Central Limit Theorem

The Central Limit Theorem (CLT) states that if you take enough random samples from any dataset, even if the data is skewed or messy, the average of those samples will start to form a bell-shaped or normal distribution. This only holds if the samples are random, independent, and large enough, usually 30 or more.

Why does this matter? Because once those averages form a normal shape, you can use all the tools from the normal distribution. You can calculate standard errors, build confidence intervals, run hypothesis tests, make estimates, and use z-scores, even if the original data wasn’t normal to begin with.