Build a Bell Curve
Watch the Central Limit Theorem in action — sample from any distribution, then see the histogram of averages converge to a perfect bell curve as trials accumulate.
Frequently Asked Questions
What is the Central Limit Theorem?
The Central Limit Theorem states that the distribution of sample means approaches a normal (bell-shaped) distribution as the sample size increases, regardless of the shape of the original population distribution. This is why normal distributions appear so often in nature and statistics.
Why does the histogram become bell-shaped?
When you average multiple random values, extreme values cancel out. A very high value in one draw tends to be offset by a lower value in another. The more values you average together, the more this cancellation smooths the distribution into a symmetric bell shape.
What happens with a sample size of 1?
With a sample size of 1, each "sample mean" is just a single random draw. The histogram of these values matches the original source distribution exactly — there is no averaging to create a bell shape.
How is the normal curve overlay calculated?
The red dashed curve is the theoretical normal distribution predicted by the CLT. Its mean equals the source distribution mean (μ), and its standard deviation equals σ/√n (the standard error). It is scaled so that the area under the curve matches the total number of trials.
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