The Law of Large Numbers states that larger samples provide better estimates of a population's parameters than do smaller samples. As the size of a sample increases, the sample statistics approach the value of the population parameters. In its simplest form, the Law of Large Numbers is sometimes stated as the idea that bigger samples are better. After a brief discussion of the history of the Law of Large Numbers, the entry discusses related concepts and provides a demonstration and the mathematical formula.


Jakob Bernoulli first proposed the Law of Large Numbers in 1713 as his “Golden Theorem.” Since that time, numerous other mathematicians (including Siméon-Denis Poisson who first coined the term Law of Large Numbers in 1837) have proven the theorem and considered its ...

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