Unbiased Estimator vs Point Estimate

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.

A point estimate is your one-number summary of a parameter before you attach any margin of uncertainty. Common ones are the sample mean $\bar{x}$ (read x-bar) for the population mean $\mu$ (the Greek letter mu), and the sample proportion $\hat{p}$ (read p-hat) for the population proportion $p$. For example, if 63 of 200 sampled voters approve, the point estimate of the population approval rate is $\hat{p} = 63/200 = 0.315$. A point estimate alone hides sampling variability, so it is usually paired with a margin of error to form a confidence interval.