The Central Limit Theorem in Action
DS 1000B — Chapter 15
Context:
None of these populations are Normal. As you increase the sample size \(n\), watch how the sampling distribution of \(\bar{X}_n\) evolves.
Does it matter what the population looks like?
Uniform — Bus Wait Times
Bimodal — Commute Times
Right-Skewed — Income
U-Shaped — Engagement
Population Distribution
Sampling Distribution of \(\bar{X}_n\)
Sample size (\(n\)):
2
10
30
50
100
Population Mean (\(\mu\))
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Population SD (\(\sigma\))
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Standard Error
—
\(\text{SE} = \sigma \,/\, \sqrt{n}\)
Mean of \(\bar{X}_n\)
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