QM110 / QM210

Central Limit Theorem Simulator

Explore one of the most powerful ideas in statistics. Watch how the distribution of sample means transforms as you change the sample size — regardless of the population shape. Then test your understanding with a short quiz.

1. Choose a Population Distribution

2. Set Sample Size

Sample size (n): 2

Population Distribution

Sampling Distribution of x̄

Statistics

Population Mean (μ)

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Population SD (σ)

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Theoretical SE (σ/√n)

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Observed SE

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At n ≥ 30, the sampling distribution is approximately normal — regardless of the population shape.

Try These Experiments

Try a bimodal population with n = 2. Then increase to n = 30. What happens to the shape?

Does the center of the sampling distribution change as n increases?

What happens to the spread (SE) as n doubles?

Ready to Test?

5 questions · 20 points each · 100 points total

Question 1 / 5 Score: 0 / 100