{"id":335,"date":"2019-08-17T13:28:00","date_gmt":"2019-08-17T13:28:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=335"},"modified":"2026-02-23T08:52:56","modified_gmt":"2026-02-23T08:52:56","slug":"calculating-interpreting-quartiles","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/calculating-interpreting-quartiles\/","title":{"rendered":"Calculating and Interpreting Quartiles, Quintiles, Deciles and Percentiles"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n\n  \"name\": \"Statistical Concepts and Market Returns (2021 Level I CFA\u00ae Exam \u2013 Reading 7)\",\n\n  \"description\": \"This CFA video lesson covers statistical concepts and market returns, explaining the distinction between descriptive and inferential statistics, populations and samples, and measurement scales like nominal, ordinal, interval, and ratio. It delves into central tendency measures, variance, standard deviation, skewness, and kurtosis, highlighting their applications in financial analysis.\",\n\n  \"uploadDate\": \"2020-06-09T00:00:00+00:00\",\n\n  \"thumbnailUrl\": \"https:\/\/analystprep.com\/path-to-thumbnail\/statistical-concepts-thumbnail.jpg\", \n\n  \"contentUrl\": \"https:\/\/youtu.be\/alD9eAT2lQU\",\n\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/alD9eAT2lQU\",\n\n  \"duration\": \"PT31M21S\",\n\n  \"publisher\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\",\n    \"logo\": {\n      \"@type\": \"ImageObject\",\n      \"url\": \"https:\/\/analystprep.com\/path-to-logo\/logo.jpg\",\n      \"width\": 600,\n      \"height\": 60\n    }\n  }\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Determine the 5th decile from the data.\",\n    \"text\": \"A mutual fund achieved the following rates of growth over an 11-month period: {3%, 2%, 7%, 8%, 2%, 4%, 3%, 7.5%, 7.2%, 2.7%, 2.09%}. Determine the 5th decile from the data.\\n\\nA. 4%\\nB. 3%\\nC. 2%\",\n    \"answerCount\": 1,\n    \"upvoteCount\": 0,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The 5th decile is the 50th percentile (the median). Sort the data in ascending order: {2%, 2%, 2.09%, 2.7%, 3%, 3%, 4%, 7%, 7.2%, 7.5%, 8%}. With n = 11, the 50th-percentile position is (n + 1) \u00d7 0.50 = 12 \u00d7 0.50 = 6, so the 6th value is 3%. Therefore, the 5th decile is 3% (Choice B).\"\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\"\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<p>Quartiles, quintiles, deciles, and percentiles are values or cut points that partition a finite number of observations into nearly equal-sized subsets. The number of partitions depends on the type of cut point involved.<\/p>\n<p><!--more--><\/p>\n<h2><strong>Quartiles<\/strong><\/h2>\n<p>They divide data into <strong>four<\/strong> parts. The first quartile, Q<sub>1<\/sub>, is referred to as the lower quartile, and the last quartile, Q<span style=\"font-size: 13.3333px; line-height: 20px;\">4<\/span>, is known as the upper quartile. Q<sub>1<\/sub> splits the data into the lower 25% of the values and the upper 75%. Similarly, the upper quartile subdivides the data into the lower 75% of the values and the upper 25%. The difference between the upper quartile and the lower quartile is known as the <strong>interquartile range<\/strong>, which indicates the spread of the middle 50% of the data.<\/p>\n<div style=\"text-align: center; margin: 22px 0;\"><a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 12px 26px; border: 2px solid #1a73e8; border-radius: 999px; color: #1a73e8; font-weight: 600; text-decoration: none; text-align: center;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"> Practice quartiles and quantile calculation questions \u2192 <\/a><\/div>\n<h2><strong>Quintiles<\/strong><\/h2>\n<p>Though rarely used in practice, quintiles split a set of data into <strong>five<\/strong> equal parts, i.e., fifths. Therefore, the second quintile splits the data into the lower 40% of the values and the upper 60%.<\/p>\n<h2><strong>Deciles<\/strong><\/h2>\n<p>Deciles subdivide data into<strong> ten<\/strong> equal parts. There are 10 deciles in any data set. For example, the fourth decile splits data into the lower 40% of the values and the upper 60%.<\/p>\n<h2><strong>Percentiles<\/strong><\/h2>\n<p>Percentiles split data into <strong>100<\/strong> equal parts, i.e., hundredths. So, for instance, the 77<sup>th <\/sup>percentile splits data into the lower 77% of the values and the upper 23%.<\/p>\n<p>Financial analysts commonly use the four types of subdivisions to rank investment performance. You should note that quartiles, quintiles, and deciles can all be expressed as percentiles. For instance, the first quartile is just the 25<sup>th <\/sup>percentile. Similarly, the fourth decile is simply the 40<sup>th <\/sup>percentile. This enables the application of the formula below.<\/p>\n<p>$$ \\text{Position of percentile}, \\text{denoted } p_y =\\cfrac {(n + 1) y}{100} $$<\/p>\n<p>Where n is the number of observations and y is the percentile.<\/p>\n<p><em>Note: you must always order the data set, usually in ascending order, before calculating any of these values.<\/em><\/p>\n<h3><strong>Example: Quartiles <\/strong><\/h3>\n<p>Given the following distribution of returns, determine the lower quartile:<\/p>\n<p>{10%\u00a0\u00a0 23%\u00a0\u00a0 12%\u00a0\u00a0 21%\u00a0\u00a0 14%\u00a0\u00a0 17%\u00a0\u00a0 16%\u00a0\u00a0 11%\u00a0\u00a0 15%\u00a0\u00a0 19%}<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>First, we have to arrange the values in ascending order:<\/p>\n<p>{10%\u00a0\u00a0 11%\u00a0\u00a0 12%\u00a0\u00a0 14%\u00a0\u00a0 15%\u00a0\u00a0 16%\u00a0\u00a0 17%\u00a0\u00a0 19%\u00a0\u00a0\u00a0 21%\u00a0\u00a0 23%}<\/p>\n<p>Next, we establish the position of the first quartile. This is simply the 25<sup>th <\/sup>percentile. Therefore:<\/p>\n<p>$$ \\begin{align*} P_{25} &amp; =\\cfrac {(10 + 1)25}{100} \\\\ &amp; = 2.75^{\\text{th}} \\text{ value}\\\\ \\end{align*} $$<\/p>\n<p>Since the value is not straightforward, we have to extrapolate between the 2<sup>nd <\/sup>and the 3<sup>rd<\/sup> data points. The 25<sup>th<\/sup> percentile is three-fourth (0.75) of the way from the 2<sup>nd<\/sup> data point (11%) to the 3<sup>rd<\/sup> data point (12%):<\/p>\n<p>$$ \\begin{align*} &amp; 11\\% + 0.75 * (12 \u2013 11) \\\\ &amp; = 11.75\\% \\end{align*} $$<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>A mutual fund achieved the following rates of growth over an 11-month period:<\/p>\n<p>{3%\u00a0\u00a0 2%\u00a0\u00a0 7%\u00a0\u00a0 8%\u00a0\u00a0 2% \u00a0\u00a04%\u00a0\u00a0 3%\u00a0\u00a0 7.5%\u00a0\u00a0 7.2%\u00a0\u00a0 2.7%\u00a0\u00a0 2.09%}<\/p>\n<p>Determine the 5<sup>th<\/sup> decile from the data.<\/p>\n<p>A. 4%<\/p>\n<p>B. 3%<\/p>\n<p>C. 2%<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is B.<\/p>\n<p>First, you should re-arrange the data in ascending order:<\/p>\n<p>{2%\u00a0\u00a0 2%\u00a0\u00a0 2.7%\u00a0\u00a0 2.09%\u00a0\u00a0 3%\u00a0\u00a0 3%\u00a0\u00a0 4%\u00a0\u00a0 7%\u00a0\u00a0 7.2%\u00a0\u00a0 7.5%\u00a0\u00a0 8%}<\/p>\n<p>Secondly, you should establish the 5<sup>th<\/sup> decile. This is simply the 50<sup>th<\/sup> percentile and is actually the <a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-of-central-tendency\/\"><strong>median<\/strong><\/a>:<\/p>\n<p>$$ \\begin{align*} P_{50} &amp; =\\cfrac {(1 + 11) 50}{100} \\\\ &amp; = 12 * 0.5 \\\\ &amp; = 6 \\text{ i}.\\text{e}. \\text{ the }6^{\\text{th}} \\text{ data point}. \\\\ \\end{align*} $$<\/p>\n<p>Therefore,<\/p>\n<p>$$ \\text{the } 5^{\\text{th}} \\text{ decile} = 50^{\\text{th}} \\text { percentile} = \\text{median} = 3\\% $$<\/p>\n<\/blockquote>\n<div class=\"notes_inv\"><hr \/><\/div>\n<div style=\"text-align: center; margin: 40px 0 10px 0;\"><a style=\"display: inline-block; padding: 14px 34px; background: #1a73e8; color: #ffffff; border-radius: 999px; font-weight: bold; text-decoration: none;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"> Start Free Trial \u2192 <\/a><\/div>","protected":false},"excerpt":{"rendered":"<p>Quartiles, quintiles, deciles, and percentiles are values or cut points that partition a finite number of observations into nearly equal-sized subsets. The number of partitions depends on the type of cut point involved.<\/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-335","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>Calculating &amp; Interpreting Quartiles | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Quartiles, quintiles, deciles, and percentiles divide data into equal parts, helping analyze distributions. 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