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No. 229 · Evidence · Statistics and Probability

Central Limit Theorem

Average enough random pieces and the averages settle into a predictable bell shape.

The Central Limit Theorem says that if you take many random samples and average each one, the averages form a bell curve as samples grow, whatever the shape of the original data. That's why averages from good samples can estimate large populations.

To use it, judge people and investments over many results, not one, track health trends with averages, and distrust conclusions built on tiny samples.

In the Almanac

“Galton’s board”, 1889 · “YouGov”, 2017

Both stories in full, three ways to use it and where it misleads.

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Central Limit Theorem

Questions

What is Central Limit Theorem?

The Central Limit Theorem says that if you take many random samples and average each one, the averages form a bell curve as samples grow, whatever the shape of the original data. That's why averages from good samples can estimate large populations.

How do you use Central Limit Theorem?

To use it, judge people and investments over many results, not one, track health trends with averages, and distrust conclusions built on tiny samples.

When does Central Limit Theorem matter?

Central Limit Theorem is one of the 68 mental models for evidence, the situations where you ask: Is this really true? Within that, it belongs to “Reading the numbers”, alongside Base Rate Fallacy, Bayes’ Theorem and Conditional Probability.

What is an example of Central Limit Theorem?

Two stories show it at work: Galton’s board (1889) and YouGov (2017). Both are told in full in The Mental Models Daily Almanac, which has two stories for each of its 365 models.

Which mental models are related to Central Limit Theorem?

Law of Large Numbers, Fat-Tailed Distributions and Overgeneralising from Small Samples. Central Limit Theorem itself comes from statistics and probability.