law of large numbers

American  

noun

Mathematics.

1. the theorem in probability theory that the number of successes increases as the number of experiments increases and approximates the probability times the number of experiments for a large number of experiments.

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law of large numbers British  

noun

1. the fundamental statistical result that the average of a sequence of n identically distributed independent random variables tends to their common mean as n tends to infinity, whence the frequency of the occurrence of an event in n independent repetitions of an experiment tends to its probability

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law of large numbers Scientific  

1. The rule or theorem that the average of a large number of independent measurements of a random quantity tends toward the theoretical average of that quantity.

2. Also called Bernoulli's law

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Etymology

Origin of law of large numbers

First recorded in 1935–40

Example Sentences

The law of large numbers hasn’t seemed to catch up to Nvidia yet.

From The Wall Street Journal • Nov. 20, 2025

In part due to the law of large numbers, Sirius is experiencing much lower growth rates in recent years and that trend is likely to continue.

From Forbes • Jan. 6, 2014

Applying the law of large numbers, which sample mean would expect to be closer to the population mean, a sample of size ten or a sample of size 100?

From Textbooks • Sep. 19, 2013

In buying Apple shares last year, when the stock was heading for seven hundred dollars, investors were willfully ignoring the law of large numbers and the laws of supply and demand.

From The Guardian • Mar. 4, 2013

The first is the law of large numbers, one of the most significant though often misunderstood theorems in probability theory, and one which people sometimes invoke to justify all sorts of bizarre conclusions.

From "Innumeracy: Mathematical Illiteracy and Its Consequences" by John Allen Paulos