Question

A sample of 25 observations has a standard deviation of 4. The sum of the squared deviations from the sample mean is 384. Why is it 384?

Answer 1

The definition of sample variance

`S² = [1/(n-1)]* Σ[(x_i) - xbar]²`

`(n-1) S² = Σ[(x_i) - xbar]²`

The sum on the right is the sum of the squared deviations from the sample mean `xbar`.

`S = 4`, so `S² = 16` where `n = 25`, so `n-1 = 24`

Therefore, the sum is `24*16 = 384`