{"id":17966,"date":"2019-09-01T16:32:58","date_gmt":"2019-09-01T21:32:58","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/prep\/?p=17966"},"modified":"2020-09-11T20:41:02","modified_gmt":"2020-09-11T20:41:02","slug":"gre-quantitative-standard-deviation","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/gre\/gre-quantitative-standard-deviation\/","title":{"rendered":"GRE Quantitative: Standard Deviation"},"content":{"rendered":"
While not frequently tested on the\u00a0GRE<\/a>, standard deviation is one of those scary sounding math concepts \u2013 like probability or combinations\/permutations \u2013 that always seems to get GRE test-takers\u2019 hearts beating fast. \u201cWait a minute,\u201d you may say to yourself when presented with a standard deviation problem. \u201cI thought all of the math on the GRE is basic algebra, geometry, and arithmetic. Doesn\u2019t standard deviation have something to do with statistics?\u201d<\/div>\n
\nFear not, brave GRE test-taker! As scary as they may sound, standard deviation problems are actually pretty easy to wrap your head around once you take the time to sit down, understand what they\u2019re all about, and try a few practice problems. In fact, the main reason these questions tend to throw GRE test-takers for a loop is\u00a0precisely\u00a0<\/em>because they show up so rarely on the test. Developing even a small measure of comfort with these question types will help ease the anxiety you may have about seeing \u201cgotcha\u201d questions on\u00a0GRE test day<\/a>.
\nFirst of all, let\u2019s talk briefly about what standard deviation means. Essentially, standard deviation measures how far from the mean different numbers are within a set. In other words, in a set of numbers, how far do all of the unique values in the set \u201cdeviate\u201d from the average? The farther away from each other the different numbers tend to be, the larger the standard deviation; the closer they are to each other, the smaller the standard deviation.
\n 
\n

Standard Deviation Practice Problems<\/h3>
<\/div><\/div><\/div>
\nBelow are two sets of numbers. According to the basic definition above, which set would you say has the greater standard deviation?
\nSet 1: \u00a04, 17, 28, 53, 88
\nSet 2: \u00a015, 23, 28, 32, 57
\nJust by looking at them, you can probably tell that Set 1 has a larger standard deviation, because the numbers in that set are more \u201cspread out\u201d than the numbers in Set 2. That\u2019s the gist of standard deviation.
\nOn the test, standard deviation questions are sometimes, but not always, simply a matter of comparing two sets. In addition, it\u2019s possible that you\u2019ll be asked to find a more specific value for the standard deviation of a set. Here\u2019s how we can do that.<\/p>\n
    \n
  1. Find the mean of the set of the numbers.<\/li>\n
  2. For each individual number in the set, calculate the difference between that number and the mean.<\/li>\n
  3. Square each of those differences.<\/li>\n
  4. Average together those new squared values.<\/li>\n
  5. Calculate the square root of the average of the squared values.<\/li>\n<\/ol>\n

    Let\u2019s try this out with the values from Set 2 above. We\u2019ll go through step by step to find the standard deviation of that set.<\/p>\n

      \n
    1. The mean, or average, of the values in Set 2 is 31.<\/li>\n
    2. The difference between 31 and each value in the set is, respectively: 16, 8, 3, 1, and 26.<\/li>\n
    3. Squaring each of those values results in: 256, 64, 9, 1, and 676.<\/li>\n
    4. Add those values together to get 1,006, then divide by 5: the average is 201.2.<\/li>\n
    5. Calculating the square root of that value results in the standard deviation of the set: 14.18.<\/li>\n<\/ol>\n

      Now, while it\u2019s good to know how to find the precise standard deviation of a set, the GRE doesn\u2019t always ask you to do so. Often, you will be asked to simply compare two sets of numbers and determine which has a larger or smaller standard deviation. However, knowing the steps to find the exact standard deviation of a set will occasionally be necessary to answer a high difficulty question.
      \n

      Try It Yourself<\/h3>
      <\/div><\/div><\/div>
      \nReady for a little practice? Here\u2019s another set of numbers (we\u2019ll call it Set 3):\u00a0 34, 36, 43, 66, 71. Using those values, answer these two questions:<\/p>\n
        \n
      1. Which has a larger standard deviation, Set 2 or Set 3?<\/li>\n
      2. What IS the standard deviation of Set 3?<\/li>\n<\/ol>\n

        Can you answer Question 1 by just looking at the two sets? Give it a guess, then check to see if you\u2019re right by finding the answer to Question 2, then comparing that value to the standard deviation of Set 2.<\/p>\n

        \t\t\t

        <\/span><\/p>\n<\/div>\n\t\t<\/div>

        \t\t\t

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

        While not frequently tested on the\u00a0GRE, standard deviation is one of those scary sounding math concepts \u2013 like probability or combinations\/permutations \u2013 that always seems to get GRE test-takers\u2019 hearts beating fast. \u201cWait a minute,\u201d you may say to yourself when presented with a standard deviation problem. \u201cI thought all of the math on the […]<\/p>\n","protected":false},"author":1,"featured_media":27060,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[68],"tags":[69,316],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/17966"}],"collection":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/comments?post=17966"}],"version-history":[{"count":2,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/17966\/revisions"}],"predecessor-version":[{"id":34545,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/17966\/revisions\/34545"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/27060"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=17966"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=17966"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=17966"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}