A sample of 20 observations has a standard deviation of 4. the sum of the squared deviations from the sample mean is:

If I understood your problem, you want to calculate the sum of the squared deviations from the sample. If so the formula of the St. Deviation is:

₋

s = √[Σ (xi - x) ² / (n-1) ], with n = sample size

₋

s² = Σ (xi - x) ² / (n-1)

4² = Σ (xi - x) ² / (20-1) = Σ (xi - x) ² / (20-1)

16 = Σ (xi - x) ² / (19)

and Σ (xi - x) ² = (16). (19) = 304