central limit theorem

American  

noun

Statistics.

1. any of several theorems stating that the sum of a number of random variables obeying certain conditions will assume a normal distribution as the number of variables becomes large.

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central limit theorem British  

noun

1. statistics the fundamental result that the sum (or mean) of independent identically distributed random variables with finite variance approaches a normally distributed random variable as their number increases, whence in particular if enough samples are repeatedly drawn from any population, the sum of the sample values can be thought of, approximately, as an outcome from a normally distributed random variable

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Etymology

Origin of central limit theorem

First recorded in 1950–55

Example Sentences

According to the central limit theorem, the larger the sample, the closer the sampling distribution of the means becomes normal.

From Textbooks • Mar. 27, 2020

It would be difficult to overstate the importance of the central limit theorem in statistical theory.

From Textbooks • Sep. 19, 2013

This sample size is large enough to allow use of the central limit theorem, so he says the standard deviation of the sampling distribution of sample means will also be 16.

From Textbooks • Sep. 19, 2013

Applying the central limit theorem, what is the distribution of these sample sums?

From Textbooks • Sep. 19, 2013

The central limit theorem states that under a wide variety of circumstances this will always be the case—averages and sums of nonnormally distributed quantities will nevertheless themselves have a normal distribution.

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