Statistics
Central Limit Theorem
Take a wildly non-Gaussian distribution, draw n samples, average them, and record the mean. Repeat. No matter the source, the distribution of those means tends to a bell curve, and it tightens as n grows.
Means collected0
Std of mean—
Faint bars at the top are the source distribution. The big histogram is the distribution of sample means, with the predicted Gaussian overlaid. Set n = 1 to see the raw source, then raise n and watch it turn into a bell.
What to observe
- Set n = 1: the big histogram is just the raw source, so Exponential and Bimodal look nothing like a bell.
- Raise n to 5, then 30. However skewed the source, the means pile into thesame Gaussian shape. That universality is the theorem.
- Watch the Std of mean readout as n grows: it shrinks like1/√n, so the bell gets narrower but four times the samples only halves the width.
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