Let the smallest integer be 1.
So, the following sets are possible along with their mean and distance from each integer from the mean...

• {1, 1, 3, 5} # mean = 2.5 # distances of integers from mean {1.5, 1.5, 0.5, 2.5}
  {1, 3, 3, 5} # mean = 3.0 # distances of integers from mean {2.0, 0.0, 0.0, 2.0}
  {1, 3, 5, 5} # mean = 3.5 # distances of integers from mean {2.5, 0.5, 1.5, 1.5}
  {1, 1, 5, 5} # mean = 3.0 # distances of integers from mean {2.0, 2.0, 2.0, 2.0}
  {1, 1, 1, 5} # mean = 2.0 # distances of integers from mean {1.0, 1.0, 1.0, 3.0}
  {1, 5, 5, 5} # mean = 4.0 # distances of integers from mean {3.0, 1.0, 1.0, 1.0}

As we can see there are two identical pairs of distances of the integers from the mean.
So, unique possible number of standard deviations are 4

Answer : B

shoudnt we consider nagetive options like (-1 -1 3 3)

vipulgoyal wrote:shoudnt we consider nagetive options like (-1 -1 3 3)

Yes, we should.
But for that particular example you chose, the answer will be different.
As possible sets are {-1, 3, 3, 3}, {-1, -1, 3, 3}, and {-1, -1, -1, 3}
So, possible number of standard deviations cannot be more than 3.

But if all the elements are positive/negative, the answer will be 4.

So, I think the problem should mention that all elements are either positive or negative, as for elements with mixed signs, the answer will be different.