Mean, Median - GMAT Descriptive Statistics

Hi

Questions testing you understanding of the link betwen Mean and Median are frequently tested in the GMAT.

Here is a basic but interesting question on the combo.

Question
Positive integers from 1 to 45, inclusive are placed in 5 groups of 9 each. What is the highest possible average of the medians of these 5 groups?
A. 25
B. 31
C. 15
D. 26
E. 23

Correct Answer
Choice B. 31 is the highest possible average of the medians.

Explanatory Answer
We need to maximize the median in each group in order to maximize the average of all the medians.

The highest possible median is 41 as there should be 4 numbers higher than the median in the group of 9.

So, if we have a group that has a, b, c, d, 41, 42, 43, 44, 45, the median will be 41.
In this set, it is essential not to use any more high values on a, b, c, or d as these do not affect the median.
So, the median of a group that comprises 1, 2, 3, 4, 41, 42, 43, 44, 45 will be 41.

The next group can be 5, 6, 7, 8, 36, 37, 38, 39, 40. The median will be 36.

To maximize medians in all the 5 groups, the medians of the 5 groups will have to be 21, 26, 31, 36 and 41.

The highest possible average of the medians will be the average of these 5 numbers = 31. 

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