Find the standard deviation of 2, 3, K, 5 and 6.

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Find the standard deviation of 2, 3, K, 5 and 6.

1. Standard deviation of 2+nK, 3+nK, (n+1)K, 5+nK, 6+nK is (2.5)^0.5
2. K is the arithmetic mean of the series 2, 3, K, 5, 6.

The OA is D.

Can any expert explain this DS question please? I need help to solve it. Thanks.

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by Jay@ManhattanReview » Thu Oct 26, 2017 6:24 am
LUANDATO wrote:Find the standard deviation of 2, 3, K, 5 and 6.

1. Standard deviation of 2+nK, 3+nK, (n+1)K, 5+nK, 6+nK is (2.5)^0.5
2. K is the arithmetic mean of the series 2, 3, K, 5, 6.

The OA is D.

Can any expert explain this DS question please? I need help to solve it. Thanks.
The standard deviation of a data set is a measure of the deviations of the numbers in the data set w.r.t. their mean. More deviated (more distant) the numbers are from the mean, the more is their standard deviation and vice-versa.

(1) Standard deviation of 2+nK, 3+nK, (n+1)K, 5+nK, and 6+nK is (2.5)^0.5

Note that if each number of a set is increased/decreased by a constant, the standard deviation of the resultant set does not change.

We are given that the standard deviation of 2 + nK, 3 + nK, K + nK, 5 + nK, and 6 + nK is √(2.5).

This implies that the standard deviation of 2 + nK - nk = 2, 3 + nK - nk = 3, K + nK - nk = K, 5 + nK - nk = 5, and 6 + nK - nk = 6 would also be √(2.5). Sufficient.

(2) K is the arithmetic mean of the series 2, 3, K, 5, 6.

Since K is the arithmetic mean of the series 2, 3, K, 5, 6, we have K = (2+3+5+6)/4 = 4.

Thus, the series is 2, 3, 4, 5, 6.

Note that the computation of Standard deviation is out of the scope of the GMAT; however, since all the values of the series are known, it can be computed.

Since this is a DS question and we only need to be sure whether we get a unique answer or not, we can be sure that we get the answer. Sufficient.

The correct answer: D

Hope this helps!

-Jay

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