Statistical inference · sample means · manipulative

Does (x̄ − μ)/(s/√n) look standard normal?

Top: pick a population shape. Bottom: z-scores of many sample means. Grow n — the mound settles on N(0,1) even when the parent is skewed.

population this sample z of x̄ N(0,1) guide

Population shape

Population

Standardised means z = (x̄ − μ)/(s/√n)

Draw samples — each contributes one z below

Draw samples

5
20
3×

Changing n recomputes every stored sample’s z from its raw draws. Play draws one sample at a time so you can watch the z histogram grow.

Working

samples
0
mean of z
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