{"id":454,"date":"2021-12-20T14:34:51","date_gmt":"2021-12-20T14:34:51","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=454"},"modified":"2022-02-09T22:13:59","modified_gmt":"2022-02-09T22:13:59","slug":"summary-of-4c","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/summary-of-4c\/","title":{"raw":"Summary of Interpreting the Mean and Median of a Dataset: 4C","rendered":"Summary of Interpreting the Mean and Median of a Dataset: 4C"},"content":{"raw":"This page would contain resource information like a glossary of terms from the section, key equations, and a reminder of concepts that were covered.\r\n\r\nMake this more relevant to what students want -- help them to build their processes, study guides, mnemonics, and memory dump material.\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Essential Concepts<\/h3>\r\n<ul>\r\n \t<li>The median stays relatively fixed in a dataset if one value changes by a large amount, the mean does not. This is indication that the mean is sensitive to the presence of extreme values in the dataset.<\/li>\r\n \t<li>When a distribution is symmetric, the mean and median occupy the same value. Under a skew, the mean is \"pulled\" in the direction of the outliers:\r\n<ul>\r\n \t<li>Right-skewed: the mean is greater than the median.<\/li>\r\n \t<li>Left-skewed: the mean is less than the median.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>The mean, under certain conditions, can be a misleading indicator of a \"typical\" observation value.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Glossary<\/h2>\r\n<dl id=\"fs-id1170572229168\" class=\"definition\">\r\n \t<dt>right-skewed (positive skew)<\/dt>\r\n \t<dd id=\"fs-id1170572229174\">most of the data is bunched up to the left of the graph with a \"tail\" of infrequent values on the right (upper) end of the distribution.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572229190\" class=\"definition\">\r\n \t<dt>symmetric<\/dt>\r\n \t<dd id=\"fs-id1170572229195\">a distribution where the values are similarly distributed on either side of the mean\/median.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572482608\" class=\"definition\">\r\n \t<dt>left-skewed (negative skew)<\/dt>\r\n \t<dd id=\"fs-id1170572482614\">most of the data is bunched up to the right of the graph with a \"tail\" of infrequent values on the left (lower) end of the distribution.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572482619\" class=\"definition\">\r\n \t<dt>resistant<\/dt>\r\n \t<dd id=\"fs-id1170572482624\">not affected by the skewness of a graph.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572482683\" class=\"definition\">\r\n \t<dt>outlier<\/dt>\r\n \t<dd id=\"fs-id1170572482689\">an unusual or extreme value, given the other values in the dataset.<\/dd>\r\n<\/dl>\r\nPut formal DCMP I Can statements to prepare for the self-check.\r\n\r\n<span style=\"background-color: #ffff00;\">These I Can Statements are new (the first three are the \"you will understand\" rephrased as an I Can):<\/span>\r\n<ul>\r\n \t<li>I can identify medians as being resistant to influence from skew and outliers.<\/li>\r\n \t<li>I can identify means as not being resistant to influence from skew and outliers.<\/li>\r\n \t<li>I can identify, in certain circumstances, when the mean is misleading.<\/li>\r\n \t<li>I can identify misleading claims made using means and suggest the most appropriate measure of center to use in different situations.<\/li>\r\n<\/ul>","rendered":"<p>This page would contain resource information like a glossary of terms from the section, key equations, and a reminder of concepts that were covered.<\/p>\n<p>Make this more relevant to what students want &#8212; help them to build their processes, study guides, mnemonics, and memory dump material.<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Essential Concepts<\/h3>\n<ul>\n<li>The median stays relatively fixed in a dataset if one value changes by a large amount, the mean does not. This is indication that the mean is sensitive to the presence of extreme values in the dataset.<\/li>\n<li>When a distribution is symmetric, the mean and median occupy the same value. Under a skew, the mean is &#8220;pulled&#8221; in the direction of the outliers:\n<ul>\n<li>Right-skewed: the mean is greater than the median.<\/li>\n<li>Left-skewed: the mean is less than the median.<\/li>\n<\/ul>\n<\/li>\n<li>The mean, under certain conditions, can be a misleading indicator of a &#8220;typical&#8221; observation value.<\/li>\n<\/ul>\n<\/div>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1170572229168\" class=\"definition\">\n<dt>right-skewed (positive skew)<\/dt>\n<dd id=\"fs-id1170572229174\">most of the data is bunched up to the left of the graph with a &#8220;tail&#8221; of infrequent values on the right (upper) end of the distribution.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572229190\" class=\"definition\">\n<dt>symmetric<\/dt>\n<dd id=\"fs-id1170572229195\">a distribution where the values are similarly distributed on either side of the mean\/median.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572482608\" class=\"definition\">\n<dt>left-skewed (negative skew)<\/dt>\n<dd id=\"fs-id1170572482614\">most of the data is bunched up to the right of the graph with a &#8220;tail&#8221; of infrequent values on the left (lower) end of the distribution.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572482619\" class=\"definition\">\n<dt>resistant<\/dt>\n<dd id=\"fs-id1170572482624\">not affected by the skewness of a graph.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572482683\" class=\"definition\">\n<dt>outlier<\/dt>\n<dd id=\"fs-id1170572482689\">an unusual or extreme value, given the other values in the dataset.<\/dd>\n<\/dl>\n<p>Put formal DCMP I Can statements to prepare for the self-check.<\/p>\n<p><span style=\"background-color: #ffff00;\">These I Can Statements are new (the first three are the &#8220;you will understand&#8221; rephrased as an I Can):<\/span><\/p>\n<ul>\n<li>I can identify medians as being resistant to influence from skew and outliers.<\/li>\n<li>I can identify means as not being resistant to influence from skew and outliers.<\/li>\n<li>I can identify, in certain circumstances, when the mean is misleading.<\/li>\n<li>I can identify misleading claims made using means and suggest the most appropriate measure of center to use in different situations.<\/li>\n<\/ul>\n","protected":false},"author":25777,"menu_order":19,"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-454","chapter","type-chapter","status-publish","hentry"],"part":621,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/454","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\/25777"}],"version-history":[{"count":11,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/454\/revisions"}],"predecessor-version":[{"id":2995,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/454\/revisions\/2995"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/621"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/454\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=454"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=454"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=454"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=454"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}