Manhattan CAT Question Std Dev

[Jimmy]

Which of the following data sets has the third largest standard deviation?
{1, 2, 3, 4, 5}
{2, 3, 3, 3, 4}
{2, 2, 2, 4, 5}
{0, 2, 3, 4, 6}
{-1, 1, 3, 5, 7}

A section of the explanation goes on to say the following, but shouldn't we take the sq root of that 4 and 2 to really find the std deviation?

The standard deviation hinges on the sum of the squared differences between the values and the mean. These calculations therefore boil down to:

Set A: (1 - 3)^2 + (3 - 3)^2 = 4
Set C: (2 - 3)^2 + (2 - 3)^2 = 2

Since the sum of the squared differences is larger in A, A has the larger standard deviation and is therefore the third largest overall.

The correct answer is A.

[rfernandez]

You are correct; standard deviation is the square root of the variance (sum of the squared differences). However, since this problem is concerned only with the relative sizes of the standard deviations, comparing the variances is sufficient.