{"id":311,"date":"2022-02-19T00:05:34","date_gmt":"2022-02-19T00:05:34","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/?post_type=chapter&#038;p=311"},"modified":"2022-05-20T16:46:22","modified_gmt":"2022-05-20T16:46:22","slug":"summary-of-comparing-variability-of-datasets","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/chapter\/summary-of-comparing-variability-of-datasets\/","title":{"raw":"Summary of Comparing Variability of Data Sets","rendered":"Summary of Comparing Variability of Data Sets"},"content":{"raw":"<h3><strong>Monitoring Your Readiness<\/strong><\/h3>\r\n<div class=\"textbox\">\r\n\r\nTo effectively plan and use your time wisely, it helps to think about what you know and do not know. For each of the following, rate how confident you are that you can successfully do that skill. Use the following descriptions to rate yourself:\r\n\r\n5\u2014I am extremely confident I can do this task.\r\n\r\n4\u2014I am somewhat confident I can do this task.\r\n\r\n3\u2014I am not sure how confident I am.\r\n\r\n2\u2014I am not very confident I can do this task.\r\n\r\n1\u2014I am definitely not confident I can do this task.\r\n\r\n<\/div>\r\n<h3 style=\"text-align: center;\">Skills Needed for Comparing Variability of Data Sets: Forming Connections<\/h3>\r\n<div align=\"center\">\r\n<table style=\"height: 107px;\">\r\n<tbody>\r\n<tr style=\"height: 10px;\">\r\n<td style=\"width: 319px; height: 10px; text-align: center;\"><strong>Skill or Concept: I can . . .<\/strong><\/td>\r\n<td style=\"width: 243px; height: 10px; text-align: center;\"><strong>Questions to check your understanding<\/strong><\/td>\r\n<td style=\"width: 113px; height: 10px; text-align: center;\"><strong>Rating\u00a0<\/strong><strong>from 1 to 5<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 26px;\">\r\n<td style=\"width: 319px; height: 26px;\">Visually assess the differences in variability, given comparative histograms or dotplots.<\/td>\r\n<td style=\"width: 243px; height: 26px; text-align: center;\">2, 3<\/td>\r\n<td style=\"width: 113px; height: 26px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 10px;\">\r\n<td style=\"width: 319px; height: 10px;\">Understand the summary statistics feature of the Describing and Exploring Quantitative Variables tool.<\/td>\r\n<td style=\"width: 243px; height: 10px; text-align: center;\">4, 5<\/td>\r\n<td style=\"width: 113px; height: 10px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 31px;\">\r\n<td style=\"width: 319px; height: 31px;\">Use technology to calculate measures of variability: standard deviation, variance, and range.<\/td>\r\n<td style=\"width: 243px; height: 31px; text-align: center;\">6-8<\/td>\r\n<td style=\"width: 113px; height: 31px;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nNow use the ratings to get ready for your next in-class activity. <strong>If your rating is a 3 or below, you should get help with the material before class.<\/strong> Remember, your instructor is going to assume that you are confident with the material and will not take class time to answer questions about it.\r\n\r\nWays to get help:\r\n<ul>\r\n \t<li>See your instructor before class for help.<\/li>\r\n \t<li>Ask your instructor for on-campus resources.<\/li>\r\n \t<li>Set up a study group with classmates so you can help each other.<\/li>\r\n \t<li>Work with a tutor.<\/li>\r\n<\/ul>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Essential Concepts<\/h3>\r\n<ul>\r\n \t<li>Variability can be measured in three ways: standard deviation, variance, and range.<\/li>\r\n \t<li>Variability can be judged from a histogram by examining the distance of the bars from the statistical center (mean or median) of the graph. If the\u00a0variability is high, equally sized or taller bars will appear away from the center of the graph. It the variability is low, the data will appear clustered around the center.<\/li>\r\n \t<li>The following steps can be applied to calculate a standard deviation by hand:\r\n<ol>\r\n \t<li>Calculate the mean of the population or sample.<\/li>\r\n \t<li>Take the difference between each data value and the mean. Then square each difference.<\/li>\r\n \t<li>Add up all the squared differences<\/li>\r\n \t<li>Divide by either the total number of observations in the case of a population or by 1 fewer than the total in the case of a sample.<\/li>\r\n \t<li>Take the square root of the result of the division in step 4.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Larger values of range indicate more variability in the data, but the range value only utilizes two observations in the entire data set to measure variability. This is not an ideal measure of spread, but when used in combination with other measures of spread, it can help you gain a clearer understanding of the spread of a distribution.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Study Tips: Evidence-based strategies for learning<\/h2>\r\n<ul>\r\n \t<li>Visual connections and contrasts associated with variability can be learned by quizzing yourself using flashcards, mnemonics, memory dumping (writing out everything you can remember onto a blank sheet of paper then comparing your output to a list of key concepts), and by making little sketches or symbols. Some examples of these include:\r\n<ul>\r\n \t<li>Visual clues of variability\r\n<ul>\r\n \t<li>Data that appears spread apart from the center has greater variability. Data that appears clustered toward the center has less variability.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>The <strong>R<\/strong>ange of a data set is the diffe<strong>R<\/strong>ence between the minimum and maximum data values in the set.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Standard deviation: a measure of variability. Gain understanding of standard deviation by paraphrasing the technical terminology out loud as though you are explaining it to a student in elementary school.\r\n<ul>\r\n \t<li>The Latin letter\u00a0<em>s<\/em> is used for samples.<\/li>\r\n \t<li>The Greek letter\u00a0[latex]\\sigma[\/latex] is used for populations.<\/li>\r\n \t<li>This Latin \/ Greek system of representation is generally true: Latin letters for samples and Greek letters for populations.\r\n<ul>\r\n \t<li>Population: [latex]\\mu[\/latex] for mean, [latex]\\sigma[\/latex] for standard deviation<\/li>\r\n \t<li>Sample:\u00a0\u00a0[latex]\\bar{x}[\/latex] for mean, [latex]s[\/latex] for standard deviation<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Variance is the square of standard deviation. Practice obtaining and calculating standard deviation and variance together.\r\n<ul>\r\n \t<li>Variance is the radicand (the value under the square root) of the standard deviation.<\/li>\r\n \t<li>Standard deviation is required to calculate variance.<\/li>\r\n \t<li>As you practice calculating standard deviation and variance in the text and assignments, pause periodically to think about why you are doing each step, how you know what steps to use to make the calculations by hand and via technology, and how you can know if your answer is reasonable or correct.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h2>Foundational Knowledge<\/h2>\r\n<ul>\r\n \t<li><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Number-Word+Combinations.pdf\">Number-Word Combinations<\/a><\/li>\r\n \t<li><a href=\"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/chapter\/comparing-variability-of-data sets-corequisite-support-activity\/\">Support Activity for Comparing Variability of Data Sets<\/a><\/li>\r\n<\/ul>\r\n<h2>Key Equations<\/h2>\r\n<ul>\r\n \t<li><strong>Deviation from the mean<\/strong><\/li>\r\n<\/ul>\r\n[latex]\\left(x-\\bar{x}\\right)[\/latex]\r\nwhere [latex]\\left(x\\right)[\/latex] is the observation in the data set, and\u00a0[latex]\\left(\\bar{x}\\right)[\/latex] is the sample mean.\r\n<ul>\r\n \t<li><strong>Standard deviation of a population<\/strong><\/li>\r\n<\/ul>\r\n[latex]\\sigma = \\sqrt{\\dfrac{\\sum \\left(x-\\mu\\right)^2}{n}}[\/latex]\r\nwhere [latex]\\sum[\/latex] is the summation of [latex]{\\left(x-\\mu\\right)^2}[\/latex] for each observation, [latex]\\left(x\\right)[\/latex] is the observation in the data set, [latex]\\left(\\mu\\right)[\/latex] is the mean, and [latex]\\left({n}\\right)[\/latex] is the number of observations.\r\n<ul>\r\n \t<li><strong>Standard deviation of a sample<\/strong><\/li>\r\n<\/ul>\r\n[latex]s=\\sqrt{\\dfrac{\\sum \\left(x-\\bar{x}\\right)^2}{n-1}} [\/latex]\r\nwhere [latex]\\sum[\/latex] is the summation of [latex]{\\left(x-\\bar{x}\\right)^2}[\/latex] for each observation, [latex]\\left(x\\right)[\/latex] is the observation in the data set, [latex]\\left(\\bar{x}\\right)[\/latex] is the mean, and [latex]\\left({n}\\right)[\/latex] is the number of observations.\r\n<ul>\r\n \t<li><strong>Variance of a population<\/strong><\/li>\r\n<\/ul>\r\n[latex]\\sigma^{2}=\\dfrac{\\sum\\left(x-\\mu\\right)^{2}}{n}[\/latex]\r\nwhere [latex]\\sum[\/latex] is the summation of [latex]{\\left(x-\\mu\\right)^2}[\/latex] for each observation, [latex]\\left(x\\right)[\/latex] is the observation in the data set, [latex]\\left(\\mu\\right)[\/latex] is the mean, and [latex]\\left({n}\\right)[\/latex] is the number of observations.\r\n<ul>\r\n \t<li><strong>Variance of a sample<\/strong><\/li>\r\n<\/ul>\r\n[latex]s^{2}=\\dfrac{\\sum\\left(x-\\bar{x}\\right)^{2}}{n-1}[\/latex]\r\nwhere [latex]\\sum[\/latex] is the summation of [latex]{\\left(x-\\bar{x}\\right)^2}[\/latex] for each observation, [latex]\\left(x\\right)[\/latex] is the observation in the data set, [latex]\\left(\\bar{x}\\right)[\/latex] is the mean, and [latex]\\left({n}\\right)[\/latex] is the number of observations.\r\n<h2>Glossary<\/h2>\r\n<dl class=\"definition\">\r\n \t<dt>\r\n<dl id=\"fs-id1170572482683\" class=\"definition\">\r\n \t<dt><strong>[latex]s[\/latex]<\/strong><\/dt>\r\n \t<dd id=\"fs-id1170572482689\">the standard deviation of a sample of observations.<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<dl id=\"fs-id1170572482619\" class=\"definition\">\r\n \t<dt><strong>[latex]\\sigma[\/latex]<\/strong><\/dt>\r\n \t<dd id=\"fs-id1170572482624\">the standard deviation of a population of observations.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572482683\" class=\"definition\">\r\n \t<dt><strong>[latex]s^{2}[\/latex]<\/strong><\/dt>\r\n \t<dd id=\"fs-id1170572482689\">the variation of a sample of observations.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572482683\" class=\"definition\">\r\n \t<dt><strong>[latex]\\sigma^{2}[\/latex]<\/strong><\/dt>\r\n \t<dd id=\"fs-id1170572482689\">the variance of a population of observations.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572229168\" class=\"definition\">\r\n \t<dt>deviation from the mean<\/dt>\r\n \t<dd id=\"fs-id1170572229174\"><span style=\"font-size: 1em;\">the distance between an observation ([latex]{x}[\/latex]) in a data set and the mean\u00a0[latex]\\left(\\bar{x}\\right)[\/latex] of the data set.<\/span><\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572482683\" class=\"definition\">\r\n \t<dt>range<\/dt>\r\n \t<dd id=\"fs-id1170572482689\">the maximum (or largest) value\u00a0\u2013 the minimum (or smallest) value.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572482608\" class=\"definition\">\r\n \t<dt>standard deviation<\/dt>\r\n \t<dd id=\"fs-id1170572482614\">a measure of how spread out observations are from the mean.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572229190\" class=\"definition\">\r\n \t<dt>variability<\/dt>\r\n \t<dd id=\"fs-id1170572229195\">a measure of how dispersed (spread out) the data are. It is often referred to as the spread, or dispersion, of a data set.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572482683\" class=\"definition\">\r\n \t<dt>variance<\/dt>\r\n \t<dd id=\"fs-id1170572482689\">the standard deviation squared.<\/dd>\r\n<\/dl>\r\n&nbsp;\r\n<h2>My Skills Checklist:<\/h2>\r\n<ul>\r\n \t<li>I can describe variability using numerical summaries and its reflection in graphical displays.<\/li>\r\n \t<li>I can use appropriate graphical displays and numerical summaries to describe variability of data with technology.<\/li>\r\n \t<li>I can find and interpret the standard deviation of data.<\/li>\r\n<\/ul>\r\n<img class=\"aligncenter wp-image-905\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/08025259\/Screen-Shot-2022-03-07-at-6.52.16-PM-1024x878.png\" alt=\"Check mark list on clipboard\" width=\"200\" height=\"171\" \/>\r\n<p style=\"text-align: center;\"><strong>Topic Complete \u2013 now test your understanding in the Self-Check.<\/strong><\/p>\r\n\r\n\r\n<hr \/>\r\n\r\n&nbsp;","rendered":"<h3><strong>Monitoring Your Readiness<\/strong><\/h3>\n<div class=\"textbox\">\n<p>To effectively plan and use your time wisely, it helps to think about what you know and do not know. For each of the following, rate how confident you are that you can successfully do that skill. Use the following descriptions to rate yourself:<\/p>\n<p>5\u2014I am extremely confident I can do this task.<\/p>\n<p>4\u2014I am somewhat confident I can do this task.<\/p>\n<p>3\u2014I am not sure how confident I am.<\/p>\n<p>2\u2014I am not very confident I can do this task.<\/p>\n<p>1\u2014I am definitely not confident I can do this task.<\/p>\n<\/div>\n<h3 style=\"text-align: center;\">Skills Needed for Comparing Variability of Data Sets: Forming Connections<\/h3>\n<div style=\"margin: auto;\">\n<table style=\"height: 107px;\">\n<tbody>\n<tr style=\"height: 10px;\">\n<td style=\"width: 319px; height: 10px; text-align: center;\"><strong>Skill or Concept: I can . . .<\/strong><\/td>\n<td style=\"width: 243px; height: 10px; text-align: center;\"><strong>Questions to check your understanding<\/strong><\/td>\n<td style=\"width: 113px; height: 10px; text-align: center;\"><strong>Rating\u00a0<\/strong><strong>from 1 to 5<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"width: 319px; height: 26px;\">Visually assess the differences in variability, given comparative histograms or dotplots.<\/td>\n<td style=\"width: 243px; height: 26px; text-align: center;\">2, 3<\/td>\n<td style=\"width: 113px; height: 26px;\"><\/td>\n<\/tr>\n<tr style=\"height: 10px;\">\n<td style=\"width: 319px; height: 10px;\">Understand the summary statistics feature of the Describing and Exploring Quantitative Variables tool.<\/td>\n<td style=\"width: 243px; height: 10px; text-align: center;\">4, 5<\/td>\n<td style=\"width: 113px; height: 10px;\"><\/td>\n<\/tr>\n<tr style=\"height: 31px;\">\n<td style=\"width: 319px; height: 31px;\">Use technology to calculate measures of variability: standard deviation, variance, and range.<\/td>\n<td style=\"width: 243px; height: 31px; text-align: center;\">6-8<\/td>\n<td style=\"width: 113px; height: 31px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>Now use the ratings to get ready for your next in-class activity. <strong>If your rating is a 3 or below, you should get help with the material before class.<\/strong> Remember, your instructor is going to assume that you are confident with the material and will not take class time to answer questions about it.<\/p>\n<p>Ways to get help:<\/p>\n<ul>\n<li>See your instructor before class for help.<\/li>\n<li>Ask your instructor for on-campus resources.<\/li>\n<li>Set up a study group with classmates so you can help each other.<\/li>\n<li>Work with a tutor.<\/li>\n<\/ul>\n<div class=\"textbox learning-objectives\">\n<h3>Essential Concepts<\/h3>\n<ul>\n<li>Variability can be measured in three ways: standard deviation, variance, and range.<\/li>\n<li>Variability can be judged from a histogram by examining the distance of the bars from the statistical center (mean or median) of the graph. If the\u00a0variability is high, equally sized or taller bars will appear away from the center of the graph. It the variability is low, the data will appear clustered around the center.<\/li>\n<li>The following steps can be applied to calculate a standard deviation by hand:\n<ol>\n<li>Calculate the mean of the population or sample.<\/li>\n<li>Take the difference between each data value and the mean. Then square each difference.<\/li>\n<li>Add up all the squared differences<\/li>\n<li>Divide by either the total number of observations in the case of a population or by 1 fewer than the total in the case of a sample.<\/li>\n<li>Take the square root of the result of the division in step 4.<\/li>\n<\/ol>\n<\/li>\n<li>Larger values of range indicate more variability in the data, but the range value only utilizes two observations in the entire data set to measure variability. This is not an ideal measure of spread, but when used in combination with other measures of spread, it can help you gain a clearer understanding of the spread of a distribution.<\/li>\n<\/ul>\n<\/div>\n<h2>Study Tips: Evidence-based strategies for learning<\/h2>\n<ul>\n<li>Visual connections and contrasts associated with variability can be learned by quizzing yourself using flashcards, mnemonics, memory dumping (writing out everything you can remember onto a blank sheet of paper then comparing your output to a list of key concepts), and by making little sketches or symbols. Some examples of these include:\n<ul>\n<li>Visual clues of variability\n<ul>\n<li>Data that appears spread apart from the center has greater variability. Data that appears clustered toward the center has less variability.<\/li>\n<\/ul>\n<\/li>\n<li>The <strong>R<\/strong>ange of a data set is the diffe<strong>R<\/strong>ence between the minimum and maximum data values in the set.<\/li>\n<\/ul>\n<\/li>\n<li>Standard deviation: a measure of variability. Gain understanding of standard deviation by paraphrasing the technical terminology out loud as though you are explaining it to a student in elementary school.\n<ul>\n<li>The Latin letter\u00a0<em>s<\/em> is used for samples.<\/li>\n<li>The Greek letter\u00a0[latex]\\sigma[\/latex] is used for populations.<\/li>\n<li>This Latin \/ Greek system of representation is generally true: Latin letters for samples and Greek letters for populations.\n<ul>\n<li>Population: [latex]\\mu[\/latex] for mean, [latex]\\sigma[\/latex] for standard deviation<\/li>\n<li>Sample:\u00a0\u00a0[latex]\\bar{x}[\/latex] for mean, [latex]s[\/latex] for standard deviation<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>Variance is the square of standard deviation. Practice obtaining and calculating standard deviation and variance together.\n<ul>\n<li>Variance is the radicand (the value under the square root) of the standard deviation.<\/li>\n<li>Standard deviation is required to calculate variance.<\/li>\n<li>As you practice calculating standard deviation and variance in the text and assignments, pause periodically to think about why you are doing each step, how you know what steps to use to make the calculations by hand and via technology, and how you can know if your answer is reasonable or correct.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>Foundational Knowledge<\/h2>\n<ul>\n<li><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Number-Word+Combinations.pdf\">Number-Word Combinations<\/a><\/li>\n<li><a href=\"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/chapter\/comparing-variability-of-data sets-corequisite-support-activity\/\">Support Activity for Comparing Variability of Data Sets<\/a><\/li>\n<\/ul>\n<h2>Key Equations<\/h2>\n<ul>\n<li><strong>Deviation from the mean<\/strong><\/li>\n<\/ul>\n<p>[latex]\\left(x-\\bar{x}\\right)[\/latex]<br \/>\nwhere [latex]\\left(x\\right)[\/latex] is the observation in the data set, and\u00a0[latex]\\left(\\bar{x}\\right)[\/latex] is the sample mean.<\/p>\n<ul>\n<li><strong>Standard deviation of a population<\/strong><\/li>\n<\/ul>\n<p>[latex]\\sigma = \\sqrt{\\dfrac{\\sum \\left(x-\\mu\\right)^2}{n}}[\/latex]<br \/>\nwhere [latex]\\sum[\/latex] is the summation of [latex]{\\left(x-\\mu\\right)^2}[\/latex] for each observation, [latex]\\left(x\\right)[\/latex] is the observation in the data set, [latex]\\left(\\mu\\right)[\/latex] is the mean, and [latex]\\left({n}\\right)[\/latex] is the number of observations.<\/p>\n<ul>\n<li><strong>Standard deviation of a sample<\/strong><\/li>\n<\/ul>\n<p>[latex]s=\\sqrt{\\dfrac{\\sum \\left(x-\\bar{x}\\right)^2}{n-1}}[\/latex]<br \/>\nwhere [latex]\\sum[\/latex] is the summation of [latex]{\\left(x-\\bar{x}\\right)^2}[\/latex] for each observation, [latex]\\left(x\\right)[\/latex] is the observation in the data set, [latex]\\left(\\bar{x}\\right)[\/latex] is the mean, and [latex]\\left({n}\\right)[\/latex] is the number of observations.<\/p>\n<ul>\n<li><strong>Variance of a population<\/strong><\/li>\n<\/ul>\n<p>[latex]\\sigma^{2}=\\dfrac{\\sum\\left(x-\\mu\\right)^{2}}{n}[\/latex]<br \/>\nwhere [latex]\\sum[\/latex] is the summation of [latex]{\\left(x-\\mu\\right)^2}[\/latex] for each observation, [latex]\\left(x\\right)[\/latex] is the observation in the data set, [latex]\\left(\\mu\\right)[\/latex] is the mean, and [latex]\\left({n}\\right)[\/latex] is the number of observations.<\/p>\n<ul>\n<li><strong>Variance of a sample<\/strong><\/li>\n<\/ul>\n<p>[latex]s^{2}=\\dfrac{\\sum\\left(x-\\bar{x}\\right)^{2}}{n-1}[\/latex]<br \/>\nwhere [latex]\\sum[\/latex] is the summation of [latex]{\\left(x-\\bar{x}\\right)^2}[\/latex] for each observation, [latex]\\left(x\\right)[\/latex] is the observation in the data set, [latex]\\left(\\bar{x}\\right)[\/latex] is the mean, and [latex]\\left({n}\\right)[\/latex] is the number of observations.<\/p>\n<h2>Glossary<\/h2>\n<dl class=\"definition\">\n<dt>\n<\/dt>\n<dt><strong>[latex]s[\/latex]<\/strong><\/dt>\n<dd id=\"fs-id1170572482689\">the standard deviation of a sample of observations.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572482619\" class=\"definition\">\n<dt><strong>[latex]\\sigma[\/latex]<\/strong><\/dt>\n<dd id=\"fs-id1170572482624\">the standard deviation of a population of observations.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572482683\" class=\"definition\">\n<dt><strong>[latex]s^{2}[\/latex]<\/strong><\/dt>\n<dd id=\"fs-id1170572482689\">the variation of a sample of observations.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572482683\" class=\"definition\">\n<dt><strong>[latex]\\sigma^{2}[\/latex]<\/strong><\/dt>\n<dd id=\"fs-id1170572482689\">the variance of a population of observations.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572229168\" class=\"definition\">\n<dt>deviation from the mean<\/dt>\n<dd id=\"fs-id1170572229174\"><span style=\"font-size: 1em;\">the distance between an observation ([latex]{x}[\/latex]) in a data set and the mean\u00a0[latex]\\left(\\bar{x}\\right)[\/latex] of the data set.<\/span><\/dd>\n<\/dl>\n<dl id=\"fs-id1170572482683\" class=\"definition\">\n<dt>range<\/dt>\n<dd id=\"fs-id1170572482689\">the maximum (or largest) value\u00a0\u2013 the minimum (or smallest) value.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572482608\" class=\"definition\">\n<dt>standard deviation<\/dt>\n<dd id=\"fs-id1170572482614\">a measure of how spread out observations are from the mean.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572229190\" class=\"definition\">\n<dt>variability<\/dt>\n<dd id=\"fs-id1170572229195\">a measure of how dispersed (spread out) the data are. It is often referred to as the spread, or dispersion, of a data set.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572482683\" class=\"definition\">\n<dt>variance<\/dt>\n<dd id=\"fs-id1170572482689\">the standard deviation squared.<\/dd>\n<\/dl>\n<p>&nbsp;<\/p>\n<h2>My Skills Checklist:<\/h2>\n<ul>\n<li>I can describe variability using numerical summaries and its reflection in graphical displays.<\/li>\n<li>I can use appropriate graphical displays and numerical summaries to describe variability of data with technology.<\/li>\n<li>I can find and interpret the standard deviation of data.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-905\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/08025259\/Screen-Shot-2022-03-07-at-6.52.16-PM-1024x878.png\" alt=\"Check mark list on clipboard\" width=\"200\" height=\"171\" \/><\/p>\n<p style=\"text-align: center;\"><strong>Topic Complete \u2013 now test your understanding in the Self-Check.<\/strong><\/p>\n<hr \/>\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-311\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">Public domain content<\/div><ul class=\"citation-list\"><li>Roller hockey ball overlaid with a green check. <strong>Authored by<\/strong>: Parutakupiu. <strong>Provided by<\/strong>: Wikimedia Commons. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Rollerhockeyball_check.svg\">https:\/\/commons.wikimedia.org\/wiki\/File:Rollerhockeyball_check.svg<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/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":175116,"menu_order":44,"template":"","meta":{"_candela_citation":"[{\"type\":\"pd\",\"description\":\"Roller hockey ball overlaid with a green check\",\"author\":\"Parutakupiu\",\"organization\":\"Wikimedia Commons\",\"url\":\"https:\/\/commons.wikimedia.org\/wiki\/File:Rollerhockeyball_check.svg\",\"project\":\"\",\"license\":\"pd\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-311","chapter","type-chapter","status-publish","hentry"],"part":1252,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/311","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/users\/175116"}],"version-history":[{"count":22,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/311\/revisions"}],"predecessor-version":[{"id":1158,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/311\/revisions\/1158"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/parts\/1252"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/311\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/media?parent=311"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapter-type?post=311"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/contributor?post=311"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/license?post=311"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}