The sample variance $s ^ { 2 }$ is an unbiased estimator of the population variance $\sigma ^ { 2 }$ when the denominator of $s ^ { 2 }$ is:
A) n.
B) n - 1.
C) n.
D) n + 1.

Question

The sample variance $s ^ { 2 }$ is an unbiased estimator of the population variance $\sigma ^ { 2 }$ when the denominator of $s ^ { 2 }$ is:
A) n. 
B) n - 1. 
C) n. 
D) n + 1.

Quizplus · Accepted Answer

The denominator of the sample variance formula is n - 1 when using the sample as an estimate of the population. This is because the sample mean is often used in place of the population mean, which reduces the degrees of freedom by 1. Using n as the denominator in the sample variance formula will result in a biased estimate of the population variance. Using F1S1F1F1F10n as the denominator is not a valid option.

The Sample Variance s2s ^ { 2 }s2 Is an Unbiased Estimator of the Population Variance

The Sample Variance $s ^ { 2 }$ Is an Unbiased Estimator of the Population Variance