{"id":8413,"date":"2012-01-04T10:23:06","date_gmt":"2012-01-04T18:23:06","guid":{"rendered":"https:\/\/magoosh.com\/gre\/?p=8413"},"modified":"2012-01-04T20:01:23","modified_gmt":"2012-01-05T04:01:23","slug":"gre-math-shortcut-statistics","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/","title":{"rendered":"GRE Math Shortcut: Statistics"},"content":{"rendered":"<p><strong><br \/>\n<\/strong><\/p>\n<p>Consider the following question:<\/p>\n<p align=\"center\"><strong>Set T consists of all multiples of 5 from 30 to 225 inclusive<\/strong><\/p>\n<table width=\"600\">\n<tbody>\n<tr>\n<th style=\"text-align: center;\"><span style=\"text-decoration: underline;\">Column A<\/span><\/th>\n<th style=\"text-align: center;\"><span style=\"text-decoration: underline;\">Column B<\/span><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">Mean of Set T<\/td>\n<td style=\"text-align: center;\">Median of Set T<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>A. The quantity in Column A is greater<br \/>\nB. The quantity in Column B is greater<br \/>\nC. The two quantities are equal<br \/>\nD. The relationship cannot be determined from the information given<\/p>\n<p>As you can imagine, we really don\u2019t want to calculate the mean and median of set T. Fortunately, we can apply a nice rule that says:<\/p>\n<p><strong><em>If the numbers in a set are equally spaced, then the mean and median of that set are equal.<\/em><\/strong><\/p>\n<p>What does it mean to have \u201cequally spaced\u201d numbers?<\/p>\n<p>\u201cEqually spaced\u201d means that, if the numbers in a set are arranged in ascending order, then the difference between any two adjacent numbers will always be the same.<\/p>\n<p>So, in the set {30, 35, 40, . . . , 215, 220, 225}, the difference between any two adjacent numbers will always equal 5. As such, the mean of this set will equal the median of this set (which means the answer to the above question is C). Notice that we can answer this question without making any calculations whatsoever. We can answer it by recognizing that the numbers in the set are equally spaced.<\/p>\n<p>Similarly, the numbers in the set {5, 8, 11, 14, 17, 20, 23} are equally spaced. As such, the mean of this set will equal the median of this set.<\/p>\n<p>As you might imagine, this little rule as a shortcut can come in handy. It will help you quickly answer the original question, and it will help you answer this one:<\/p>\n<p style=\"text-align: center;\"><strong>Set X: {-27, -20, -13, -6, 1, 8, 15}<\/strong><strong><\/strong><\/p>\n<p style=\"text-align: center;\"><strong>Set Y: {-23, -19, -15, -11, -7, -3, 1, 5, 9, 13}<\/strong><\/p>\n<table width=\"600\">\n<tbody>\n<tr>\n<th style=\"text-align: center;\"><span style=\"text-decoration: underline;\">Column A<\/span><\/th>\n<th style=\"text-align: center;\"><span style=\"text-decoration: underline;\">Column B<\/span><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">Mean of set X<\/td>\n<td style=\"text-align: center;\">Mean of set Y<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>A. The quantity in Column A is greater<br \/>\nB. The quantity in Column B is greater<br \/>\nC. The two quantities are equal<br \/>\nD. The relationship cannot be determined from the information given<\/p>\n<p><span style=\"text-decoration: underline;\">Column A<\/span>: Since the numbers in set X are equally spaced, the mean will equal the median. We can quickly find the median by locating the middlemost element: {-27, -20, -13, <strong>-6<\/strong>, 1, 8, 15}.\u00a0 Set X has 7 elements and the middlemost element is <strong>-6<\/strong>. So, the median of set X is -6, which means the mean of set X is -6 as well.<\/p>\n<p><span style=\"text-decoration: underline;\">Column B<\/span>: The numbers in set Y are also equally spaced, so the mean will equal the median. Set Y has 10 elements, so there are two middlemost elements: {-23, -19, -15, -11, <strong>-7<\/strong>, <strong>-3<\/strong>, 1, 5, 9, 13}.\u00a0 As such, the median of set Y will equal the average (mean) of <strong>-7<\/strong> and <strong>-3<\/strong>, which is -5. So, if the median of set Y is -5, then the mean of set Y is -5 as well<\/p>\n<p>So, using our rule, we found that Column A = -6, and Column B= -5. As such, the answer to the question is B.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Consider the following question: Set T consists of all multiples of 5 from 30 to 225 inclusive Column A Column B Mean of Set T Median of Set T &nbsp; A. The quantity in Column A is greater B. The quantity in Column B is greater C. The two quantities are equal D. The relationship [&hellip;]<\/p>\n","protected":false},"author":11,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[39,25],"tags":[],"ppma_author":[12266],"class_list":["post-8413","post","type-post","status-publish","format-standard","hentry","category-data-analysis","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>GRE Math Shortcut: Statistics - Magoosh Blog \u2014 GRE\u00ae Test<\/title>\n<meta name=\"description\" content=\"Here is a helpful GRE Statistics tip about the relationship of the mean and median of a set of equally spaced numbers!\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GRE Math Shortcut: Statistics\" \/>\n<meta property=\"og:description\" content=\"Here is a helpful GRE Statistics tip about the relationship of the mean and median of a set of equally spaced numbers!\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/\" \/>\n<meta property=\"og:site_name\" content=\"Magoosh Blog \u2014 GRE\u00ae Test\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/Magoosh\/\" \/>\n<meta property=\"article:published_time\" content=\"2012-01-04T18:23:06+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2012-01-05T04:01:23+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/magoosh.com\/gre\/files\/2016\/09\/Magoosh-Facebook-Default-Pic.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"628\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Brent\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@MagooshGRE\" \/>\n<meta name=\"twitter:site\" content=\"@MagooshGRE\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Brent\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/\"},\"author\":{\"name\":\"Brent\",\"@id\":\"https:\/\/magoosh.com\/gre\/#\/schema\/person\/b2fbd67daad89818fde8859916e23409\"},\"headline\":\"GRE Math Shortcut: Statistics\",\"datePublished\":\"2012-01-04T18:23:06+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/\"},\"wordCount\":481,\"commentCount\":12,\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gre\/#organization\"},\"articleSection\":[\"GRE Data Analysis\",\"GRE Math\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/\",\"url\":\"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/\",\"name\":\"GRE Math Shortcut: Statistics - Magoosh Blog \u2014 GRE\u00ae Test\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gre\/#website\"},\"datePublished\":\"2012-01-04T18:23:06+00:00\",\"description\":\"Here is a helpful GRE Statistics tip about the relationship of the mean and median of a set of equally spaced numbers!\",\"breadcrumb\":{\"@id\":\"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/magoosh.com\/gre\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"GRE Math Shortcut: Statistics\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/magoosh.com\/gre\/#website\",\"url\":\"https:\/\/magoosh.com\/gre\/\",\"name\":\"Magoosh Blog \u2014 GRE\u00ae Test\",\"description\":\"Everything you need to know about the GRE\",\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gre\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/magoosh.com\/gre\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/magoosh.com\/gre\/#organization\",\"name\":\"Magoosh\",\"url\":\"https:\/\/magoosh.com\/gre\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/gre\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/magoosh.com\/gre\/files\/2019\/04\/Magoosh-logo-purple-60h.png\",\"contentUrl\":\"https:\/\/magoosh.com\/gre\/files\/2019\/04\/Magoosh-logo-purple-60h.png\",\"width\":265,\"height\":60,\"caption\":\"Magoosh\"},\"image\":{\"@id\":\"https:\/\/magoosh.com\/gre\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/Magoosh\/\",\"https:\/\/twitter.com\/MagooshGRE\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/magoosh.com\/gre\/#\/schema\/person\/b2fbd67daad89818fde8859916e23409\",\"name\":\"Brent\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/gre\/#\/schema\/person\/image\/2c44c3d2b5d811cb2cc2f7b52e98a186\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/10b86d22636e4b773ca09b355ca87734de1952dba2b74eaa4ce2f13249accba4?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/10b86d22636e4b773ca09b355ca87734de1952dba2b74eaa4ce2f13249accba4?s=96&d=mm&r=g\",\"caption\":\"Brent\"},\"description\":\"Brent Hanneson is a master tutor with over 20 years of teaching experience. He developed all the math content for Magoosh Test Prep. Brent plays ice hockey in his free time.\",\"url\":\"https:\/\/magoosh.com\/gre\/author\/brent\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"GRE Math Shortcut: Statistics - Magoosh Blog \u2014 GRE\u00ae Test","description":"Here is a helpful GRE Statistics tip about the relationship of the mean and median of a set of equally spaced numbers!","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:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/","og_locale":"en_US","og_type":"article","og_title":"GRE Math Shortcut: Statistics","og_description":"Here is a helpful GRE Statistics tip about the relationship of the mean and median of a set of equally spaced numbers!","og_url":"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/","og_site_name":"Magoosh Blog \u2014 GRE\u00ae Test","article_publisher":"https:\/\/www.facebook.com\/Magoosh\/","article_published_time":"2012-01-04T18:23:06+00:00","article_modified_time":"2012-01-05T04:01:23+00:00","og_image":[{"width":1200,"height":628,"url":"https:\/\/magoosh.com\/gre\/files\/2016\/09\/Magoosh-Facebook-Default-Pic.png","type":"image\/png"}],"author":"Brent","twitter_card":"summary_large_image","twitter_creator":"@MagooshGRE","twitter_site":"@MagooshGRE","twitter_misc":{"Written by":"Brent","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/#article","isPartOf":{"@id":"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/"},"author":{"name":"Brent","@id":"https:\/\/magoosh.com\/gre\/#\/schema\/person\/b2fbd67daad89818fde8859916e23409"},"headline":"GRE Math Shortcut: Statistics","datePublished":"2012-01-04T18:23:06+00:00","mainEntityOfPage":{"@id":"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/"},"wordCount":481,"commentCount":12,"publisher":{"@id":"https:\/\/magoosh.com\/gre\/#organization"},"articleSection":["GRE Data Analysis","GRE Math"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/","url":"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/","name":"GRE Math Shortcut: Statistics - Magoosh Blog \u2014 GRE\u00ae Test","isPartOf":{"@id":"https:\/\/magoosh.com\/gre\/#website"},"datePublished":"2012-01-04T18:23:06+00:00","description":"Here is a helpful GRE Statistics tip about the relationship of the mean and median of a set of equally spaced numbers!","breadcrumb":{"@id":"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/magoosh.com\/gre\/gre-math-shortcut-statistics\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/magoosh.com\/gre\/"},{"@type":"ListItem","position":2,"name":"GRE Math Shortcut: Statistics"}]},{"@type":"WebSite","@id":"https:\/\/magoosh.com\/gre\/#website","url":"https:\/\/magoosh.com\/gre\/","name":"Magoosh Blog \u2014 GRE\u00ae Test","description":"Everything you need to know about the GRE","publisher":{"@id":"https:\/\/magoosh.com\/gre\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/magoosh.com\/gre\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/magoosh.com\/gre\/#organization","name":"Magoosh","url":"https:\/\/magoosh.com\/gre\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/magoosh.com\/gre\/#\/schema\/logo\/image\/","url":"https:\/\/magoosh.com\/gre\/files\/2019\/04\/Magoosh-logo-purple-60h.png","contentUrl":"https:\/\/magoosh.com\/gre\/files\/2019\/04\/Magoosh-logo-purple-60h.png","width":265,"height":60,"caption":"Magoosh"},"image":{"@id":"https:\/\/magoosh.com\/gre\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/Magoosh\/","https:\/\/twitter.com\/MagooshGRE"]},{"@type":"Person","@id":"https:\/\/magoosh.com\/gre\/#\/schema\/person\/b2fbd67daad89818fde8859916e23409","name":"Brent","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/magoosh.com\/gre\/#\/schema\/person\/image\/2c44c3d2b5d811cb2cc2f7b52e98a186","url":"https:\/\/secure.gravatar.com\/avatar\/10b86d22636e4b773ca09b355ca87734de1952dba2b74eaa4ce2f13249accba4?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/10b86d22636e4b773ca09b355ca87734de1952dba2b74eaa4ce2f13249accba4?s=96&d=mm&r=g","caption":"Brent"},"description":"Brent Hanneson is a master tutor with over 20 years of teaching experience. He developed all the math content for Magoosh Test Prep. Brent plays ice hockey in his free time.","url":"https:\/\/magoosh.com\/gre\/author\/brent\/"}]}},"authors":[{"term_id":12266,"user_id":11,"is_guest":0,"slug":"brent","display_name":"Brent","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/10b86d22636e4b773ca09b355ca87734de1952dba2b74eaa4ce2f13249accba4?s=96&d=mm&r=g","user_url":"","last_name":"Hanneson","first_name":"Brent","description":"Brent Hanneson is a master tutor with over 20 years of teaching experience. He developed all the math content for Magoosh Test Prep. Brent plays ice hockey in his free time."}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/posts\/8413","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/comments?post=8413"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/posts\/8413\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/media?parent=8413"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/categories?post=8413"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/tags?post=8413"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/ppma_author?post=8413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}