Most reported values for distributions that are based on a sample should be referred to as what?

Most reported values for distributions that are based on a sample should be referred to as what?

• A. Sample variance
• B. Population variance
• C. Standard deviation
• D. Range

Answer: (A)

When data come from a sample, the spread you report as a variance is the sample variance. This term signals that the value is derived from a subset of the population, not the entire population. The sample variance, denoted with the n−1 in the denominator, serves as an unbiased estimator of the true population variance, reflecting the idea that you’re estimating a population parameter from limited data. In contrast, population variance describes the true variance of every member of the population and isn’t obtained from a sample. The standard deviation is related but different—it's the square root of the variance—so if the focus is specifically on the variance itself, the correct term is the sample variance. The range measures a different aspect of spread (from min to max) and is not a variance, so it doesn’t fit here.

When data come from a sample, the spread you report as a variance is the sample variance. This term signals that the value is derived from a subset of the population, not the entire population. The sample variance, denoted with the n−1 in the denominator, serves as an unbiased estimator of the true population variance, reflecting the idea that you’re estimating a population parameter from limited data. In contrast, population variance describes the true variance of every member of the population and isn’t obtained from a sample. The standard deviation is related but different—it's the square root of the variance—so if the focus is specifically on the variance itself, the correct term is the sample variance. The range measures a different aspect of spread (from min to max) and is not a variance, so it doesn’t fit here.