{"id":138,"date":"2017-04-15T03:17:44","date_gmt":"2017-04-15T03:17:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/conceptstest1\/chapter\/summarizing-data-graphically-and-numerically-review\/"},"modified":"2020-01-17T22:45:31","modified_gmt":"2020-01-17T22:45:31","slug":"summarizing-data-graphically-and-numerically-review","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/chapter\/summarizing-data-graphically-and-numerically-review\/","title":{"raw":"Putting It Together: Summarizing Data Graphically and Numerically","rendered":"Putting It Together: Summarizing Data Graphically and Numerically"},"content":{"raw":"<h2><strong>Let\u2019s Summarize<\/strong><\/h2>\r\nIn <em>Summarizing Data Graphically and Numerically<\/em>, we focused on describing the <em>distribution of a quantitative variable<\/em>.\r\n<ul>\r\n \t<li>To analyze the distribution of a quantitative variable, we describe the <em>overall pattern of the data<\/em> (shape, center, spread) and any <em>deviations from the pattern<\/em> (outliers). We use three types of graphs to analyze the distribution of a quantitative variable: dotplots, histograms, and boxplots.<\/li>\r\n \t<li>We described the <em>shape <\/em>of a distribution as left-skewed, right-skewed, symmetric with a central peak (bell-shaped), or uniform. Not all distributions have a simple shape that fits into one of these categories.<\/li>\r\n \t<li>The <em>center <\/em>of a distribution is a typical value that represents the group. We have two different measurements for determining the center of a distribution: mean and median.\r\n<ul>\r\n \t<li>The <em>mean <\/em>is the average. We calculate the mean by adding the data values and dividing by the number of individual data points. The <em>mean <\/em>is the <em> fair share<\/em> measure. The mean is also called the <em>balancing point<\/em> of a distribution. If we measure the distance between each data point and the mean, the distances are balanced on each side of the mean.<\/li>\r\n \t<li>The <em>median <\/em>is the physical center of the data when we make an ordered list. It has the same number of values above it as below it.<\/li>\r\n \t<li><strong>General Guidelines for Choosing a Measure of Center<\/strong>\r\n<ul>\r\n \t<li><em>Always plot the data. <\/em>We need to use a graph to determine the shape of the distribution. By looking at the shape, we can determine which measure of center best describes the data.<\/li>\r\n \t<li>Use the mean as a measure of center <em>only <\/em>for distributions that are reasonably symmetric with a central peak. When outliers are present, the mean is not a good choice.<\/li>\r\n \t<li>Use the median as a measure of center for all other cases.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>The <em>spread <\/em>of a distribution is a description of how the data varies. We studied three ways to measure spread: <em>range<\/em> (max \u2013 min), the <em>interquartile range<\/em> (Q3 \u2013 Q1), and the <em>standard deviation<\/em>. When we use the median, Q1 to Q3 gives a typical range of values associated with the middle 50% of the data. When we use the mean, Mean \u00b1 SD gives a typical range of values.\r\n<ul>\r\n \t<li>The interquartile range (IQR) measures the variability in the middle half of the data.<\/li>\r\n \t<li>Standard deviation measures roughly the average distance of data from the mean.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><em>Outliers <\/em>are data points that fall outside the overall pattern of the distribution. When using the median and IQR to measure center and spread, we use the 1.5 * IQR interval to identify outliers. Specifically, points outside the interval Q1 \u2013 1.5 * IQR to Q3 + 1.5 * IQR are labeled as outliers.<\/li>\r\n<\/ul>\r\n<h2>Contribute!<\/h2><div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div><a href=\"https:\/\/docs.google.com\/document\/d\/1dKulIgGmAvpYGhHQX_tKBAQABzELZIVbI7I-0oKdXTU\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a>","rendered":"<h2><strong>Let\u2019s Summarize<\/strong><\/h2>\n<p>In <em>Summarizing Data Graphically and Numerically<\/em>, we focused on describing the <em>distribution of a quantitative variable<\/em>.<\/p>\n<ul>\n<li>To analyze the distribution of a quantitative variable, we describe the <em>overall pattern of the data<\/em> (shape, center, spread) and any <em>deviations from the pattern<\/em> (outliers). We use three types of graphs to analyze the distribution of a quantitative variable: dotplots, histograms, and boxplots.<\/li>\n<li>We described the <em>shape <\/em>of a distribution as left-skewed, right-skewed, symmetric with a central peak (bell-shaped), or uniform. Not all distributions have a simple shape that fits into one of these categories.<\/li>\n<li>The <em>center <\/em>of a distribution is a typical value that represents the group. We have two different measurements for determining the center of a distribution: mean and median.\n<ul>\n<li>The <em>mean <\/em>is the average. We calculate the mean by adding the data values and dividing by the number of individual data points. The <em>mean <\/em>is the <em> fair share<\/em> measure. The mean is also called the <em>balancing point<\/em> of a distribution. If we measure the distance between each data point and the mean, the distances are balanced on each side of the mean.<\/li>\n<li>The <em>median <\/em>is the physical center of the data when we make an ordered list. It has the same number of values above it as below it.<\/li>\n<li><strong>General Guidelines for Choosing a Measure of Center<\/strong>\n<ul>\n<li><em>Always plot the data. <\/em>We need to use a graph to determine the shape of the distribution. By looking at the shape, we can determine which measure of center best describes the data.<\/li>\n<li>Use the mean as a measure of center <em>only <\/em>for distributions that are reasonably symmetric with a central peak. When outliers are present, the mean is not a good choice.<\/li>\n<li>Use the median as a measure of center for all other cases.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>The <em>spread <\/em>of a distribution is a description of how the data varies. We studied three ways to measure spread: <em>range<\/em> (max \u2013 min), the <em>interquartile range<\/em> (Q3 \u2013 Q1), and the <em>standard deviation<\/em>. When we use the median, Q1 to Q3 gives a typical range of values associated with the middle 50% of the data. When we use the mean, Mean \u00b1 SD gives a typical range of values.\n<ul>\n<li>The interquartile range (IQR) measures the variability in the middle half of the data.<\/li>\n<li>Standard deviation measures roughly the average distance of data from the mean.<\/li>\n<\/ul>\n<\/li>\n<li><em>Outliers <\/em>are data points that fall outside the overall pattern of the distribution. When using the median and IQR to measure center and spread, we use the 1.5 * IQR interval to identify outliers. Specifically, points outside the interval Q1 \u2013 1.5 * IQR to Q3 + 1.5 * IQR are labeled as outliers.<\/li>\n<\/ul>\n<h2>Contribute!<\/h2>\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\n<p><a href=\"https:\/\/docs.google.com\/document\/d\/1dKulIgGmAvpYGhHQX_tKBAQABzELZIVbI7I-0oKdXTU\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a><\/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-138\">\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":24,"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":"fb6b59cc-272e-4e75-96bc-c199957ae3b0","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-138","chapter","type-chapter","status-publish","hentry"],"part":43,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/138","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/users\/163"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/138\/revisions"}],"predecessor-version":[{"id":2254,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/138\/revisions\/2254"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/parts\/43"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/138\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/media?parent=138"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapter-type?post=138"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/contributor?post=138"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/license?post=138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}