VIII · Statistics & inference

Central Limit Theorem

What it is

The sum of many independent random variables, regardless of their distribution, approaches a normal distribution. Convergence is O(1/√n).

Where it lives

Why averages "look normal" even when individual measurements aren't. The basis of A/B testing, confidence intervals, load-test analysis.

The key insight

Heavy-tailed distributions (Pareto, log-normal) approach normality slowly. Use medians or trimmed means for log-normal data; the CLT lies for small n.