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.