{"id":1835,"date":"2016-08-30T17:53:45","date_gmt":"2016-08-31T00:53:45","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=1835"},"modified":"2020-01-15T10:47:50","modified_gmt":"2020-01-15T18:47:50","slug":"common-gmat-topic-descriptive-statistics","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/common-gmat-topic-descriptive-statistics\/","title":{"rendered":"Common GMAT Topic: Descriptive Statistics"},"content":{"rendered":"<p>Here&#8217;s a whirlwind tour of one of the\u00a0<a href=\"https:\/\/magoosh.com\/gmat\/what-kind-of-math-is-on-the-gmat-breakdown-of-quant-concepts-by-frequency\/\">most frequently tested sets of concepts on the GMAT Quantitative section<\/a>: GMAT statistics. You don&#8217;t have to be an expert on statistics: a little goes a long way. Let&#8217;s learn some basic descriptive statistics formulas and go from there.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh-company-site.s3.amazonaws.com\/wp-content\/uploads\/sites\/3\/2016\/08\/30174450\/GMAT-statistics-600x314.png\" alt=\"gmat statistics, statistics gmat, descriptive statistics formulas\" width=\"600\" height=\"314\" class=\"aligncenter size-large wp-image-7061\" \/><\/p>\n<h2>Descriptive Statistics Formulas<\/h2>\n<h3>The Mean<\/h3>\n<p>One very important GMAT Statistics idea is the <strong>mean<\/strong>.\u00a0 The mean is just the ordinary average: add up all the items on the list, and divide by the number of items.\u00a0 As a formula, that&#8217;s<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-7036\" src=\"https:\/\/magoosh-company-site.s3.amazonaws.com\/wp-content\/uploads\/sites\/3\/2016\/08\/29140012\/average-formula.jpg\" alt=\"average formula, gmat statistics, statistics gmat, descriptive statistics formulas\" width=\"229\" height=\"48\" \/><\/p>\n<p>Notice, we can rewrite that as: <strong>(sum of items) = average*(number of items)<\/strong>.\u00a0 Rewritten in <a href=\"https:\/\/magoosh.com\/gmat\/gmat-averages-and-sums-formulas\/\">sum form<\/a>, it becomes one of the most powerful statistics formulas on the GMAT.\u00a0 For more exotic kinds of averages you may see on descriptive statistics on the GMAT, see this post on <a href=\"https:\/\/magoosh.com\/gmat\/gmat-math-weighted-averages\/\">Weighted Averages<\/a>.<\/p>\n<h3>The Median<\/h3>\n<p>Another important GMAT Statistics idea is the <strong>median<\/strong>.\u00a0 When we put the list in ascending order, the median is the middle.\u00a0 If there are an odd number of items on the list, the middle item equals the median: for example, in the seven-element set {3, 5, 7, 9, 13, 15, 17}, the median is the fourth number, 9.\u00a0 If there are an even number of items on the list, then the median is the average of the two middle numbers; for example, in the eight-element set {3, 5, 7, 9, 13, 15, 17, 17}, the median is 11 (the average of the fourth &amp; fifth entries, 9 and 13).\u00a0 Notice: when the number of items on the list is even, the median can equal a number not on the list.\u00a0 Numbers above and below the median can be equal to the median, and that doesn&#8217;t change the fact that it&#8217;s a median; for example, the median of the set {1, 3, 3, 3, 3, 3, 74, 89, 312} is just 3, the fifth number of that nine-element set.<\/p>\n<p>Also, notice that an absurdly large number, far away from the rest of the set, such as 312 in this last set, has zero effect on the median, although it would have a big effect on the mean.\u00a0 As long as the middle numbers stays in the middle, changes to the values of the outer numbers has no effect on the median; by contrast, changing any number in the set changes the mean.<\/p>\n<p>Both the mean and the median are &#8220;statistical measures of center&#8221;\u2014that is, they are different ways of responding to the question &#8220;which number is most representative of the set?&#8221;\u00a0 The median simply &#8220;chunks&#8221; the set, whereas the mean &#8220;feels&#8221; each number.\u00a0 Changing \u00a0the value a single number, especially toward the high or low end of the set, never changes the median and always would change the mean.<\/p>\n<h3>Range<\/h3>\n<p>The GMAT loves this statistical measure, because it&#8217;s so simple.\u00a0 The <strong>range<\/strong> is the difference between the maximum value and the minimum value.\u00a0 In the set {3, 5, 7, 9, 13, 15, 17}, the range = 17 \u2013 3 = 14.\u00a0 In the set {1, 3, 3, 3, 3, 3, 74, 89, 312}, the range = 312 \u2013 1 = 311.\u00a0 Notice that the range, unlike the mean or median, is always positive (it would be zero if the max and min were the same number!)\u00a0 For the range, the only thing that matters is the top and bottom values in the set: those two values are the only two numbers that the range &#8220;feels.&#8221;\u00a0 We could change the values of almost every number in the middle of the set, and the range would not change at all.<\/p>\n<h3>Standard Deviation<\/h3>\n<p>The range is a statistical measure of the spread from the highest to the lowest value, but it doesn&#8217;t &#8220;feel&#8221; the numbers in between.\u00a0 The <strong>standard deviation<\/strong> is also a statistical measure of spread, that is to say, an indication of how far apart the numbers on the list are from each other.\u00a0 Like the mean and unlike the range or median, the standard deviation &#8220;feels&#8221; every number on the list.\u00a0\u00a0 It has a technical definition that we can forego here; the majority of appearances of standard deviation on the GMAT revolve around a few simple ideas about it.<\/p>\n<p>a) Like the range, the standard deviation is always zero or positive, never negative.<\/p>\n<p>b) If all the entries of the list are equal, the standard deviation = 0.\u00a0 In other words, they don&#8217;t deviate at all, because they&#8217;re all the same. For GMAT statistics, you should know that this is the only way to get a minimum standard deviation of zero.<\/p>\n<p>c) If you add\/subtract a constant to\/from every number on a list, that doesn&#8217;t change the standard deviation at all.\u00a0 It&#8217;s just like taking the batch of data points and sliding them up or down the number line: that process doesn&#8217;t change how far apart they are from each other.<\/p>\n<p>d) If you multiply\/divide a list by a constant, then you also multiply\/divide the standard deviation by this constant.<\/p>\n<p>I&#8217;ll add an additional rule that really could only come into play in a very difficult upper-700s question of GMAT statistics:<\/p>\n<p>e) If all the entries are<em>the same distance from the mean<\/em>, that distance is the standard deviation.\u00a0 For example, in the set {3, 3, 3, 7, 7, 7}, the mean = 5, and every number &#8220;deviates&#8221; from the mean by exactly two units, so the standard deviation = 2.<\/p>\n<p>See this post for\u00a0<a href=\"https:\/\/magoosh.com\/gmat\/standard-deviation-on-the-gmat\/\">more on standard deviation<\/a>.<\/p>\n<h2>GMAT Statistics Practice<\/h2>\n<p>If you master these simple ideas, you will dominate on Descriptive Statistics in the GMAT Quantitative section.\u00a0 Here are some GMAT statistics practice questions:<\/p>\n<p>1)\u00a0<a href=\"http:\/\/gmat.magoosh.com\/questions\/112\" target=\"_blank\" rel=\"noopener noreferrer\">http:\/\/gmat.magoosh.com\/questions\/112<\/a><\/p>\n<p>2)\u00a0<a href=\"https:\/\/magoosh.com\/gmat\/gmat-math-weighted-averages\/\" target=\"_blank\" rel=\"noopener noreferrer\">http:\/\/gmat.magoosh.com\/questions\/938<\/a><\/p>\n<p>3)\u00a0<a href=\"http:\/\/gmat.magoosh.com\/questions\/937\" target=\"_blank\" rel=\"noopener noreferrer\">http:\/\/gmat.magoosh.com\/questions\/937<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><em>Editor\u2019s Note: This post was originally published in May, 2012\u00a0and has been updated for freshness, accuracy, and comprehensiveness.<\/em><\/p>\n<p>&nbsp;<\/p>\n<h4>Special Note:<\/h4>\n<p>To find out where statistics sit in the &#8220;big picture&#8221; of GMAT Quant, and what other Quant concepts you should study, check out our post entitled:<\/p>\n<p><a href=\"https:\/\/magoosh.com\/gmat\/what-kind-of-math-is-on-the-gmat-breakdown-of-quant-concepts-by-frequency\/\">What Kind of Math is on the GMAT? Breakdown of Quant Concepts by Frequency<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here&#8217;s a whirlwind tour of one of the\u00a0most frequently tested sets of concepts on the GMAT Quantitative section: GMAT statistics. You don&#8217;t have to be an expert on statistics: a little goes a long way. Let&#8217;s learn some basic descriptive statistics formulas and go from there. Descriptive Statistics Formulas The Mean One very important GMAT [&hellip;]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[112],"tags":[],"ppma_author":[13209],"class_list":["post-1835","post","type-post","status-publish","format-standard","hentry","category-math"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Common GMAT Topic: Descriptive Statistics - Magoosh Blog \u2014 GMAT\u00ae Exam<\/title>\n<meta name=\"description\" content=\"Ready for a whirlwind tour of GMAT statistics? 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Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's Youtube video explanations.","sameAs":["https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured"],"award":["Magna cum laude from Harvard"],"knowsAbout":["GMAT"],"knowsLanguage":["English"],"jobTitle":"Content Creator","worksFor":"Magoosh","url":"https:\/\/magoosh.com\/gmat\/author\/mikemcgarry\/"}]}},"authors":[{"term_id":13209,"user_id":26,"is_guest":0,"slug":"mikemcgarry","display_name":"Mike M\u1d9cGarry","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g","user_url":"","last_name":"M\u1d9cGarry","first_name":"Mike","description":"Mike served as a GMAT Expert at Magoosh, helping create hundreds of lesson videos and practice questions to help guide GMAT students to success. He was also featured as \"member of the month\" for over two years at <a href=\"https:\/\/gmatclub.com\/blog\/2012\/09\/mike-mcgarrys-gmat-experience\/\" rel=\"noopener noreferrer\">GMAT Club<\/a>. Mike holds an A.B. in Physics (graduating <em>magna cum laude<\/em>) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's <a href=\"https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured\" rel=\"noopener noreferrer\">Youtube <\/a>video explanations and resources like <a href=\"https:\/\/magoosh.com\/gmat\/whats-a-good-gmat-score\/\" rel=\"noopener noreferrer\">What is a Good GMAT Score?<\/a> and the <a href=\"https:\/\/magoosh.com\/gmat\/gmat-diagnostic-test\/\" rel=\"noopener noreferrer\">GMAT Diagnostic Test<\/a>."}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/1835","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/users\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/comments?post=1835"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/1835\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=1835"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=1835"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=1835"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=1835"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}