The Law of Large Numbers
See sample averages march toward the true mean as the trial count grows. A live animation that makes the Law of Large Numbers click — no formulas required.
I.02 / LAW OF LARGE NUMBERS
Law of Large Numbers
CLT showed that averages become normal. But does the sample mean actually converge to the true mean as n grows? That guarantee is the Law of Large Numbers. CLT describes the shape; LLN says the center won't run away.
10 heads in a row at the start of a coin-flip? Not that weird.
But flip it 10,000 times and the head-ratio locks onto almost exactly 0.5.
That's the Law of Large Numbers — the more samples you draw, the more observed values get pulled toward the truth.
This is why statistics counts as evidence, not a vague hunch.
Trials0
Current mean—
Theoretical0.50