Question

If the variance of a data set is correctly computed with the formula using n -1 in the denominator, which of the following is true? A. the data set is a population. B. . the data set is a sample. C. the data set could be either a sample or a population. D. the data set is from a census.

Answer 1

B. . the data set is a sample

Explanation:

Given that the variance of a data set is correctly computed with the formula using n -1 in the denominator

We know by central limit theorem, that for large samples randomly drawn, the mean of the samples follow a normal distribution.

Here variance of the mean would be variance of population divided by degrees of freedom.

when sample size is n, we have degree of freedom n-1.

Hence only for samples of sizes n, where degree of freedom is n-1 we divide variance by n-1.

Answer is

B. . the data set is a sample