🟢 Stats: Central Limit Theorem — The Foundation of Everything

What it says: Take many random samples of size n from ANY distribution. The distribution of sample means will be approximately normal, with: - Mean = population mean - Standard deviation = σ/√n (called standard error)

Why it matters: This is why normal distribution-based tests (z-test, t-test, confidence intervals) work even when the underlying data isn't normal. As long as n ≥ ~30, CLT kicks in.

The √n factor: Larger samples → smaller standard error → narrower CI → more precise. But it's √n, not n. Quadrupling sample size only halves uncertainty.