convergence
central limit theorem in action
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.
live simulation
source distribution
sample means · n = 1
mean of means
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std of means
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theoretical std
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samples
0