Confidence Interval

When we estimate something from a sample, such as the average spending of all customers based on a survey of a few hundred, the estimate will not be exactly right. A confidence interval shows how precise the estimate is.

For example, a survey might find that customers spend an average of 50 per visit, with a 95% confidence interval of about 46 to 54. This means that if the survey were repeated many times and an interval calculated each time in the same way, about 95% of those intervals would contain the true average.

The width of the interval depends on the amount of variation in the data and the sample size. Larger samples and less variable data give narrower, more precise intervals. A higher confidence level, such as 99% instead of 95%, gives a wider interval.

Confidence intervals are often more informative than a single estimate or a simple test of significance, because they show both the estimate and its uncertainty. In finance, they are used in surveys, risk models, forecasts and research. They depend on assumptions about the data and sampling method, and they do not account for biases in how the sample was collected.