A comparison of variance estimators with known and unknown population means

Variance is a concept that is key, yet often difficult to estimate in statistics. In this paper, we consider the problem of estimating the population variance when the population mean is known. We compare two estimators, one that incorporates the known population mean and another which estimates the population mean. The standard normal, standard exponential, and t distribution with 3 degrees of freedom are considered, with sample sizes of 5, 20, 50, and 100. It is determined that both estimators are unbiased. For the normal and exponential distributions, both estimators have similar variances; however, the estimator that incorporates the known mean has marginally lower variance, and thus is recommended. For the t(3) distribution, the variances of the estimators do not exist