Problem Solving

Ian Stewart Vol 2 Q195

The arithmetic mean of set S is zero. If T = {2:22, 1:96, 1:68, 1:62, 1:94, 2:16}
is the subset of S consisting of all those elements in S which are more than two but less than three standard deviations away from the arithmetic mean of S, what could
be equal to the standard deviation of S?
A) 0.54
B) 0.77
C) 0.82
D) 0.97
E) 1.62

I am unable to solve this. Please help

This actually seems fine, assuming that T = {2.22, 1.96, 1.68, 1.62, 1.94, 2.16}, and is clearly within the scope of the GMAT.

Let's call d the standard deviation. We know the mean is zero, so using the least and greatest values in the set, we have

0 + 2d < 1.62 < 0 + 3d

and

0 + 2d < 2.22 < 0 + 3d

The first equation tells us that d < .81 < (3/2)d, so the standard deviation must be less than .81: eliminate C, D, and E.

The second equation tells us that (2/3)d < .74 < d, so the standard deviation must be greater than .54: eliminate A.

We're left with B, so that's the choice!

By the way, just Googled to find the text of the problem, and it seems like T was meant to be in ascending order: {-2.22, -1.96, -1.68, 1.62, 1.94, 2.16}. Happily enough, though the answer doesn't change, since the sign on the standard deviation doesn't matter.

Be careful to post the text properly in the future, though: it makes a huge difference.

See here for another good standard deviation question: https://www.beatthegmat.com/gmat-prep-qu ... 77848.html