{"id":363,"date":"2021-08-17T13:28:00","date_gmt":"2021-08-17T13:28:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=363"},"modified":"2026-01-13T12:58:30","modified_gmt":"2026-01-13T12:58:30","slug":"unimodal-distribution-mean-mode-median","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/unimodal-distribution-mean-mode-median\/","title":{"rendered":"Unimodal Distribution \u2013 Locations of the Mean, Mode and the Median"},"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 introduces statistical concepts and market returns, covering key topics such as descriptive vs. inferential statistics, population vs. sample, measurement scales, frequency distributions, central tendency, variance, standard deviation, and skewness. Designed to make statistics approachable, it offers practical insights into data interpretation and decision-making.\",\n  \"uploadDate\": \"2019-09-20T00:00:00+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\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/cdn.analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/05082832\/page-601.jpg\",\n  \"caption\": \"Image showing Symmetrical Distribution.\",\n  \"width\": 1463,\n  \"height\": 972,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/cdn.analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/05084552\/page-63a.jpg\",\n  \"caption\": \"Image showing a positively skewed curve.\",\n  \"width\": 1373,\n  \"height\": 860,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/cdn.analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/05084608\/page-63b.jpg\",\n  \"caption\": \"Image showing a negatively skewed curve.\",\n  \"width\": 1373,\n  \"height\": 860,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\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\"\n  title=\"YouTube video player\"\n  frameborder=\"0\"\n  allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\"\n  referrerpolicy=\"strict-origin-when-cross-origin\"\n  allowfullscreen>\n<\/iframe>\n\n\n\n<p>A unimodal distribution is a distribution that has one clear peak. The values increase first, rising to a single highest point where they then start to decrease. A unimodal distribution can either be symmetrical or nonsymmetrical.<\/p>\n<p>A symmetrical distribution is one where the mean, mode, and median are all equal. In such a distribution, the intervals of gains or losses exhibit the same frequency. For instance, if we have a symmetrical distribution with a mean return of zero, then the frequency of losses between -2% and -1% will be equal to the frequency of gains between 1% and 2%.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-16942 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-601.jpg\" alt=\"Image showing Symmetrical Distribution\" width=\"1463\" height=\"972\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-601.jpg 1463w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-601-300x199.jpg 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-601-768x510.jpg 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-601-1024x680.jpg 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-601-400x266.jpg 400w\" sizes=\"auto, (max-width: 1463px) 100vw, 1463px\" \/><\/p>\n<p>A distribution that deviates from the symmetrical distribution is said to be <strong>nonsymmetrical, <\/strong>and that\u2019s how we end up having positive skewness and negative skewness.<\/p>\n<h2><strong>Unimodal Distribution \u2013 Positively Skewed<\/strong><\/h2>\n<p>This is the tendency of a given frequency curve leaning towards the <strong>left. Conversely, the<\/strong>\u00a0\u2018tail\u2019 extends to the right. In this distribution, candidates should note the following:<\/p>\n<ol>\n<li>The mean is bigger than both the median and the mean.<\/li>\n<li>The median always occurs between the mode and the mean.<\/li>\n<li>The observations below the mean are more than those above it.<\/li>\n<\/ol>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-16947 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-63a.jpg\" alt=\"Image showing a positively skewed curve\" width=\"1373\" height=\"860\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-63a.jpg 1373w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-63a-300x188.jpg 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-63a-768x481.jpg 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-63a-1024x641.jpg 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-63a-400x251.jpg 400w\" sizes=\"auto, (max-width: 1373px) 100vw, 1373px\" \/><\/p>\n<p>A good example of a positively skewed distribution would be the age distribution in a <strong>developing<\/strong> country.<\/p>\n<h2><strong>Unimodal Distribution \u2013 Negatively Skewed<\/strong><\/h2>\n<p>This is a frequency curve where the long tail extends to the <strong>left. <\/strong>It has the following characteristics:<\/p>\n<ol>\n<li>The mode is usually bigger than both the median and the mean.<\/li>\n<li>The median is found between the mean and the mode.<\/li>\n<li>The observations above the mean are usually more than those below it.<\/li>\n<\/ol>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-16948 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-63b.jpg\" alt=\"Image showing Negatively Skewed Curve\" width=\"1373\" height=\"860\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-63b.jpg 1373w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-63b-300x188.jpg 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-63b-768x481.jpg 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-63b-1024x641.jpg 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-63b-400x251.jpg 400w\" sizes=\"auto, (max-width: 1373px) 100vw, 1373px\" \/><\/p>\n<p>A good example of a negatively skewed distribution would be the age distribution in a <strong>developed<\/strong> country.<\/p>\n<div class=\"notes_inv\"><hr \/><\/div>","protected":false},"excerpt":{"rendered":"<p>A unimodal distribution is a distribution that has one clear peak. The values increase first, rising to a single highest point where they then start to decrease. A unimodal distribution can either be symmetrical or nonsymmetrical. A symmetrical distribution is&#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-363","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 v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Understanding Unimodal Distributions | CFA Level 1<\/title>\n<meta name=\"description\" content=\"A unimodal distribution can either be symmetrical or non-symmetrical and has one clear peak. 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