Unbiased and Biased Estimators
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, =μ. On the other hand, since ≠σ, 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.