{"id":52,"date":"2017-04-15T03:15:22","date_gmt":"2017-04-15T03:15:22","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/conceptstest1\/chapter\/dotplots-1-of-2\/"},"modified":"2017-05-28T00:01:32","modified_gmt":"2017-05-28T00:01:32","slug":"dotplots-1-of-2","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/chapter\/dotplots-1-of-2\/","title":{"raw":"Dotplots (1 of 2)","rendered":"Dotplots (1 of 2)"},"content":{"raw":"&nbsp;\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Describe the distribution of quantitative data using a dot plot.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3>Introduction<\/h3>\r\nWhen we work with data, the data is usually in a table. In this form, we can easily see the variable value for each individual. But when we analyze data, we are not focused on information about an individual. We want to describe a group of individuals. In data analysis, our goal is to describe patterns in the data and create a useful summary about a group. A table is not a useful way to view data because patterns are hard to see in a table. For this reason, our first step in data analysis is to create a graph of the <strong>distribution <\/strong>of the variable.\r\n\r\nIn a graph that summarizes the distribution of a variable, we can see\r\n<ul>\r\n \t<li>the possible values of the variable.<\/li>\r\n \t<li>the number of individuals with each variable value or interval of values.<\/li>\r\n<\/ul>\r\nIn this module, <em>Summarizing Data Graphically and Numerically<\/em>, we focus on summarizing the distribution of a quantitative variable. We discuss the distribution of a categorical variable in depth in the module <em>Relationships in Categorical Data with Intro to Probability<\/em>.\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\n<h2>Breakfast Cereals<\/h2>\r\nHere are two graphs of the variable <em>protein<\/em> for a group of breakfast cereals targeted at children.\r\n\r\nIn both graphs, the individuals and the variable are the same:\r\n<ul>\r\n \t<li>Individuals: Children\u2019s cereals<\/li>\r\n \t<li>Variable: Grams of protein in a serving of cereal<\/li>\r\n<\/ul>\r\nLet\u2019s compare the graphs to determine which graph is a better summary of the distribution of protein.\r\n\r\n<img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031518\/m2_summarizing_data_topic_2_1__m2_1_dataset_image2.png\" alt=\"Case value graph showing protein content of various cereals\" width=\"493\" height=\"273\" \/>\r\n\r\nThis graph is called a <strong>case-value graph<\/strong>. You can see the names of the individual cereals (the cases) and the amount of protein in a serving of each cereal (the variable values). For example, Apple Jacks has 2 grams of protein in a serving. This graph is NOT a good way to summarize the distribution of protein values because we cannot easily determine the number of cereals with each protein amount.\r\n\r\nFor example, how many cereals have 2 grams of protein in a serving? This graph does not make it easy to answer this question. We have to move across the graph and count the cereals with 2 grams of protein. In this way, a case-value graph is like a table. We cannot easily see patterns in the data or determine the number of individuals with a given variable value.\r\n\r\nHere is a second graph of the same data. This graph is called a <strong>dotplot<\/strong>. A dotplot gives a better summary of the distribution of protein.\r\n\r\n<img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031520\/m2_summarizing_data_topic_2_1__m2_1_dataset_image3.png\" alt=\"Dotplot of protein content of various cereals, where most of the cereals have between one to two grams of protein.\" width=\"423\" height=\"153\" \/>\r\n\r\nIn a dotplot, each dot represents one individual. Here, each dot is a children\u2019s cereal. The numbers on the horizontal axis are the variable values. The vertical axis gives the count of cereals. We can easily see that 10 children\u2019s cereals have 2 grams of protein in a serving.\r\n\r\nFrom the dotplot, we can easily describe the distribution of protein. Here are some observations about this distribution:\r\n<ul>\r\n \t<li>The amount of protein in a serving varies from 1 to 6 grams.<\/li>\r\n \t<li>Most of the cereals have 1 or 2 grams of protein in a serving.<\/li>\r\n \t<li>Larger amounts of protein are less typical.<\/li>\r\n \t<li>One cereal has 6 grams of protein. This much protein is unusual for this group of children\u2019s cereals.<\/li>\r\n<\/ul>\r\nThese observations are a good summary of the data.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Learn By Doing<\/h3>\r\nhttps:\/\/assessments.lumenlearning.com\/assessments\/3421\r\n\r\nhttps:\/\/assessments.lumenlearning.com\/assessments\/3422\r\n\r\n<\/div>\r\n&nbsp;","rendered":"<p>&nbsp;<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Describe the distribution of quantitative data using a dot plot.<\/li>\n<\/ul>\n<\/div>\n<h3>Introduction<\/h3>\n<p>When we work with data, the data is usually in a table. In this form, we can easily see the variable value for each individual. But when we analyze data, we are not focused on information about an individual. We want to describe a group of individuals. In data analysis, our goal is to describe patterns in the data and create a useful summary about a group. A table is not a useful way to view data because patterns are hard to see in a table. For this reason, our first step in data analysis is to create a graph of the <strong>distribution <\/strong>of the variable.<\/p>\n<p>In a graph that summarizes the distribution of a variable, we can see<\/p>\n<ul>\n<li>the possible values of the variable.<\/li>\n<li>the number of individuals with each variable value or interval of values.<\/li>\n<\/ul>\n<p>In this module, <em>Summarizing Data Graphically and Numerically<\/em>, we focus on summarizing the distribution of a quantitative variable. We discuss the distribution of a categorical variable in depth in the module <em>Relationships in Categorical Data with Intro to Probability<\/em>.<\/p>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<h2>Breakfast Cereals<\/h2>\n<p>Here are two graphs of the variable <em>protein<\/em> for a group of breakfast cereals targeted at children.<\/p>\n<p>In both graphs, the individuals and the variable are the same:<\/p>\n<ul>\n<li>Individuals: Children\u2019s cereals<\/li>\n<li>Variable: Grams of protein in a serving of cereal<\/li>\n<\/ul>\n<p>Let\u2019s compare the graphs to determine which graph is a better summary of the distribution of protein.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031518\/m2_summarizing_data_topic_2_1__m2_1_dataset_image2.png\" alt=\"Case value graph showing protein content of various cereals\" width=\"493\" height=\"273\" \/><\/p>\n<p>This graph is called a <strong>case-value graph<\/strong>. You can see the names of the individual cereals (the cases) and the amount of protein in a serving of each cereal (the variable values). For example, Apple Jacks has 2 grams of protein in a serving. This graph is NOT a good way to summarize the distribution of protein values because we cannot easily determine the number of cereals with each protein amount.<\/p>\n<p>For example, how many cereals have 2 grams of protein in a serving? This graph does not make it easy to answer this question. We have to move across the graph and count the cereals with 2 grams of protein. In this way, a case-value graph is like a table. We cannot easily see patterns in the data or determine the number of individuals with a given variable value.<\/p>\n<p>Here is a second graph of the same data. This graph is called a <strong>dotplot<\/strong>. A dotplot gives a better summary of the distribution of protein.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031520\/m2_summarizing_data_topic_2_1__m2_1_dataset_image3.png\" alt=\"Dotplot of protein content of various cereals, where most of the cereals have between one to two grams of protein.\" width=\"423\" height=\"153\" \/><\/p>\n<p>In a dotplot, each dot represents one individual. Here, each dot is a children\u2019s cereal. The numbers on the horizontal axis are the variable values. The vertical axis gives the count of cereals. We can easily see that 10 children\u2019s cereals have 2 grams of protein in a serving.<\/p>\n<p>From the dotplot, we can easily describe the distribution of protein. Here are some observations about this distribution:<\/p>\n<ul>\n<li>The amount of protein in a serving varies from 1 to 6 grams.<\/li>\n<li>Most of the cereals have 1 or 2 grams of protein in a serving.<\/li>\n<li>Larger amounts of protein are less typical.<\/li>\n<li>One cereal has 6 grams of protein. This much protein is unusual for this group of children\u2019s cereals.<\/li>\n<\/ul>\n<p>These observations are a good summary of the data.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Learn By Doing<\/h3>\n<p>\t<iframe id=\"lumen_assessment_3421\" class=\"resizable\" src=\"https:\/\/assessments.lumenlearning.com\/assessments\/load?assessment_id=3421&#38;embed=1&#38;external_user_id=&#38;external_context_id=&#38;iframe_resize_id=lumen_assessment_3421\" frameborder=\"0\" style=\"border:none;width:100%;height:100%;min-height:400px;\"><br \/>\n\t<\/iframe><\/p>\n<p>\t<iframe id=\"lumen_assessment_3422\" class=\"resizable\" src=\"https:\/\/assessments.lumenlearning.com\/assessments\/load?assessment_id=3422&#38;embed=1&#38;external_user_id=&#38;external_context_id=&#38;iframe_resize_id=lumen_assessment_3422\" frameborder=\"0\" style=\"border:none;width:100%;height:100%;min-height:400px;\"><br \/>\n\t<\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/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-52\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Concepts in Statistics. <strong>Provided by<\/strong>: Open Learning Initiative. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/oli.cmu.edu\">http:\/\/oli.cmu.edu<\/a>. <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>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":163,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Concepts in Statistics\",\"author\":\"\",\"organization\":\"Open Learning Initiative\",\"url\":\"http:\/\/oli.cmu.edu\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"8a937e72-a277-4731-b7b2-5dba75bafefb","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-52","chapter","type-chapter","status-web-only","hentry"],"part":43,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/52","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/wp\/v2\/users\/163"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/52\/revisions"}],"predecessor-version":[{"id":1314,"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/52\/revisions\/1314"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/pressbooks\/v2\/parts\/43"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/52\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/wp\/v2\/media?parent=52"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapter-type?post=52"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/wp\/v2\/contributor?post=52"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/wp\/v2\/license?post=52"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}