Need Help in Statistics Question

[puneetkhurana2000]

This is from 800score.com

Question: J is a collection of 4 odd integers whose range is 4. The standard deviation of J must be one of how many numbers?

A) 3
B) 4
C) 5
D) 6
E) 7

I don't even understand what we need to calculate.

Thanks

[The Iceman]

I don't even understand what we need to calculate.

Thanks

You need to find all the possible distinct standard deviations possible.

Since the range is 4, let's take a set whose extreme numbers are 1 and 5.

The following are all the set possibilities:

1,1,1,5
1,1,3,5
1,1,5,5
1,3,3,5
1,3,5,5
1,5,5,5

Now in order to check the distinctness of SDs we can just check the sum of the squared values of (xi - mean of that set), which can be same if we have similar lists of modulus values of xi - mean. In other words we need to compare how far from the mean are these numbers populated in each set.

Among the six sets, there are two pairs of sets that have same SDs respectively. Hence, number of distinct SDs = 6-2 = 4

B wins