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by vipulgoyal » Tue May 21, 2013 9:53 pm
E is a collection of four odd integers and the greatest difference between any two integers in E is 4. The standard deviation of E must be one of how many numbers?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

My take 5
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by Atekihcan » Tue May 21, 2013 10:38 pm
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
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by vipulgoyal » Wed May 22, 2013 12:11 am
shoudnt we consider nagetive options like (-1 -1 3 3)
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by Atekihcan » Wed May 22, 2013 12:20 am
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.
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