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Section 2 · Lecture 10 · Sampling Distribution

The Central Limit Theorem

Take many samples of size n from a population and work out the sample mean ȳ of each one. Whatever shape the population has, once n is large the distribution of Ȳ is approximately Normal, Ȳ ≈ N(μ, σ²/n).

Population shape

Sample size, n

Take samples

The population, Y

The latest sample

The sampling distribution of Ȳ

histogram of all the sample means ȳ N(μ, σ²/n), as the CLT predicts population mean μ

Samples drawn

0

Average of the ȳ values

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SD of the ȳ values

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Working it out