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Before explaining what an unbiased estimator is, let us explain what an estimator is.
An estimator is a value or range of values used to estimate or approximate a population parameter.
For example, we call the sample mean, x̄ , an estimator of the population mean or μ.
It turns out that the sample mean or x̄ is the best way to estimate the population mean unlike the sample median, sample midrange, or sample mode.
Why is this the case? It is because the sample mean will have a smaller standard deviation than the other sample statistics such as the median or the mode.
For this reason, we call the sample mean or x̄ an unbiased estimator because of its tendency to center about the value of the population.
Generally speaking whenever the mean of a sample statistic is equal to the value of the corresponding population parameter, we call that sample statistic an unbiased estimator.