Unbiased and Biased Estimators

A statistic is called an unbiased estimator of a population parameter if the mean of the sampling distribution of the statistic is equal to the value of the parameter. For example, the sample mean, , is an unbiased estimator of the population mean, . In symbols, . On the other hand, since , the sample standard deviation, , gives a biased estimate of .

For a small population of positive integers, this Demonstration illustrates unbiased versus biased estimators by displaying all possible samples of a given size, the corresponding sample statistics, the mean of the sampling distribution, and the value of the parameter. Note: for the sample proportion, it is the proportion of the population that is even that is considered.