categorical data or quantitative data.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/29214357\/12210424505_2da556e2df_z.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1021\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/29214357\/12210424505_2da556e2df_z.jpg\" alt=\"vertical lines of colored circles\" width=\"640\" height=\"321\" \/><\/a><\/p>\n<div>\n<div class=\"textbox\">\n<div>\n<h3>Quantitative and categorical data<\/h3>\n<\/div>\n<div>\n<p><strong>Categorical (qualitative) data<\/strong> are pieces of information that allow us to classify the objects under investigation into various categories.<\/p>\n<p><strong>Quantitative data<\/strong> are responses that are numerical in nature and with which we can perform meaningful arithmetic calculations.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>We might conduct a survey to determine the name of the favorite movie that each person in a math class saw in a movie theater.<\/p>\n<p>When we conduct such a survey, the responses would look like: <em>Finding Nemo<\/em>, <em>The Hulk<\/em>, or <em>Terminator 3: Rise of the Machines<\/em>. We might count the number of people who give each answer, but the answers themselves do not have any numerical values: we cannot perform computations with an answer like &#8220;<em>Finding Nemo<\/em>.&#8221; Is this categorical or quantitative data?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q914414\">Show Solution<\/span><\/p>\n<div id=\"q914414\" class=\"hidden-answer\" style=\"display: none\">This would be categorical data.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>A survey could ask the number of movies you have seen in a movie theater in the past 12 months (0, 1, 2, 3, 4, . . .).\u00a0Is this categorical or quantitative data?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q798578\">Show Solution<\/span><\/p>\n<div id=\"q798578\" class=\"hidden-answer\" style=\"display: none\">This would be quantitative data.Other examples of quantitative data would be the running time of the movie you saw most recently (104 minutes, 137 minutes, 104 minutes, . . .) or the amount of money you paid for a movie ticket the last time you went to a movie theater ($5.50, $7.75, $9, . . .).<\/div>\n<\/div>\n<\/div>\n<p>Sometimes, determining whether or not data is categorical or quantitative can be a bit trickier. \u00a0In the next example, teh data collected is in numerical form, but it is not quantitative data. \u00a0Read on to find out why.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<div id=\"attachment_1453\" style=\"width: 254px\" class=\"wp-caption alignleft\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/09002155\/Screen-Shot-2017-02-08-at-4.21.15-PM.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1453\" class=\"wp-image-1453\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/09002155\/Screen-Shot-2017-02-08-at-4.21.15-PM-300x230.png\" alt=\"Map of Portland, OR with zip codes.\" width=\"244\" height=\"187\" \/><\/a><\/p>\n<p id=\"caption-attachment-1453\" class=\"wp-caption-text\">Zip Codes for Portland, OR<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Suppose we gather respondents&#8217; ZIP codes in a survey to track their geographical location. Is this categorical or quantitative?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q103310\">Show Solution<\/span><\/p>\n<div id=\"q103310\" class=\"hidden-answer\" style=\"display: none\">ZIP codes are numbers, but we can&#8217;t do any meaningful mathematical calculations with them (it doesn&#8217;t make sense to say that 98036 is &#8220;twice&#8221; 49018\u00a0\u2014 that&#8217;s like saying that Lynnwood, WA is &#8220;twice&#8221; Battle Creek, MI, which doesn&#8217;t make sense at all), so ZIP codes are really categorical data.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>A survey about the movie you most recently attended includes the question &#8220;How would you rate the movie you just saw?&#8221; with these possible answers:<\/p>\n<p>1 &#8211; it was awful<br \/>\n2 &#8211; it was just OK<br \/>\n3 &#8211; I liked it<br \/>\n4 &#8211; it was great<br \/>\n5 &#8211; best movie ever!<\/p>\n<p>Is this categorical or quantitative?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q286755\">Show Solution<\/span><\/p>\n<div id=\"q286755\" class=\"hidden-answer\" style=\"display: none\">\n<div>\n<p>Again, there are numbers associated with the responses, but we can&#8217;t really do any calculations with them: a movie that rates a 4 is not necessarily twice as good as a movie that rates a 2, whatever that means; if two people see the movie and one of them thinks it stinks and the other thinks it&#8217;s the best ever it doesn&#8217;t necessarily make sense to say that &#8220;on average they liked it.&#8221;<\/p>\n<\/div>\n<p>As we study movie-going habits and preferences, we shouldn&#8217;t forget to specify the population under consideration. If we survey 3-7 year-olds the runaway favorite might be <em>Finding Nemo<\/em>. 13-17 year-olds might prefer <em>Terminator 3<\/em>. And 33-37 year-olds might prefer . . . well, <em>Finding Nemo<\/em>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>The examples in this page are discussed further in the following video:<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Qualitative and Quantitative\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/mxZqyB01qPY?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Classify each measurement as categorical or quantitative.<\/p>\n<ol>\n<li>Eye color of a group of people<\/li>\n<li>Daily high temperature of a city over several weeks<\/li>\n<li>Annual income<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q122772\">Show Solution<\/span><\/p>\n<div id=\"q122772\" class=\"hidden-answer\" style=\"display: none\">1. Categorical. \u00a02. Quantitative 3. Quantitative<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=6743&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe><\/p>\n<\/div>\n<\/div>\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-303\">\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>Screenshot: Portland Zip Codes. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Categorizing Data. <strong>Authored by<\/strong>: David Lippman. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\">http:\/\/www.opentextbookstore.com\/mathinsociety\/<\/a>. <strong>Project<\/strong>: Math in Society. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Some cheerful data. <strong>Authored by<\/strong>: dirkcuys. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/flic.kr\/p\/jAZBNr\">https:\/\/flic.kr\/p\/jAZBNr<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Qualitative and Quantitative. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/mxZqyB01qPY\">https:\/\/youtu.be\/mxZqyB01qPY<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID 6743. <strong>Authored by<\/strong>: Lippman, David. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community LicenseCC-BY + GPL<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t 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