Question

given a variable with 10 scores: 3, 7, 9, 10, 12, 14, 17, 18, 20, 20, what is the denominator when calculating the variance and standard deviation?
○ 8
○ 9
○ 10
○ 11

Explanation:

Step1: Recall Variance/SD Formula

For a population (all scores given, no sampling), variance \( \sigma^2 = \frac{\sum (x_i - \mu)^2}{N} \), where \( N \) is the number of scores.

Step2: Identify \( N \)

The data has 10 scores (3, 7, 9, 10, 12, 14, 17, 18, 20, 20), so \( N = 10 \). The denominator for population variance/SD is \( N = 10 \).

Answer:

C. 10 (assuming options are labeled as A.8, B.9, C.10, D.11; if original options have 10 as the third, e.g., "10" option, the answer is the option with 10, like "10" or the corresponding identifier.)