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MENTAL MODEL · M3933

Central Limit Theorem

Central Limit Theorem
TechnicalHigh supportProbability Theory
Included
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Version 1.0.0 · Updated 2026-07-30

CORE DEFINITION

Regardless of the shape of the original distribution, as long as the sample size is sufficiently large, the distribution of the sample mean will approach a normal distribution. This is the most important theorem in statistics, providing the theoretical foundation for "sampling surveys," "hypothesis testing," and "confidence intervals."

SCAFFOLDING EFFECT

psychology

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Confidence in seeing the big from the small. It explains why we can infer "population" characteristics through "sampling" (such as opinion polls), and why results from "large samples" are more reliable. Understanding this helps correctly interpret "sampling error" and "statistical significance," and avoid being misled by "small sample bias."

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The sum of a large number of independent and identically distributed variables approaches a normal distribution, allowing many practical aggregates to be approximated by the normal distribution and supporting statistical inference.

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Source support: Explicit

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    en.wikipedia.orghttps://en.wikipedia.org/wiki/Central_limit_theoremZH · Explicit
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