THE KEYSTONE IDEA, MADE VISIBLE

Where the sample mean lives

The single hardest idea in the course: the sampling distribution. The top chart is the whole population of Geneva pizza prices — deliberately not bell-shaped. Each time you draw a sample of size n and compute its mean, that one number drops onto the bottom chart. Draw thousands and watch what the means do.

① The population — all prices (fixed)

Skewed: lots of cheap places, a long tail of pricey ones. This is NOT a bell.

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population mean µ

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population SD σ

Population shape

Sample size n 5

② The sampling distribution of the mean x̄

Same x-axis as the population above — so you can see it concentrate.

samples drawn

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mean of the means

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SD of the means

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σ/√n (theory)

Pick a sample size and start drawing.

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