Is standard deviation of Set A > standard deviation of Se

[GMATinsight]

Is standard deviation of Set A > standard deviation of Set B?

1) Mean of Set A > Mean of Set B
2) Number of terms in Set A > Number of terms in Set B

Source: www.GMATinsight.com

Answer: option E

[deloitte247]

Standard deviation of a set is obtained from;
$$S.D=\sqrt{\frac{summation\left(X_i-X\right)^2}{N}}$$
$$where\ x_i=each\ element\ in\ the\ set$$
$$x=mean\ of\ the\ set$$
$$and\ N=Number\ of\ element\ in\ the\ set$$
These three information are necessary to determine the standard deviation of set A and B.
Statement 1 do not provide all the details and thus makes it not sufficient alone.
Statement 2 also do not provide all the details and thus, is not sufficient alone.

Therefore, statement 1 and 2 together also do not provide all the details and thus, both are not sufficient together. Hence, option E is correct<i class="em em-blush"></i>

[Brent@GMATPrepNow]

Is standard deviation of Set A > standard deviation of Set B?

1) Mean of Set A > Mean of Set B
2) Number of terms in Set A > Number of terms in Set B

Target question: Is standard deviation of Set A > standard deviation of Set B?

Head straight to...
Statements 1 and 2 COMBINED
We can quickly come up with 2 cases that satisfy BOTH statements:

Case a: Set A = {4, 4, 4, 4} and set B = {1, 2, 3}. Notice that both statements are satisfied here. In this case the standard deviation of Set A = 0, and the standard deviation of Set B is NOT 0.
IMPORTANT: the standard deviation of a set of values is always greater than or equal to zero. So, if the standard deviation of Set B is not 0, then the standard deviation of Set B must be POSITIVE.
In this case, the answer to the target question is NO, the standard deviation of Set A is NOT greater than the standard deviation of Set B

Case b: Set A = {1, 2, 3, 4 and set B = {0, 0, 0}. In this case the standard deviation of Set A is some POSITIVE value, and the standard deviation of Set B is 0.
In this case, the answer to the target question is YES, the standard deviation of Set A IS greater than the standard deviation of Set B
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent