# 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?

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 $24 \cdot 16 = 384$