Point Estimate vs Confidence Interval

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.

A confidence interval gives a range for an unknown population parameter instead of a single guess, acknowledging that samples vary. Its width reflects the uncertainty in the estimate: more data and less spread give a narrower interval. For example, a 95% confidence interval of 52% plus or minus 3% for support runs from 49% to 55%. The general form is $\text{estimate} \pm (\text{critical value}) \times (\text{standard error})$, where the standard error measures the typical size of sampling error.