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If the positive number d is the standard deviation of n, k and p then the standard deviation of n+1, k+1, and p+1 is...

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by BTGmoderatorLU » Mon Jan 04, 2021 12:10 pm

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E

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Source: GMAT Prep

If the positive number d is the standard deviation of n, k and p then the standard deviation of n+1, k+1, and p+1 is

A. d+3
B. d+1
C. 6d
D. 3d
E. d

The OA is E
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Re: If the positive number d is the standard deviation of n, k and p then the standard deviation of n+1, k+1, and p+1 is

by deloitte247 » Thu Jan 07, 2021 5:47 am
The standard deviation of a set of numbers will not change if the same number is added to every number of the set. Assuming that n, k, p = 1, 2, 3 respectively
$$SD=\sqrt{\frac{\left(1-2\right)^2+\left(2-2\right)^2+\left(3-2\right)^2}{3}}=\sqrt{\frac{1+0+1}{3}}=\sqrt{\frac{2}{3}}$$
$$for\ n+1,\ k+1,\ and\ p+1\ =>\ 2,\ 3,\ 4$$
$$SD=\sqrt{\frac{\left(2-3\right)^2+\left(3-3\right)^2+\left(4-3\right)^2}{3}}=\sqrt{\frac{1+0+1}{3}}=\sqrt{\frac{2}{3}}$$
So the standard deviation d for n, p, and k remains unchanged for n+1, p+1, and k+1

$$Answer\ =\ E$$
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