{"id":12447,"date":"2012-11-12T14:11:01","date_gmt":"2012-11-12T22:11:01","guid":{"rendered":"https:\/\/magoosh.com\/gre\/?p=12447"},"modified":"2019-07-16T11:38:41","modified_gmt":"2019-07-16T18:38:41","slug":"boxplots-on-the-gre","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gre\/boxplots-on-the-gre\/","title":{"rendered":"Boxplots on the GRE"},"content":{"rendered":"

Boxplots are one data format you may see on the GRE Data Interpretation questions<\/a>. \u00a0First, try these practice questions.<\/p>\n

(The following diagram applies to questions #1-3<\/em>)<\/p>\n

The following boxplot shows the 2012 season runs batted in (RBIs) of 280 American League batters (the top 280 batters in terms of number of plate appearances).<\/p>\n

\"\"<\/a><\/p>\n

1) What is the size of the IQR of this distribution?<\/p>\n

    \n
  1. 25<\/li>\n
  2. 47<\/li>\n
  3. 56<\/li>\n
  4. 83<\/li>\n
  5. 140<\/li>\n<\/ol>\n

    2) How many AL hitters hit more than 25 RBIs in 2012?<\/p>\n

      \n
    1. 9<\/li>\n
    2. 56<\/li>\n
    3. 83<\/li>\n
    4. 114<\/li>\n
    5. 140<\/li>\n<\/ol>\n

      3) B. J. Upton of the Tampa Bay Rays hit 78 RBIs in 2012; this is the 90th percentile value on this chart.\u00a0 How many players hit between 56 and 78 RBIs?<\/p>\n

        \n
      1. 14<\/li>\n
      2. 22<\/li>\n
      3. 28<\/li>\n
      4. 34<\/li>\n
      5. 42<\/li>\n<\/ol>\n

        (BTW, that max value of 139 RBIs is Miguel Cabrera<\/a>, after his extraordinary Triple Crown year.)<\/p>\n

         <\/p>\n

        Five-number summary<\/h2>\n

        In this previous post<\/a>, I discussed the idea of quartiles and IQR, tools that statisticians use to “chunk” a data set.\u00a0 Sometimes, statisticians add to this the median & minimum & maximum to create something called the “five-number summary<\/strong>”<\/p>\n

        1. maximum<\/p>\n

        2. third quarter, Q3, the 75th percentile<\/p>\n

        3. median, 50th percentile<\/p>\n

        4. first quartile, Q1, the 25th percentile<\/p>\n

        5. minimum<\/p>\n

        The beauty of the five-number summary is that it divides the entire data set into quarters — between any two numbers on the five-number summary is exactly 25% of the data.<\/p>\n

         <\/p>\n

        A visual approach<\/h2>\n

        Because statisticians, like all human beings, are highly visual folks, they created a visual way to display the five-number summary.\u00a0 This visual form is called a boxplot<\/strong>.\u00a0 Boxplots were created by the brilliant statistician John Tukey<\/a> in 1977.\u00a0 The five vertical lines represent the five numbers of the five-number summary, and the “box” in the middle, from Q1 to Q3, represents the IQR, i.e., the middle 50% of the data.\u00a0 Between any two adjacent vertical lines are 25% of the data points.<\/p>\n

         <\/p>\n

        Strikeouts<\/h2>\n

        Here’s an example of a boxplot using real baseball data.\u00a0 The data here are the 2012 season total for strikeouts pitched (by all National League pitchers who pitched at least 75 innings in the season).<\/p>\n

        \"\"<\/a><\/p>\n

        Half of all the NL pitchers here pitched between Q1 = 83 and Q3 = 161 strikeouts in the year — these are the pitchers in the IQR, the big blue box in the center.\u00a0 Only 25% of the pitchers in this group struck out fewer than 83 batters— this “bottom 25%” is on the “lower arm”, from 38 to 83.\u00a0 Only 25% of these pitchers struck out more than 161 batters in the 2012 season —- this “top 25%” is on the “upper arm”, from 161 to 230.\u00a0 (BTW, that maximum value, 230 strikeouts, is R. A. Dickey<\/a>, the knuckleball<\/a> star pitcher of the NY Mets!)\u00a0 On a Data Interpretation question, ETS could give you a boxplot and expect you to read all the five-number summary information (including percentiles) from it.<\/p>\n

        If you found the practice questions difficult the first time around, you may want to go back and give them another look, before you read the solutions below.<\/p>\n

         <\/p>\n

        Practice questions explanations<\/h2>\n

        1) The IQR is the distance from Q1 to Q3.\u00a0 From the boxplot, we read that Q1 = 9 and Q3 = 56, and the difference between them is 56 \u2013 9 = 47<\/strong>.\u00a0 Answer = B<\/strong><\/p>\n

        2) From the boxplot, we read that 25 RBIs is the median, so that number divides the list in half.\u00a0 There are 280 hitters on this list: half must be above the median, and half below.\u00a0 Therefore, there are 140<\/strong> hitters above the median value of 25 RBIs.\u00a0 Answer = E<\/strong>.<\/p>\n

        3) Upton, at 78 RBIs, is the 90th percentile.\u00a0 From the boxplot, we read that 56 RBIs, is Q3, i.e. the 75th percentile.\u00a0 Between the 75th percentile and the 90th percentile is 15% of the list.\u00a0 There are 280 hitters on the list, so 15% of 280 = 0.15*280 = 42.\u00a0 There are 42<\/strong> hitters between 56 RBIs and 78 RBIs.\u00a0 Answer = E<\/strong>.<\/p>\n

         <\/p>\n","protected":false},"excerpt":{"rendered":"

        Boxplots are one data format you may see on the GRE Data Interpretation questions. \u00a0First, try these practice questions. (The following diagram applies to questions #1-3) The following boxplot shows the 2012 season runs batted in (RBIs) of 280 American League batters (the top 280 batters in terms of number of plate appearances). 1) What […]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25,10764],"tags":[],"ppma_author":[12267],"class_list":["post-12447","post","type-post","status-publish","format-standard","hentry","category-math","category-math-practice"],"acf":[],"yoast_head":"\nBoxplots on the GRE - Magoosh Blog \u2014 GRE\u00ae Test<\/title>\n<meta name=\"description\" content=\"Here are some practice questions and explanations for the boxplots on the GRE Data Interpretation section.\" \/>\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\/boxplots-on-the-gre\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Boxplots on the GRE\" \/>\n<meta property=\"og:description\" content=\"Here are some practice questions and explanations for the boxplots on the GRE Data Interpretation section.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/gre\/boxplots-on-the-gre\/\" \/>\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=\"2012-11-12T22:11:01+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-07-16T18:38:41+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/magoosh.com\/gre\/files\/2012\/11\/bp_img1.png\" \/>\n<meta name=\"author\" content=\"Mike M\u1d9cGarry\" \/>\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=\"Mike M\u1d9cGarry\" \/>\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\/boxplots-on-the-gre\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gre\/boxplots-on-the-gre\/\"},\"author\":{\"name\":\"Mike M\u1d9cGarry\",\"@id\":\"https:\/\/magoosh.com\/gre\/#\/schema\/person\/320346c205075513344435baf9b0521b\"},\"headline\":\"Boxplots on the GRE\",\"datePublished\":\"2012-11-12T22:11:01+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/gre\/boxplots-on-the-gre\/\"},\"wordCount\":594,\"commentCount\":19,\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gre\/#organization\"},\"articleSection\":[\"GRE Math\",\"Shorter GRE Math Practice\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/gre\/boxplots-on-the-gre\/\",\"url\":\"https:\/\/magoosh.com\/gre\/boxplots-on-the-gre\/\",\"name\":\"Boxplots on the GRE - 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