See that no matter how skewed the underlying population is, the distribution of sample means becomes more bell-shaped and less spread out as sample size grows (the Central Limit Theorem), with spread shrinking as σ/√n.
Population Mean
4.00Mean of Sample Means
4.11Empirical SE
1.904Theoretical SE = σ/√n
1.789Standard error: SE = σ / √nSample mean: x̄ = (1/n)·ΣxᵢAs n grows, the distribution of x̄ approaches a normal shape regardless of the population's shape.Select the Skewed population and set sample size to 2. Draw samples and notice the histogram of sample means is still lopsided, not bell-shaped.
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