Explain Confidence Intervals

**How would you explain a confidence interval to a non-technical audience?**

This is the same question as problem #2 in the Statistics Chapter of Ace the Data Science Interview!

Suppose we want to estimate some parameters of a population. For example, we might want to estimate the average height of males in the U.S. Given some data from a sample, we can compute a sample mean for what we think the value is, as well as a range of values around that mean. Following the previous example, we could obtain the heights of 1,000 random males in the U.S. and compute the average height, or the sample mean. This sample mean is a type of point estimate and, while useful, will vary from sample to sample. Thus, we can’t tell anything about the variation in the data around this estimate, which is why we need a range of values through a confidence interval.

Confidence intervals are a range of values with a lower and an upper bound such that if you were to sample the parameter of interest a large number of times, the 95% confidence interval would contain the true value of this parameter 95% of the time. We can construct a confidence interval using the sample standard deviation and sample mean. The level of confidence is determined by a margin of error that is set beforehand. The narrower the confidence interval, the more precise the estimate, since there is less uncertainty associated with the point estimate of the mean.