{"id":1996,"date":"2021-09-17T15:06:38","date_gmt":"2021-09-17T15:06:38","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=1996"},"modified":"2022-02-18T05:32:15","modified_gmt":"2022-02-18T05:32:15","slug":"summary-review-8","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-review-8\/","title":{"raw":"Summary: Review","rendered":"Summary: Review"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<strong>Interval Notation<\/strong>\r\n<div align=\"left\">\r\n<table style=\"height: 126px;\">\r\n<tbody>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 188.906px;\"><strong>Inequality<\/strong><\/td>\r\n<td style=\"height: 14px; width: 178.094px;\"><strong>Interval Notation<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 188.906px;\">[latex]a&lt;x&lt;b[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 178.094px;\">[latex](a,b)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 188.906px;\">[latex]x&gt;a[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 178.094px;\">[latex](a,\u221e)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 188.906px;\">[latex]x&lt;b[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 178.094px;\">[latex](\u2212\u221e,b)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 188.906px;\">[latex]x\u2265a[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 178.094px;\">[latex][a,\u221e)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 188.906px;\">[latex]x\u2264b[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 178.094px;\">[latex](\u2212\u221e,b][\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 188.906px;\">[latex]a\u2264x&lt;b[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 178.094px;\">[latex][a,b)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 188.906px;\">[latex]a&lt;x\u2264b[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 178.094px;\">[latex](a,b][\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 188.906px;\">[latex]a\u2264x\u2264b[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 178.094px;\">[latex][a,b][\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nFor a finite interval [latex](a,b), (a,b], [a,b) \\ \\mathrm{or} \\ [a,b][\/latex].\r\n<ul>\r\n \t<li>The width is [latex]b-a[\/latex]<\/li>\r\n \t<li>The midpoint is [latex]\\frac{a+b}{2}[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\n<strong>Population and sample mean, variance, and standard deviation<\/strong>\r\n<div align=\"left\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Population\u00a0<\/strong><\/td>\r\n<td><strong>Sample<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Population size [latex]N[\/latex]<\/td>\r\n<td>Sample size [latex]n[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Population mean [latex]\\mu = \\frac{\\sum{x}}{N}[\/latex]<\/td>\r\n<td>Sample mean [latex]\\overline{x}=\\frac{\\sum{x}}{n}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Population variance [latex]\\sigma ^2. = \\frac{\\sum{(x- \\mu)^2}}{N}[\/latex]<\/td>\r\n<td>Sample variance [latex]s^2=\\frac{\\sum{(x-\\overline{x})^2}}{n-1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Population standard deviation [latex]\\sigma = \\sqrt{\\frac{\\sum{(x-\\mu)^2}}{N}}[\/latex]<\/td>\r\n<td>Sample standard deviation [latex]s=\\sqrt{\\frac{\\sum{(x-\\overline{x})^2}}{n-1}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Glossary<\/h2>\r\n<ul>\r\n \t<li aria-level=\"1\"><strong>interval:\u00a0<\/strong>a set of numbers in which a solution falls<\/li>\r\n \t<li aria-level=\"1\"><strong>population:\u00a0<\/strong>the entire group of individuals or objects of interest<\/li>\r\n \t<li aria-level=\"1\"><strong>parameter:<\/strong> a numerical characteristic of a population<\/li>\r\n \t<li aria-level=\"1\"><strong>sample:<\/strong> portion, or subset, of a population<\/li>\r\n \t<li aria-level=\"1\"><strong>statistic:<\/strong> a numerical characteristic of a sample<\/li>\r\n<\/ul>\r\n<\/div>","rendered":"<h2>Key Concepts<\/h2>\n<p><strong>Interval Notation<\/strong><\/p>\n<div style=\"text-align: left;\">\n<table style=\"height: 126px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 188.906px;\"><strong>Inequality<\/strong><\/td>\n<td style=\"height: 14px; width: 178.094px;\"><strong>Interval Notation<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 188.906px;\">[latex]a<x<b[\/latex]<\/td>\n<td style=\"height: 14px; width: 178.094px;\">[latex](a,b)[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 188.906px;\">[latex]x>a[\/latex]<\/td>\n<td style=\"height: 14px; width: 178.094px;\">[latex](a,\u221e)[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 188.906px;\">[latex]x<b[\/latex]<\/td>\n<td style=\"height: 14px; width: 178.094px;\">[latex](\u2212\u221e,b)[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 188.906px;\">[latex]x\u2265a[\/latex]<\/td>\n<td style=\"height: 14px; width: 178.094px;\">[latex][a,\u221e)[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 188.906px;\">[latex]x\u2264b[\/latex]<\/td>\n<td style=\"height: 14px; width: 178.094px;\">[latex](\u2212\u221e,b][\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 188.906px;\">[latex]a\u2264x<b[\/latex]<\/td>\n<td style=\"height: 14px; width: 178.094px;\">[latex][a,b)[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 188.906px;\">[latex]a<x\u2264b[\/latex]<\/td>\n<td style=\"height: 14px; width: 178.094px;\">[latex](a,b][\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 188.906px;\">[latex]a\u2264x\u2264b[\/latex]<\/td>\n<td style=\"height: 14px; width: 178.094px;\">[latex][a,b][\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>For a finite interval [latex](a,b), (a,b], [a,b) \\ \\mathrm{or} \\ [a,b][\/latex].<\/p>\n<ul>\n<li>The width is [latex]b-a[\/latex]<\/li>\n<li>The midpoint is [latex]\\frac{a+b}{2}[\/latex]<\/li>\n<\/ul>\n<\/div>\n<p><strong>Population and sample mean, variance, and standard deviation<\/strong><\/p>\n<div style=\"text-align: left;\">\n<table>\n<tbody>\n<tr>\n<td><strong>Population\u00a0<\/strong><\/td>\n<td><strong>Sample<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Population size [latex]N[\/latex]<\/td>\n<td>Sample size [latex]n[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Population mean [latex]\\mu = \\frac{\\sum{x}}{N}[\/latex]<\/td>\n<td>Sample mean [latex]\\overline{x}=\\frac{\\sum{x}}{n}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Population variance [latex]\\sigma ^2. = \\frac{\\sum{(x- \\mu)^2}}{N}[\/latex]<\/td>\n<td>Sample variance [latex]s^2=\\frac{\\sum{(x-\\overline{x})^2}}{n-1}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Population standard deviation [latex]\\sigma = \\sqrt{\\frac{\\sum{(x-\\mu)^2}}{N}}[\/latex]<\/td>\n<td>Sample standard deviation [latex]s=\\sqrt{\\frac{\\sum{(x-\\overline{x})^2}}{n-1}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Glossary<\/h2>\n<ul>\n<li aria-level=\"1\"><strong>interval:\u00a0<\/strong>a set of numbers in which a solution falls<\/li>\n<li aria-level=\"1\"><strong>population:\u00a0<\/strong>the entire group of individuals or objects of interest<\/li>\n<li aria-level=\"1\"><strong>parameter:<\/strong> a numerical characteristic of a population<\/li>\n<li aria-level=\"1\"><strong>sample:<\/strong> portion, or subset, of a population<\/li>\n<li aria-level=\"1\"><strong>statistic:<\/strong> a numerical characteristic of a sample<\/li>\n<\/ul>\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-1996\">\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>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>College Algebra. <strong>Authored by<\/strong>: Jay Abramson, et al. Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/read-describe-solutions-to-inequalities-2\/\">https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/read-describe-solutions-to-inequalities-2\/<\/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>Unit 10: Solving Equations and Inequalities, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/dm-opentext\">http:\/\/nrocnetwork.org\/dm-opentext<\/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>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":169134,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Jay Abramson, et al. 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