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

The sampling distribution for the difference between the means is normal in accordance with the central limit theorem.

From Textbooks • Nov. 29, 2017

From the central limit theorem, we know that as n gets larger and larger, the sample means follow a normal distribution.

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

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

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