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Mean, Median and Mode on the GRE

Over the last six months, I’ve gone through quite a few Revised GRE prep books. One thing I’ve noticed missing is difficult questions relating to mean, median, and mode. Sure, most books describe how to find the average, and what the difference between the mean and the median. Many already know the above, but mean, median and mode questions on the actual Revised GRE are going to require much more practice than you are going to get from simply applying the basic formulas.

Below are five questions that should hopefully give you a good mental workout. If you whip through them, answering all correctly, then you are very well prepared for the concepts you’ll find on the GRE. If you stumble, don’t despair. Remember, we have plenty more questions like these—some that are every more difficult—waiting for you at


1. Set S is comprised of six distinct positive integers less than 10. Which of the following must be true?

I: The median is an integer

II: The median is less than the average

III: The range of digits in Set S is less than 8


(A)  I only

(B)  I & II

(C)  II & III

(D) III only

(E)  None of the above.


2. A list is comprised of five positive integers: 4, 4, x, 7, y. What is the range of the possible values of the medians?

(A)  2

(B)  3

(C)  6

(D) 7

(E)  Cannot be determined by information provided.


3. The average of five positive integers is less than 20. What is the smallest possible median of this set?

(A)  19

(B)  10

(C)  4

(D) 3

(E)  1


4. Set S is comprised of 37 integers

Column A Column B
The median of Set S The mean of the lowest and the highest term


  1. The quantity in Column A is greater
  2. The quantity in Column B is greater
  3. The two quantities are equal
  4. The relationship cannot be determined from the information given


1. A good idea is to choose numbers. For instance, just using 1, 2, 3, 4, 5, 6 we can see that the first condition does not need to be true. The median of this range of numbers is 3.5. For the second condition, we can also use numbers and determine that the average and the median are equal. Therefore the second condition also does not have to hold true. Finally, for the third condition, the range of digits is 9 – 1 = 8. The third condition says less than 8. Therefore the answer is (E) none of the above.

2. Here we want to find the lowest possible median and the great possible median. Then we want to subtract the least possible median from the greatest possible median to find the range of the medians. If x and y are less than or equal to 4, then the median is 4. If x and y are greater than or equal to 7, the median is 7. Therefore the range of median is 3, Answer (B).

3. Choosing numbers will help us on this one. If we choose 1, 1, 1, 1, 16, the sum is equal to 20. The median is 1, Answer (E).

4. This is a conceptual problem. Nonetheless we can still pick numbers. Imagine all 37 numbers are the number ‘1’. The mean is ‘1’ and the average of the least and greatest is 1. n this case both columns are equal (C).Now, just change the last number to a 3. That is you have the number ‘1’ 36 times and the number three. The median is still 1. But now the average of the least and greatest is greater than ‘1.’  In this case column (B) is larger. If the answer switches depending on the numbers we use, the answer is (D).

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