convergence

The Central Limit Theorem: the mean of n independent samples approaches a normal distribution as n grows — regardless of the source distribution's shape.

σ_means = σ_source / √n

This is why confidence intervals and hypothesis tests work. The spread of sample means shrinks predictably as 1/√n, making estimation more precise with larger samples.

references

Fischer. "A History of the Central Limit Theorem." Springer, 2011.

Le Cam. "The Central Limit Theorem around 1935." Statistical Science, 1986.