Why is it common to refer to variance estimates derived from a sample as sample variance?

Why is it common to refer to variance estimates derived from a sample as sample variance?

• A. Because most reported values are based on a sample
• B. Because population variance is never used
• C. Because sample variance uses the population mean
• D. Because they are identical

Answer: (A)

The main idea is that variance is a property of the whole population, but in practice we almost never know the entire population and rely on a sample to estimate it. When you compute a measure of spread from that sample, you’re producing a number that serves as an estimate of the true population variance. That’s why we call it the sample variance: it’s derived from the sample data and used to estimate the population variance. Since most reported variances come from samples, this naming convention is standard. It isn’t exactly the true population variance because different samples yield different estimates (sampling variability). While the calculation uses the sample mean rather than the unknown population mean, that aspect is about estimation, not the reason for the terminology. The idea that they are identical is not correct.

The main idea is that variance is a property of the whole population, but in practice we almost never know the entire population and rely on a sample to estimate it. When you compute a measure of spread from that sample, you’re producing a number that serves as an estimate of the true population variance. That’s why we call it the sample variance: it’s derived from the sample data and used to estimate the population variance. Since most reported variances come from samples, this naming convention is standard. It isn’t exactly the true population variance because different samples yield different estimates (sampling variability). While the calculation uses the sample mean rather than the unknown population mean, that aspect is about estimation, not the reason for the terminology. The idea that they are identical is not correct.