Consider the following sets: L = {3, 4, 5, 5, 6, 7} M = {2,

[BTGmoderatorDC]

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

[Jay@ManhattanReview]

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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[Scott@TargetTestPrep]

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

Since all the numbers in set N are the same, the standard deviation (SD) of set N is 0, and its SD is the smallest since the SD of any set can't be less than 0.

Since the other two sets have at least two distinct numbers, their SDs are greater than 0. Now, let's delve deeper into these two sets. We see that they both have a mean of 5. However, the numbers in set L are much closer to 5 (all within 2 units of 5) than those in set M (all are 3 units from 5); therefore, set L has a smaller SD than set M. So the order of the sets ranked by their SDs from least to greatest is: N, L, M.

Answer: D