{"id":11750,"date":"2012-05-30T16:23:38","date_gmt":"2012-05-30T23:23:38","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/?p=11750"},"modified":"2012-05-30T16:23:38","modified_gmt":"2012-05-30T23:23:38","slug":"common-gmat-topic-descriptive-statistics","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/common-gmat-topic-descriptive-statistics\/","title":{"rendered":"Common GMAT Topic: Descriptive Statistics"},"content":{"rendered":"

\"\"Here\u2019s a whirlwind tour of one of the\u00a0most frequently tested sets of concepts on the GMAT Quantitative section<\/a>. You don\u2019t have to be an expert on statistics: a little goes a long way.<\/p>\n

 <\/p>\n

The Mean<\/h2>\n

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\u2019s<\/p>\n

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

Notice, we can rewrite that as: (sum of items) = average*(number of items).\u00a0 Rewritten in that form, it becomes one of the most powerful formulas on the GMAT, see this post:\u00a0https:\/\/magoosh.com\/gmat\/2012\/gmat-averages-and-sums-formulas\/<\/a>\u00a0for more details.<\/p>\n

 <\/p>\n

The Median<\/h2>\n

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 & 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\u2019t change the fact that it\u2019s 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>\n

Range<\/h2>\n

The GMAT loves this one, because it\u2019s so simple.\u00a0 The range 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.<\/p>\n

 <\/p>\n

Standard Deviation<\/h2>\n

The range is a measure of the spread from the highest to the lowest value, but it doesn\u2019t \u201cfeel\u201d the numbers in between.\u00a0 The standard deviation is also a 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, the standard deviation \u201cfeels\u201d 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

a) If all the entries of the list are equal, the standard deviation = 0.\u00a0 In other words, they don\u2019t deviate at all, because they\u2019re all the same.<\/p>\n

b) If you add\/subtract a constant to\/from every number on a list, that doesn\u2019t change the standard deviation at all.\u00a0 It\u2019s just like taking the batch of data points and sliding them up or down the number line: that process doesn\u2019t change how far apart they are from each other.<\/p>\n

c) If you multiply\/divide a list by a constant, then you also multiply\/divide the standard deviation by this constant.<\/p>\n

I\u2019ll add an additional rule that really could only come into play in a very difficult upper-700s question:<\/p>\n

d) If all the entries are\u00a0the 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 \u201cdeviates\u201d from the mean by exactly two units, so the standard deviation = 2.<\/p>\n

 <\/p>\n

If you master these simple ideas, you will dominate on Descriptive Statistics in the GMAT Quantitative section.\u00a0 Here are some practice questions:<\/p>\n

1)\u00a0https:\/\/gmat.magoosh.com\/questions\/112<\/a><\/p>\n

2)\u00a0https:\/\/gmat.magoosh.com\/questions\/938<\/a><\/p>\n

3)\u00a0https:\/\/gmat.magoosh.com\/questions\/937<\/a><\/p>\n

 <\/p>\n

This post was written by Mike McGarry, GMAT expert at Magoosh<\/a>, and originally posted here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

Here\u2019s a whirlwind tour of one of the\u00a0most frequently tested sets of concepts on the GMAT Quantitative section. You don\u2019t have to be an expert on statistics: a little goes…<\/p>\n","protected":false},"author":133,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,783,243,718,717,736],"tags":[],"class_list":["post-11750","post","type-post","status-publish","format-standard","hentry","category-gmat","category-magoosh-blog","category-blog","category-data-sufficiency-gmat","category-problem-solving-gmat","category-quant-gmat","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/11750","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/users\/133"}],"replies":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/comments?post=11750"}],"version-history":[{"count":2,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/11750\/revisions"}],"predecessor-version":[{"id":11754,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/11750\/revisions\/11754"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=11750"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=11750"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=11750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}