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GRE Math Shortcut: Statistics


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

 

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 cannot be determined from the information given

As you can imagine, we really don’t want to calculate the mean and median of set T. Fortunately, we can apply a nice rule that says:

If the numbers in a set are equally spaced, then the mean and median of that set are equal.

What does it mean to have “equally spaced” numbers?

“Equally spaced” 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.

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.

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.

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:

Set X: {-27, -20, -13, -6, 1, 8, 15}

Set Y: {-23, -19, -15, -11, -7, -3, 1, 5, 9, 13}

Column A Column B
Mean of set X Mean of set Y

 

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 cannot be determined from the information given

Column A: 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, -6, 1, 8, 15}.  Set X has 7 elements and the middlemost element is -6. So, the median of set X is -6, which means the mean of set X is -6 as well.

Column B: 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, -7, -3, 1, 5, 9, 13}.  As such, the median of set Y will equal the average (mean) of -7 and -3, which is -5. So, if the median of set Y is -5, then the mean of set Y is -5 as well

So, using our rule, we found that Column A = -6, and Column B= -5. As such, the answer to the question is B.

 

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12 Responses to GRE Math Shortcut: Statistics

  1. brit123 August 18, 2014 at 10:04 am #

    Hello,
    For the first example, I selected choice D since I was unsure if any of the numbers repeated. For questions like this, is it safe to assume none of the numbers occur more than once?

    • Chris Lele
      Chris Lele August 18, 2014 at 1:17 pm #

      Hmm…that’s a good question. I’m not a 100% sure on that, and it does seem a bit misleading. I’d be inclined to edit this question so it is ambiguous that each of the multiples appears exactly once. Sorry for any confusion 🙂

      • brit123 August 18, 2014 at 1:50 pm #

        Thank you so much! 😀

  2. Hema June 18, 2014 at 6:30 am #

    Great tip 🙂 i used to skip such questions(example 1), due to lack of time. with this tip, it sounds so simple..Thank !!

  3. arya January 19, 2014 at 10:31 am #

    absolutely, love the tactics!!! can u please post, more of such nice tactics..it will be very much helpful.

    • Chris Lele
      Chris Lele January 23, 2014 at 10:56 am #

      Great! Happy you found that helpful :). We’ll try to keep posting such helpful tips.

  4. akanksha October 9, 2013 at 12:14 am #

    its great shortcut.. reduces whole calculation.. thanks Brent 🙂

  5. Inny July 31, 2013 at 6:42 am #

    Wow, excellent shortcut! Super helpful 🙂

  6. naga June 21, 2012 at 9:41 am #

    nice tactic..wish to learn many tactics like this…

  7. abhay May 26, 2012 at 12:05 pm #

    thanks…nice shortcut particularly the second application.

    • Margarette Jung
      Margarette May 29, 2012 at 10:56 am #

      You’re welcome, glad we could help! 🙂


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