Note that mean of all the sets are 3.
Now, standard deviation is nothing but the average measure of how far away are the elements from the mean.

Now, elements of option A are uniformly distributed.
Elements of options E and D are more away from 3 than the elements of A, so their standard deviation must be greater than A.
Similarly elements of options B and C are closer to 3 than the elements of A, so their standard deviation must be less than A.

So, option A must have the third highest standard deviation.

Answer : A

Here is solution with standard deviation calculation.

A. {1, 2, 3, 4, 5} # mean = 3 # stdev = √[(2² + 1² + 0² + 1² + 2²)/5] = √2
B. {2, 3, 3, 3, 4} # mean = 3 # stdev = √[(1² + 0² + 0² + 0² + 1²)/5] = √(2/5) = √(0.4)
C. {2, 2, 2, 4, 5} # mean = 3 # stdev = √[(1² + 1² + 1² + 1² + 2²)/5] = √(8/5) = √(1.6)
D. {0, 2, 3, 4, 6} # mean = 3 # stdev = √[(3² + 1² + 0² + 1² + 3²)/5] = √4
E. {-1, 1, 3, 5, 7} # mean = 3 # stdev = √[(4² + 2² + 0² + 2² + 4²)/5] = √10

Brent@GMATPrepNow wrote:

vipulgoyal wrote: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}

My take E, experts please suggest without calculating SD

So far, all of the official GMAT questions involving SD (comparing the SD's of several lists of numbers) that I've seen can be answered by "eyeballing" the values and comparing how spread apart they are.

So, for example, the values in E are spread apart the most, so E has the greatest SD.
The values in D are spread apart the second most, so D has the second greatest SD.

Now let's look at the values are packed together the most.
The values in B are the most tightly packed, so B has the smallest SD
The values in C are next most tightly packed, so C has the second smallest SD

So, the SDs from least to greatest are: B, C, A, D, E

So A has the third largest standard deviation..

Cheers,
Brent

Thanks Brent for the solution

One query though

Can we say the smaller the range the smaller the SD for the set( provided the comparison is made with sets containing equal number of elements)? I know on actual GMAT we wont be calculating the SD for Each set. But i have tried so many problems using the above (so called) rule.And my guess was correct each time.