What does a confidence interval represent?

A confidence interval represents a range of values within which we can expect a population parameter, such as a mean or proportion, to fall, with a specified level of probability. This concept is fundamental in statistics, as it provides a measure of uncertainty around an estimate derived from a sample. For instance, if we calculate a 95% confidence interval for a mean, it implies that if we were to take many samples and calculate a confidence interval for each, approximately 95% of those intervals would contain the true population mean.

This range is determined by the sample data and reflects the variability introduced by only observing a portion of the population. It acknowledges that while we can make estimates based on sampled data, there is always a degree of uncertainty associated with those estimates. By specifying a confidence level—often 90%, 95%, or 99%—we can communicate how confident we are that the true value lies within the computed range.

In contrast, defining a confidence interval does not correspond to a definitive number or an average of data points, nor is it concerned with the collection of data. Rather, it focuses on the interpretation of sample data and the inference of population parameters based on probability.