A sample of 20 observations has a standard deviation of 4. The sum of the squared deviations from the sample mean is:
A) 400
B) 320
C) 304
D) 288
E) 180

Question

Quizplus · Accepted Answer

The sum of the squared deviations from the sample mean is equal to (n-1) times the sample variance. Since we only have the standard deviation given, we need to use the formula:

sample variance = (standard deviation)^2

sample variance = 4^2 = 16

Then, the sum of the squared deviations from the sample mean is:

(n-1) * sample variance = 19 * 16 = 304

Therefore, the answer is C.

A Sample of 20 Observations Has a Standard Deviation of 4