# Why is an “unbiased estimator” called as such?

Why is an “unbiased estimator” called as such?
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The bias of an estimator $\stackrel{^}{\theta }$ for a parameter $\theta$ is defined as
$\mathrm{B}\mathrm{i}\mathrm{a}\mathrm{s}\left(\stackrel{^}{\theta }\right)=\mathbb{E}\left(\stackrel{^}{\theta }\right)-\theta .$
Thus "unbiased" is exactly the same as having $\mathrm{B}\mathrm{i}\mathrm{a}\mathrm{s}\left(\stackrel{^}{\theta }\right)=0.$.
For an intuitive explanation, suppose we have a population of people living in a small village who have heights $65",65",67",68",78",$, but the person who is $78"$ tall is a hermit who doesn't like being sampled. If we construct an estimate for the population mean by sampling two people who are not hermits, call this $\stackrel{^}{\mu },$, we would get
$E\left(\stackrel{^}{\mu }\right)=\frac{65"+66"+66"+66.5"+66.5"+67.5"}{\left(\genfrac{}{}{0}{}{4}{2}\right)}=\frac{397.5"}{6}=66.25",$
while $\mu =68.6".$". Thus, this estimator has a bias of $66.25"-68.6"=-2.35".$. But we should expect that this estimator would be biased, since it isn't taking a representative sample of the population, so this agrees with intuition.