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Unbiased and Biased Estimators

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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 .

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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.

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Contributed by: Marc Brodie (Wheeling Jesuit University) (March 2011)
Open content licensed under CC BY-NC-SA

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Snapshots 4 and 5 illustrate the fact that even if a statistic (in this case the median) is not an unbiased estimator of the parameter, it is possible for the mean of the sampling distribution to equal the value of the parameter for a specific population.

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