A sample of $n=4$ scores has ${\mathrm{SS}}_S=60$. What is the variance for this sample?

• A. $\frac{60}{1}=60$
• B. $\frac{60}{2}=30$
• C. $\frac{60}{4-1}=\frac{60}{3}=20$
• D. $\frac{60}{4}=15$

Answer: (C)

Verified step by step guidance

1. Identify the sample size, which is given as \(n = 4\), and the sum of squares, \(SS = 60\). The sum of squares is the total of squared deviations from the sample mean.
2. Recall the formula for the sample variance, which is \(s^2 = \frac{SS}{n - 1}\). This formula uses \(n - 1\) in the denominator because it is an unbiased estimator of the population variance when using sample data.
3. Substitute the known values into the formula: \(s^2 = \frac{60}{4 - 1}\).
4. Simplify the denominator: \$4 - 1 = 3\(, so the variance formula becomes \)s^2 = \frac{60}{3}$.
5. Interpret the result as the sample variance, which measures the average squared deviation of the scores from their mean, adjusted for the sample size.