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🔔 The Normal Distribution and the Central Limit Theorem

A live 3D demonstration of the Central Limit Theorem: draw repeated samples from lopsided, skewed or two-humped distributions and watch the histogram of their averages converge on a bell curve.

AI & Machine Learning3DAdvanced60 FPS

Pick a lopsided, exponential or two-humped population, draw repeated samples of size n from it, and watch the 3D histogram of the sample averages sharpen into a bell curve — live, no matter how strange the population looks.

🔬 What It Demonstrates

The teal row is the fixed population you're sampling from; the green row is the sampling distribution of the mean. As n grows, the green histogram narrows toward σ/√n and its shape converges on the theoretical normal curve overlay, regardless of the population's own shape.

🎮 How to Use

Choose a population shape, raise the sample size n, and increase draw speed to accumulate sample means quickly. Compare the live mean and predicted standard deviation against the growing histogram, and reset whenever you change n to see the shape rebuild from scratch.

💡 Did You Know?

The CLT holds for almost any population with finite variance — it's why averages of noisy, skewed real-world measurements so often end up looking like a tidy bell curve.

⚙ Under the hood

A live 3D demonstration of the Central Limit Theorem: draw repeated samples from lopsided, skewed or two-humped distributions and watch the histogram of their averages converge on a bell curve.

machine-learningdata-sciencestatisticsprobabilityalgorithmsdistributionThree.js

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install