Why Most People Get Descriptive Statistics Wrong (And How to Fix It)

I review pull requests that include statistical summaries at least a few times a month. The most common mistake is not a wrong formula. It is using the wrong formula in the right place. Specifically, confusing population standard deviation with sample standard deviation. If that distinction sounds trivial, it is not. It changes your results, and the downstream decisions built on those results, in ways that compound as your data grows. The core measures and when they mislead Descriptive statistics boil down to a few categories: central tendency (mean, median, mode), spread (range, variance, standard deviation), and distribution shape (skewness, kurtosis). Most people can calculate a mean. The problems start with spread. Mean vs. median. The mean of [1, 2, 3, 4, 100] is 22. The median is 3. If you are summarizing user response times and one outlier spiked to 100 seconds because of a cold cache, the mean tells a story that does not match reality. Median is robust to outliers. Mean is not.