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Which of the following two data values when included in the

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by GMATinsight » Tue Jun 13, 2017 12:58 am
Which of the following two data values when included in the set {1, 2, 3, 4, 5} will result in the new set with lowest standard deviation

A) (1,5)
B) (2,3)
C) (2,4)
D) (1,3)
E) (3,3)

SOURCE: www.GMATinsight.com

Answer: Option E
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by Jay@ManhattanReview » Tue Jun 13, 2017 1:13 am
GMATinsight wrote:Which of the following two data values when included in the set {1, 2, 3, 4, 5} will result in the new set with lowest standard deviation

A) (1,5)
B) (2,3)
C) (2,4)
D) (1,3)
E) (3,3)

SOURCE: www.GMATinsight.com

Answer: Option E
We see that the mean of the given set {1, 2, 3, 4, 5} is 3.

Standard Deviation is a measure of the spread of elements w.r.t. mean. Closer the elements are to the mean of the set, lesser the Standard Deviation (SD) is.

Since the values of the Option E (3, 3) elements is 3 each, the deviation w.r.t. mean (3) is 0, thus SD would be least if we include these two elements.

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Sets & Statistics Guide

-Jay
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