BTGmoderatorDC wrote:Consider the following sets:
L = {3, 4, 5, 5, 6, 7}
M = {2, 2, 2, 8, 8, 8}
N = {15, 15, 15, 15, 15, 15}
Rank those three sets from least standard deviation to greatest standard deviation.
A. L, M, N
B. M, L, N
C. M, N, L
D. N, L, M
E. N, M, L
OA D
Source: Magoosh
The standard deviation measures the spread of the data w.r.t. its mean value. It is applied in comparing sets of data which may have the same mean but a different range. For example, the mean of the following two is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. However, the second is clearly more spread out. If a set has a low standard deviation, the values are not spread out too much.
Note that each term of the set N = {15, 15, 15, 15, 15, 15} is the same; thus, among the terms, there is no deviation at all. Or, SD = 0. So, least value of SD among set N, L, and M must be for set N.
The correct answer must be either D or E.
Again, note that the computation of SD is out of the scope of the GMAT; however, its analysis is within the scope.
L = {3, 4, 5, 5, 6, 7}
Mean = 5
We see that the smallest term (3) is 2 away from the mean (5) and the largest term (7) is also 2 away from the mean (5).
M = {2, 2, 2, 8, 8, 8}
Mean = 5
We see that the smallest term (2) is 3 away from the mean (5) and the largest term (8) is also 3 away from the mean (5).
Since the spread of terms for Set M is greater than that for Set L, SD for Set M > SD for Set M.
So, the rank these three sets from the least standard deviation to the greatest standard deviation is N, L, M.
Hope this helps.
The correct answer:
D
Hope this helps!
-Jay
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