Central Limit Theorem Demo
The central limit theorem says the average of enough independent samples is approximately normal, no matter how weird the population you draw from. This demo lets you pick a population shape — uniform, strongly skewed, bimodal or a single die — then repeatedly draws samples of size n and stacks their means into a histogram. The sampling distribution of the mean tightens and turns bell-shaped as n grows, and a normal curve with the predicted mean and standard error is overlaid so you can watch the theorem hold.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- The sample means centre on the population mean μ with standard error σ/√n, so they cluster tighter as n grows.
- The population can be any shape — skewed or bimodal — yet the distribution of its sample means still approaches a normal curve.
- Bigger samples converge faster; heavily skewed populations need a larger n before the bell shape appears.
- Runs 100% in your browser — simulations are computed locally on your device.
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