Point estimate

A point estimate is the value a statistic takes in the one sample you collected, offered as the estimate of a parameter you cannot observe. Each parameter has a standard partner: $\bar{x}$ (x-bar) estimates $\mu$ (mu), $\hat{p}$ (p-hat) estimates $p$, and $s$ estimates $\sigma$ (sigma). The word point is doing work in that phrase. It signals a single value with no width attached to it.

If 63 of 200 randomly sampled voters approve, the point estimate is $\hat{p} = \frac{63}{200} = 0.315$. That number alone says nothing about how far off it might be. Attach a margin of error and the picture changes: the standard error is $\sqrt{\frac{0.315(0.685)}{200}} = 0.0328$, so with $z^* = 1.96$ the margin is 0.064 and the 95% interval runs from 0.251 to 0.379. An estimate that looked exact carries a span of nearly 13 points around it.

The misreading is a missing word. "Thirty-one and a half percent of voters approve" states a sample statistic as though it were the population parameter. It is one draw from a sampling distribution centered at $p$, and the chance it equals $p$ exactly is essentially zero. Notation carries the distinction, so writing $p$ where you computed $\hat{p}$ claims something you did not compute.

An unbiased point estimate is still allowed to be far off. Unbiasedness is a property of the procedure across all samples, not a promise about this one, so knowing that $\bar{x}$ is unbiased does not license treating $\bar{x}$ as $\mu$. For a difference, the point estimate is the difference of the two point estimates, $\hat{p}_1 - \hat{p}_2$ or $\bar{x}_1 - \bar{x}_2$, and it sits at the center of the matching interval.

Topic 3.1 is Estimators, where point estimates are judged on bias and on variability.