The most important theorem in statistics, made visible. No matter how weird the source distribution, the average of enough samples is always bell-shaped.
Central Limit TheoremLive
means go normal
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The central limit theorem is why the normal distribution is everywhere: no matter how skewed or lumpy the source distribution, the distribution of sample means becomes bell-shaped as the sample size grows. Try a heavily skewed exponential at n=1, then raise n and watch it turn normal.
Reading this result: At n=10 the sample means are already piling into a bell even though the exponential source is not normal — the central limit theorem kicking in.
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How it works
The central limit theorem says the distribution of sample means approaches a normal distribution as the sample size grows, regardless of the underlying distribution. Start with a skewed exponential or a lumpy bimodal source, then raise the sample size and watch the histogram of means converge to the familiar bell curve.
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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Is this central limit theorem simulator tool really free?▾
Yes. Central Limit Theorem runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
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How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.