What does a confidence interval represent in statistics?

A confidence interval represents a range of values, derived from a sample of data, that is likely to contain the true population parameter. It indicates the degree of uncertainty or certainty in the estimation of that parameter. The broader the confidence interval, the less precise the estimate, while a narrower interval indicates a more precise estimate. Typically, confidence intervals are constructed around a sample statistic, such as a mean, and are often associated with a specified level of confidence, such as 95% or 99%. This means that if we were to take many samples and construct a confidence interval from each one, we expect that a certain percentage of those intervals would contain the true parameter value.

In contrast, the other options refer to different statistical concepts: the average of a sample denotes the central value of data, the variability of the sample mean describes how much the sample means differ from one another, and the significance level pertains to hypothesis testing and indicates the probability of rejecting the null hypothesis when it is actually true. Each of these concepts serves a different purpose in statistical analysis and does not encapsulate the definition of a confidence interval.