Question

A sample of n=4 scores has SS=108
-Compute the variance for this sample

Answer 1

The sample variance (S^2) of a set with n=4 and a sum of squares (SS) of 108 is 36, by dividing SS by the degrees of freedom which is n - 1.

Step-by-step explanation:

To compute the variance for the sample with n=4 scores and a given sum of squares (SS) of 108, we apply the formula for sample variance:

S2 = SS / (n - 1)

Substituting the given values, we have:

S2 = 108 / (4 - 1)

S2 = 108 / 3

S2 = 36

So, the sample variance (S2) is 36. This process used the fact that to estimate the population variance more accurately from sample data, we divide by one less than the sample size (n - 1), which gives us what is known as the degrees of freedom (df).