Unbiased estimator

An estimator is unbiased when its sampling distribution is centered on the parameter it estimates, though any single estimate still varies around that center. For example, the sample mean is unbiased for the population mean because $E(\bar{x}) = \mu$ (the expected value of x-bar equals mu). Likewise the sample proportion is unbiased for the population proportion, since $E(\hat{p}) = p$ (the expected value of p-hat equals p). Bias concerns where the sampling distribution is centered, not how spread out it is.