Shape of the distribution of the sample mean

Sample size · n = 1
 
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Original distribution

Distribution of one observation, X

PMF / PDFMean μ

Sample mean

Distribution of the sample mean, X̄ₙ

Simulated sample meansMean μ

Centered and scaled sample mean

Distribution of the standardized sample mean, Zₙ = √n (X̄ₙ − μ) / σ

Simulated Zₙ