{"id":340,"date":"2019-08-17T13:28:00","date_gmt":"2019-08-17T13:28:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=340"},"modified":"2026-09-23T20:27:33","modified_gmt":"2026-09-23T20:27:33","slug":"measures-dispersion-examples","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/","title":{"rendered":"Measures of Dispersion"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Statistical Concepts and Market Returns (2021 Level I CFA\u00ae Exam \u2013 Reading 7)\",\n  \"description\": \"This video covers Statistical Concepts and Market Returns, exploring descriptive vs. inferential statistics, measurement scales, probability distributions, and key concepts like variance, standard deviation, skewness, and kurtosis. Learn how to interpret data, analyze frequency distributions, and measure central tendency and dispersion for financial analysis.\",\n  \"uploadDate\": \"2019-07-09T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/alD9eAT2lQU\/maxresdefault.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/alD9eAT2lQU\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/alD9eAT2lQU\",\n  \"duration\": \"PT31M21S\"\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/#qapage-question-1\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/#question-1\",\n    \"name\": \"Given the population data {12, 13, 54, 56, 25}, what is the population standard deviation?\",\n    \"text\": \"You have been given the following data:\\n{12, 13, 54, 56, 25}\\nAssuming this is complete data from a certain population, the population standard deviation is closest to:\\nA. 19.34.\\nB. 374.\\nC. 1,870.\",\n    \"answerCount\": 1,\n    \"author\": {\n      \"@type\": \"Organization\",\n      \"name\": \"AnalystPrep\"\n    },\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/#answer-1\",\n      \"text\": \"A. 19.34. The population mean is \u03bc = (12 + 13 + 54 + 56 + 25) \/ 5 = 32. The population variance is \u03c3\u00b2 = [(12\u221232)\u00b2 + (13\u221232)\u00b2 + (54\u221232)\u00b2 + (56\u221232)\u00b2 + (25\u221232)\u00b2] \/ 5 = 1870 \/ 5 = 374. Therefore, the population standard deviation is \u03c3 = \u221a374 \u2248 19.34.\",\n      \"author\": {\n        \"@type\": \"Organization\",\n        \"name\": \"AnalystPrep\"\n      }\n    }\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\"\n  width=\"611\"\n  height=\"344\"\n  src=\"https:\/\/www.youtube.com\/embed\/alD9eAT2lQU?rel=0&#038;modestbranding=1&#038;playsinline=1\"\n  title=\"YouTube video player\"\n  frameborder=\"0\"\n  allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\"\n  allowfullscreen>\n<\/iframe>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Measures of dispersion are used to describe the variability or spread in a sample or population. They are usually used in conjunction with measures of central tendency such as the mean and the median. These are the range, variance, absolute deviation, and standard deviation. They are important because they give us an idea of how well the measures of central tendency represent the data. For example, if the standard deviation is large, there are large differences between individual data points. Consequently, the mean may not be representative of the data.<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Range<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">It is the <strong>difference<\/strong> between the highest and the lowest scores in a set of data i.e.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ \\text{Range} = \\text{maximum value} \u2013 \\text{minimum value} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 1<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Consider the following scores of 10 CFA Level 1 candidates:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">78&nbsp;&nbsp; 56&nbsp;&nbsp; 67&nbsp;&nbsp; 51&nbsp;&nbsp; 43&nbsp;&nbsp; 89&nbsp;&nbsp; 57&nbsp;&nbsp; 67&nbsp;&nbsp; 78&nbsp;&nbsp; 50<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ \\text{Range} = 89 \u2013 43 = 46 $$<\/p>\n\n\n\n<div style=\"margin:28px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\" style=\"display:block;width:100%;padding:12px 24px;border-radius:999px;background:#1a73e8;color:#ffffff;font-size:15px;font-weight:500;text-align:center;text-decoration:none;box-sizing:border-box;\">\n    Practice Dispersion Questions with Our Free Trial.\n  <\/a>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Mean Absolute Deviation (MAD)<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">It is a measure of dispersion representing the <strong>average of the absolute values<\/strong> of the deviations of individual observations from the arithmetic mean. Therefore:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ \\text{MAD} \\frac { \\sum { |{ X }_{ i }-\\bar { X } | } }{ n } $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Remember that the sum of deviations from the <a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-of-central-tendency\/\">arithmetic means<\/a> is always zero, and that\u2019s why we are using the <strong>absolute<\/strong> <strong>values<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 2<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">6 investment analysts attain the following returns on six different investments:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">{12%&nbsp;&nbsp; 4%&nbsp;&nbsp; 23%&nbsp;&nbsp; 8%&nbsp;&nbsp; 9%&nbsp;&nbsp; 16%}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Calculate the mean absolute deviation and interpret it.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">First, we have to calculate the arithmetic mean:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ X =\\cfrac {(12 + 4 + 23 + 8 + 9 + 16)}{6} = 12\\% $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Next, we can now compute the MAD:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ \\begin{align*} \\text{MAD} &amp; = \\cfrac {\\left\\{ |12 \u2013 12|+ |4 \u2013 12| + |23 \u2013 12| + |8 \u2013 12| + |9 \u2013 12| + |16 \u2013 12| \\right\\}} {6} \\\\ &amp; =\\cfrac {30}{6} \\\\ &amp; = 5\\% \\\\ \\end{align*} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Interpretation: it means that on average, an individual return deviates 5% from the mean return of 12%.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Population Variance and Population Standard Deviation<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The population variance, denoted by \u03c3<sup>2<\/sup>, is the average of the squared deviations from the mean. Therefore:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ { \\sigma }^{ 2 }=\\frac { \\left\\{ \\sum { { \\left( { X }_{ i }-\\mu \\right) }^{ 2 } } \\right\\} }{ N } $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">And the standard deviation is simply the square root of variance.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 3<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Working with data from example 2 above, the variance will be calculated as follows:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ \\begin{align*} { \\sigma }^{ 2 } &amp; =\\frac { \\left\\{ { \\left( 12-12 \\right) }^{ 2 }+{ \\left( 4-12 \\right) }^{ 2 }+{ \\left( 23-12 \\right) }^{ 2 }+{ \\left( 8-12 \\right) }^{ 2 }+{ \\left( 9-12 \\right) }^{ 2 }+{ \\left( 16-12 \\right) }^{ 2 } \\right\\} }{ 6 } \\\\ &amp; = 37.67(\\%^2) \\\\ &amp; = 0.003767 \\\\ \\end{align*} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the average variation from the mean (0.12) is 0.003767.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The standard deviation is 0.003767<sup>1\/2<\/sup> = 0.06137 or 6.14%.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Analysts use the standard deviation, instead of the variance, to interpret returns since it is much easier to comprehend.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Sample Variance and Sample Standard Deviation<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The sample variance, S<sup>2<\/sup>, is the measure of dispersion that applies when we are working with a sample as opposed to a population. (The two have been distinguished <a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/statistics-terms-explained-examples\/\">here<\/a>)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ { S }^{ 2 }=\\frac { \\left\\{ \\sum { { \\left( { X }_{ i }- \\bar { X } \\right) }^{ 2 } } \\right\\} }{ n-1 } $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Note that we are dividing by n \u2013 1. This is necessary so as to remove <strong>bias<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The sample standard deviation, S, is simply the square root of the sample variance.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 4<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Assume that the returns realized in example 2 above were sampled from a population comprising 100 returns. Compute the sample mean and the corresponding sample variance.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The sample mean will still be 12%.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ \\begin{align*} { S }^{ 2 } &amp; =\\frac { \\left\\{ { \\left( 12-12 \\right) }^{ 2 }+{ \\left( 4-12 \\right) }^{ 2 }+{ \\left( 23-12 \\right) }^{ 2 }+{ \\left( 8-12 \\right) }^{ 2 }+{ \\left( 9-12 \\right) }^{ 2 }+{ \\left( 16-12 \\right) }^{ 2 } \\right\\} }{ 5 } \\\\ &amp; = 45.20(\\%^2) \\\\ &amp; = 0.00452 \\\\ \\end{align*} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ \\begin{align*} S &amp; = 0.00452^{\\frac {1}{2}} \\\\ &amp; = 0.0672 \\end{align*} $$<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<h3 class=\"wp-block-heading\"><strong>Question<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">You have been given the following data:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">{12&nbsp;&nbsp; 13&nbsp;&nbsp; 54&nbsp;&nbsp; 56&nbsp;&nbsp; 25}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Assuming this is complete data from a certain population, the population standard deviation is <em>closest<\/em> to:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>19.34.<\/li>\n\n\n\n<li>374.<\/li>\n\n\n\n<li>1,870.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">The correct answer is A.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Working:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ \\mu =\\cfrac {(12 + 13 + \\cdots +25)}{5} =\\cfrac {160}{5} = 32 $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ \\begin{align*} { \\sigma }^{ 2 } &amp; =\\frac { \\left\\{ { \\left( 12-32 \\right) }^{ 2 }+{ \\left( 13-32 \\right) }^{ 2 }+{ \\left( 54-32 \\right) }^{ 2 }+{ \\left( 56-32 \\right) }^{ 2 }+{ \\left( 25-32 \\right) }^{ 2 } \\right\\} }{ 5 } \\\\ &amp; =\\cfrac {1870}{5} = 374 \\\\ \\end{align*} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ \\sigma = 19.34 $$<\/p>\n<\/blockquote>\n\n\n\n<div class=\"notes_inv\">\n<hr><\/div>\n\n\n\n<div style=\"text-align:center;margin:35px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\" style=\"display:inline-block;padding:15px 35px;border-radius:999px;background:#1a73e8;color:#ffffff;font-size:17px;font-weight:600;text-decoration:none;\">\n    Start Free Trial \u2192\n  <\/a>\n\n  <p style=\"margin:25px 0 0;font-size:16px;line-height:1.6;text-align:center;\">\n    Master CFA Level I Quantitative Methods concepts, including measures of dispersion, variance, standard deviation, range, and related calculations with study notes, practice questions, and video lessons.\n  <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Measures of dispersion are used to describe the variability or spread in a sample or population. They are usually used in conjunction with measures of central tendency such as the mean and the median. These are the range, variance, absolute&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-340","post","type-post","status-publish","format-standard","hentry","category-quantitative-methods","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Measures of Dispersion Explained | CFA Level 1 - AnalystPrep<\/title>\n<meta name=\"description\" content=\"Learn key measures of dispersion, including range, variance, and standard deviation, to assess data variability in statistical analysis.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Measures of Dispersion Explained | CFA Level 1 - AnalystPrep\" \/>\n<meta property=\"og:description\" content=\"Learn key measures of dispersion, including range, variance, and standard deviation, to assess data variability in statistical analysis.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/\" \/>\n<meta property=\"og:site_name\" content=\"AnalystPrep | CFA\u00ae Exam Study Notes\" \/>\n<meta property=\"article:published_time\" content=\"2019-08-17T13:28:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-09-23T20:27:33+00:00\" \/>\n<meta name=\"author\" content=\"Ngari Joseph\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Ngari Joseph\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/measures-dispersion-examples\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/measures-dispersion-examples\\\/\"},\"author\":{\"name\":\"Ngari Joseph\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/#\\\/schema\\\/person\\\/ddbf15286b86900dfa9f8ac2603c3914\"},\"headline\":\"Measures of Dispersion\",\"datePublished\":\"2019-08-17T13:28:00+00:00\",\"dateModified\":\"2026-09-23T20:27:33+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/measures-dispersion-examples\\\/\"},\"wordCount\":660,\"articleSection\":[\"Quantitative Methods\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/measures-dispersion-examples\\\/\",\"url\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/measures-dispersion-examples\\\/\",\"name\":\"Measures of Dispersion Explained | CFA Level 1 - AnalystPrep\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/#website\"},\"datePublished\":\"2019-08-17T13:28:00+00:00\",\"dateModified\":\"2026-09-23T20:27:33+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/#\\\/schema\\\/person\\\/ddbf15286b86900dfa9f8ac2603c3914\"},\"description\":\"Learn key measures of dispersion, including range, variance, and standard deviation, to assess data variability in statistical analysis.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/measures-dispersion-examples\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/measures-dispersion-examples\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/measures-dispersion-examples\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Measures of Dispersion\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/#website\",\"url\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/\",\"name\":\"AnalystPrep | CFA\u00ae Exam Study Notes\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/#\\\/schema\\\/person\\\/ddbf15286b86900dfa9f8ac2603c3914\",\"name\":\"Ngari Joseph\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/wp-content\\\/uploads\\\/2016\\\/08\\\/male3-512-150x150.png\",\"url\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/wp-content\\\/uploads\\\/2016\\\/08\\\/male3-512-150x150.png\",\"contentUrl\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/wp-content\\\/uploads\\\/2016\\\/08\\\/male3-512-150x150.png\",\"caption\":\"Ngari Joseph\"}}]}<\/script>\n<meta property=\"og:video\" content=\"https:\/\/www.youtube.com\/embed\/alD9eAT2lQU\" \/>\n<meta property=\"og:video:type\" content=\"text\/html\" \/>\n<meta property=\"og:video:duration\" content=\"1882\" \/>\n<meta property=\"og:video:width\" content=\"480\" \/>\n<meta property=\"og:video:height\" content=\"270\" \/>\n<meta property=\"ya:ovs:adult\" content=\"false\" \/>\n<meta property=\"ya:ovs:upload_date\" content=\"2019-08-17T13:28:00+00:00\" \/>\n<meta property=\"ya:ovs:allow_embed\" content=\"true\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Measures of Dispersion Explained | CFA Level 1 - AnalystPrep","description":"Learn key measures of dispersion, including range, variance, and standard deviation, to assess data variability in statistical analysis.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/","og_locale":"en_US","og_type":"article","og_title":"Measures of Dispersion Explained | CFA Level 1 - AnalystPrep","og_description":"Learn key measures of dispersion, including range, variance, and standard deviation, to assess data variability in statistical analysis.","og_url":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/","og_site_name":"AnalystPrep | CFA\u00ae Exam Study Notes","article_published_time":"2019-08-17T13:28:00+00:00","article_modified_time":"2026-09-23T20:27:33+00:00","author":"Ngari Joseph","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Ngari Joseph","Est. reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/#article","isPartOf":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/"},"author":{"name":"Ngari Joseph","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/ddbf15286b86900dfa9f8ac2603c3914"},"headline":"Measures of Dispersion","datePublished":"2019-08-17T13:28:00+00:00","dateModified":"2026-09-23T20:27:33+00:00","mainEntityOfPage":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/"},"wordCount":660,"articleSection":["Quantitative Methods"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/","url":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/","name":"Measures of Dispersion Explained | CFA Level 1 - AnalystPrep","isPartOf":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#website"},"datePublished":"2019-08-17T13:28:00+00:00","dateModified":"2026-09-23T20:27:33+00:00","author":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/ddbf15286b86900dfa9f8ac2603c3914"},"description":"Learn key measures of dispersion, including range, variance, and standard deviation, to assess data variability in statistical analysis.","breadcrumb":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/analystprep.com\/cfa-level-1-exam\/"},{"@type":"ListItem","position":2,"name":"Measures of Dispersion"}]},{"@type":"WebSite","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#website","url":"https:\/\/analystprep.com\/cfa-level-1-exam\/","name":"AnalystPrep | CFA\u00ae Exam Study Notes","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/analystprep.com\/cfa-level-1-exam\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/ddbf15286b86900dfa9f8ac2603c3914","name":"Ngari Joseph","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/08\/male3-512-150x150.png","url":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/08\/male3-512-150x150.png","contentUrl":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/08\/male3-512-150x150.png","caption":"Ngari Joseph"}}]},"og_video":"https:\/\/www.youtube.com\/embed\/alD9eAT2lQU","og_video_type":"text\/html","og_video_duration":"1882","og_video_width":"480","og_video_height":"270","ya_ovs_adult":"false","ya_ovs_upload_date":"2019-08-17T13:28:00+00:00","ya_ovs_allow_embed":"true"},"_links":{"self":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/340","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/comments?post=340"}],"version-history":[{"count":38,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/340\/revisions"}],"predecessor-version":[{"id":64586,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/340\/revisions\/64586"}],"wp:attachment":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/media?parent=340"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/categories?post=340"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/tags?post=340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}