What is a confidence interval in statistics?

A confidence interval is a statistical tool that provides a range of values, derived from sample data, within which we can reasonably expect the true population parameter to lie. It is constructed using a specified confidence level, commonly set at 95% or 99%. This means that if we were to take numerous samples and compute a confidence interval from each sample, we would expect the true population parameter to fall within these intervals at the specified confidence level in that proportion of the intervals.

This definition highlights that a confidence interval does more than just provide a single estimate; it also offers a way to quantify the uncertainty associated with that estimate. It acknowledges the variability inherent in sampling and provides a more informative measure than a single point estimate, which lacks any indication of uncertainty or variability.

The other options do not accurately capture the nature of a confidence interval. A single value used to estimate a population parameter represents a point estimate, not a confidence interval, which inherently provides a range. The concept of the range of data points in a sample pertains to data distribution but does not reflect the estimation of population parameters. Similarly, indicating the variability of data points around a central value refers to measures like standard deviation or variance but does not encompass the purpose or structure of a confidence interval.