Central Limit Theorem Demonstrator
Watch one of statistics' most surprising results happen live: average enough random samples from almost any distribution, and the result approaches a normal bell curve.
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How the Central Limit Theorem Demonstrator works
The Central Limit Theorem is one of the most important results in statistics: no matter how skewed or unusual the original distribution is, the distribution of sample means — averages of repeated random samples — tends toward a normal bell curve as the sample size grows, provided the samples are independent and identically distributed.
To make the effect visible, this demo intentionally draws from a skewed source distribution (squared uniform values, which pile up heavily near zero) rather than an already-normal one — increase the sample size (n) and watch the resulting histogram of sample means smooth into a recognisable bell shape even though no individual draw looks bell-shaped at all.
How to use it
Frequently asked questions
Why use a squared uniform distribution instead of something simpler?
A skewed source distribution makes the Central Limit Theorem's effect more visually striking — averaging enough samples pulls even a heavily skewed source toward a symmetric bell shape.
What sample size shows the effect best?
Try n=1 first to see the raw skewed shape, then increase to n=10, 30, and 50 to watch the histogram of means progressively smooth into a bell curve.
Why does this theorem matter practically?
It's the mathematical foundation behind why so many statistical methods — confidence intervals, hypothesis tests, quality control charts — can safely assume normality for sample means, even when the underlying data isn't normal.