{"id":8958,"date":"2012-05-21T09:00:33","date_gmt":"2012-05-21T16:00:33","guid":{"rendered":"https:\/\/magoosh.com\/gre\/?p=8958"},"modified":"2013-08-09T10:35:15","modified_gmt":"2013-08-09T17:35:15","slug":"gre-math-percentiles-and-quartiles","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gre\/gre-math-percentiles-and-quartiles\/","title":{"rendered":"GRE Math: Percentiles and Quartiles"},"content":{"rendered":"

Fact<\/span>: An 8 year old boy who is 4’5″ (53 inches) tall is in the 86th percentile for height for his age.<\/p>\n

What on earth does that mean?\u00a0 Well, the percentile of an individual tells you what percent of the population has a value of a variable is below that individual’s value of the variable.\u00a0 For example, to say that a 4’5″ 8 year-old boy is in the 86th percentile for height for his age, we are saying: gather together all 8 year-old boys on Earth, and measure their heights; if you sort out all the 8 year-old boys who have a height less than 4’5″, they will comprise approximately 86% of the population.\u00a0\u00a0 That boy is taller than 86% of other boys his age \u2013 that means he’s in the 86% percentile.<\/p>\n

Percentiles is a relatively unlikely topic to see on the GRE, but if it does show up, here are a few handy facts to have up your sleeve.<\/p>\n

 <\/p>\n

Biggest and Smallest<\/h2>\n

A few details to clarify.\u00a0 The individual with the lowest value of the variable, with the minimum value, is not bigger than anyone, so the lowest percentile, the percentile of the rock-bottom minimum, is the 0th percentile.\u00a0 If my score is in the 0th percentile, then I am not higher than anyone.<\/p>\n

What’s trickier is the maximum score.\u00a0 If my score is the highest score, I am higher than everybody else, but that’s not<\/em><\/strong> the 100th percentile, because in order to be higher than 100% of the population, higher than everyone, I would have to have a score higher than my own score: a paradox!\u00a0 In fact, for this very reason, there’s no such thing as a 100th percentile.\u00a0 The person with the highest score is higher than everybody else, but not higher than herself, so she’s in the 99th percentile.\u00a0 If we are sticking with whole numbers, the 99th percentile is the highest possible percentile.\u00a0 If we go to decimals, we can get higher with the 99.9th percentile (1 out of a 1000), the 99.99th percentile (1 out of 10000), etc.<\/p>\n

 <\/p>\n

Median and Quartiles<\/h2>\n

The median is the middle of a list: the median divides a list into an “upper half” and a “lower half.”\u00a0\u00a0\u00a0 This means, the median is higher than the lower half of the population, higher than 50%, so the median is the 50th percentile.\u00a0 Now, we have to be careful here.\u00a0 On a list with only three members — e.g. {2, 4, 7} — the median is the middle number, here 4, but that number is higher than only one number out of three — so 4 is the 33rd percentile of that list.\u00a0 In a technical sense, the median is not always the 50th percentile.<\/p>\n

In some sense, though, that’s a specious objection.\u00a0 When there are only 3 members on a list, nobody in their right mind talks about percentiles.\u00a0 When the total number is less than a few hundred, there’s seldom talk of a percentile.\u00a0 Percentiles, by their very nature, are a way to make sense of tens of thousands, even millions of individuals.\u00a0 How many 8 year-old boys are there on Earth?\u00a0 Who knows, but it’s certainly a very very large number.\u00a0 That’s where percentiles are used in practice.<\/p>\n

When the number of folks in the group is that large, then for all intents and purposes,the median is the 50th percentile.\u00a0 If you are familiar with the idea of quartiles<\/a>, then the first quartile is the 25th percentile and the third quartile is the 75th percentile, again, when the group sizes are truly huge.<\/p>\n

 <\/p>\n

Practice Questions<\/h2>\n

1) Sasha took a nationwide standardized test that is graded on a scale from 20 to 60.\u00a0 Sasha got one of the best scores recorded on that this test.<\/p>\n

 <\/p>\n

Column A\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Column B<\/strong><\/p>\n

Sasha’s score \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0the percentile of Sasha’s score<\/p>\n

 <\/p>\n

(A) The quantity in Column A is greater.<\/p>\n

(B) The quantity in Column B is greater.<\/p>\n

(C) The two quantities are equal.<\/p>\n

(D) The relationship cannot be determined from the information given.<\/p>\n

 <\/p>\n

2) Alice took nationwide standardize test that is graded on a scale from 0 to 100.\u00a0 Alice scored the highest score recorded on this test.<\/p>\n

Column A \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Column B<\/strong><\/p>\n

Alice’s score \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 the percentile of Alice’s score<\/p>\n

 <\/p>\n

(A) The quantity in Column A is greater.<\/p>\n

(B) The quantity in Column B is greater.<\/p>\n

(C) The two quantities are equal.<\/p>\n

(D) The relationship cannot be determined from the information given.<\/p>\n

 <\/p>\n

3) A large distribution of score is normally distributed<\/p>\n

Column A<\/strong><\/p>\n

score that’s one standard deviation above the mean<\/p>\n

Column B<\/strong><\/p>\n

score that has the 80th percentile<\/p>\n

(A) The quantity in Column A is greater.<\/p>\n

(B) The quantity in Column B is greater.<\/p>\n

(C) The two quantities are equal.<\/p>\n

(D) The relationship cannot be determined from the information given.<\/p>\n

\n

 <\/p>\n<\/div>\n

Practice Questions Answers and Explanations<\/h2>\n

(1)\u00a0B<\/strong>; (2)\u00a0D<\/strong>; (3)\u00a0A<\/strong>;<\/p>\n

1) We know that Sasha is near the top of the scoring distribution, so that would mean a score with a percentile close to the 99th percentile.\u00a0 Because of the scoring scale, the score is not going to be above 60, so the percentile is clearly bigger.\u00a0 Answer = B<\/strong>.<\/p>\n

2) Alice got the highest score, so by definition, that’s the 99th percentile.\u00a0 What we don’t know is: how hard was this test?\u00a0 What score was the highest score?\u00a0 If it was a particularly challenging test, it could be that the highest score anyone achieved was only, say, a 73.\u00a0 In that case, the percentile would be greater.\u00a0 If, on the other hand, it was possible to get a perfect score, and Alice did in fact do that, then her score of a 100 would be greater than the percentile.\u00a0 We don’t have enough information to decide.\u00a0 Answer = D<\/strong>.<\/p>\n

3) Here, it might be helpful to brush up on\u00a0Normal Distribution<\/a>.\u00a0 On a normal distribution, it’s always true that 68% of the populations lies within one standard deviation of the mean.\u00a0 That means, half of that, 34%, lie between the mean and one standard deviation above the mean.\u00a0 The score that is one standard deviation is higher than the 34% between the mean and one standard deviation above the mean, as well as than the 50% below the mean.\u00a0 That means, a score that lies one standard deviation above the mean is the 50 + 34 = 84th percentile.\u00a0 Thus, it’s higher than a score in the 80th percentile.\u00a0 Answer = A<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

Fact: An 8 year old boy who is 4’5″ (53 inches) tall is in the 86th percentile for height for his age. What on earth does that mean?\u00a0 Well, the percentile of an individual tells you what percent of the population has a value of a variable is below that individual’s value of the variable.\u00a0 […]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[39,25],"tags":[],"ppma_author":[12267],"class_list":["post-8958","post","type-post","status-publish","format-standard","hentry","category-data-analysis","category-math"],"acf":[],"yoast_head":"\nGRE Math: Percentiles and Quartiles - Magoosh Blog \u2014 GRE\u00ae Test<\/title>\n<meta name=\"description\" content=\"Here are a few handy facts to have up your sleeve about the Percentiles and Quartiles on the GRE Math, as well as some practice questions!\" \/>\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-percentiles-and-quartiles\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GRE Math: Percentiles and Quartiles\" \/>\n<meta property=\"og:description\" content=\"Here are a few handy facts to have up your sleeve about the Percentiles and Quartiles on the GRE Math, as well as some practice questions!\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/gre\/gre-math-percentiles-and-quartiles\/\" \/>\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=\"2012-05-21T16:00:33+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2013-08-09T17:35:15+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=\"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=\"5 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-percentiles-and-quartiles\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gre\/gre-math-percentiles-and-quartiles\/\"},\"author\":{\"name\":\"Mike M\u1d9cGarry\",\"@id\":\"https:\/\/magoosh.com\/gre\/#\/schema\/person\/320346c205075513344435baf9b0521b\"},\"headline\":\"GRE Math: Percentiles and Quartiles\",\"datePublished\":\"2012-05-21T16:00:33+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/gre\/gre-math-percentiles-and-quartiles\/\"},\"wordCount\":1055,\"commentCount\":42,\"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-percentiles-and-quartiles\/\",\"url\":\"https:\/\/magoosh.com\/gre\/gre-math-percentiles-and-quartiles\/\",\"name\":\"GRE Math: Percentiles and Quartiles - 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