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

See Examples For:

central limit theorem

Since we know that the population standard deviation is σ − 1 , according to the central limit theorem, the standard deviation for the sample means is σ = 1 = 0.1 .

From Textbooks ● Mar. 27, 2020

X¯ ~ N ⎛22, 22 ⎞ by the central limit theorem for sample means.

From Textbooks ● Mar. 27, 2020

The sample size of 30 is sufficiently large in this example to apply the central limit theorem.

From Textbooks ● Sep. 19, 2013

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

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