A population of $n=10$ scores has mean $\mu =21$ and standard deviation $\sigma =3$. What is the population variance?

• A. $10$
• B. $3^2=9$
• C. $21$
• D. $3$

Answer: (B)

Verified step by step guidance

1. Recall the definition of population variance, which is the square of the population standard deviation.
2. Identify the given population standard deviation \( \sigma = 3 \).
3. Use the formula for population variance: \( \sigma^2 = (\text{population standard deviation})^2 \).
4. Substitute the given value into the formula: \( \sigma^2 = 3^2 \).
5. Calculate the square of 3 to find the population variance (do not compute the final value here, just set up the expression).