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Distribution of Sample Means, the Central Limit Theorem If we take a new sample, the sample mean varies. Thus the sample mean has a distribution, called the sampling distribution. Central Limit Theorem says that as sample size, n, gets larger, the distribution of sample means is approximately –Normal, and has –Same mean as original distribution; that is, Mean = –Standard deviation = original standard deviation over square root sample size; that is, Standard Deviation =

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Normal with varied µ and σ = 1

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Normal with varied σ and µ = 0

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Standard Normal with µ = 0 and σ = 1 Symmetric: Mean = 0 Stretches from about -3 to 3

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