A researcher records a sample of 30 exam scores and finds that the population variance for these data is larger than the sample variance.Is this possible?
A) Yes, the population variance is usually larger than the sample variance.
B) No, the population variance will only be larger when at least 50 scores are recorded.
C) No, the sample variance will be larger because SS is divided by degrees of freedom in the denominator of the variance formula.
D) Not possible to know because the scores are not given.

Question

Quizplus · Accepted Answer

The sample variance is typically larger than the population variance because, in its calculation, the sum of squared deviations (SS) is divided by the degrees of freedom (n-1 for a sample) rather than by the total number of observations (n for a population). This adjustment accounts for the fact that the sample is an estimate of the population, leading to a slightly inflated variance to compensate for the estimation error.

A Researcher Records a Sample of 30 Exam Scores and Finds