BTGmoderatorDC wrote:Dataset W: –9, –3, 3, 9
Dataset X: 2, 4, 6, 8
Dataset Y: 100, 101, 102, 103
Dataset Z: 7, 7, 7, 7
Which of the following choices lists the four datasets above in order from least standard deviation to greatest standard deviation?
(A) Z, W, X, Y,
(B) Z, W, Y, X
(C) Z, Y, W, X
(D) Z, Y, X, W
(E) Z, X, Y, W
OA D
Source: Manhattan Prep
Note that the computation of standard deviation is not within the scope of the GMAT; however, its interpretation is within the scope.
Standard deviation is a measure of how much far or close values of the dataset are to the arithmetic mean. Closer the values are to the mean, lesser is the standard deviation (SD) of the dataset and vice-versa.
Seeing the given four sets X, Y, W and Z, we observe that SD of set Z = 0 since each element is the same, thus, among them, there is no deviation at all. However, this does not help since, in all the five options, the first set is Z. I think the options are not crafted well. There is no significance of set Z for this question.
Let's analyze sets X, Y and W.
Dataset W: –9, –3, 3, 9: Mean = 0; Each value is away from the mean either to left or to right. It does not matter whether the deviation is positive or negative; SD is always a non-negative number.
Dataset X: 2, 4, 6, 8: Mean = 5; Each value is away from the mean either to left or to right.
Dataset Y: 100, 101, 102, 103: Mean = 101.5; Each value is away from the mean either to left or to right.
You can observe that compared to the values of sets X and W, the values of set Y are relatively quite closer to its mean (101.5), thus, its SD must be least among the sets. So, the correct answer must be either C or D.
Similarly, you can observe that compared to the values of sets W, the values of set X are relatively quite closer to its mean (5), thus, its SD must be less than that of set W. So, the correct answer must be D.
The correct answer:
D
Hope this helps!
-Jay
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