# central limit theorem

## central limit theorem

*noun*

## Definition of *CENTRAL LIMIT THEOREM*

**:**any of several fundamental theorems of probability and statistics that state the conditions under which the distribution of a sum of independent random variables is approximated by the normal distribution;

*especially*

**:**one which is much applied in sampling and which states that the distribution of a mean of a sample from a population with finite variance is approximated by the normal distribution as the number in the sample becomes large

## First Known Use of *CENTRAL LIMIT THEOREM*

1951

## central limit theorem

*noun*

*(Concise Encyclopedia)*

In statistics, any of several fundamental theorems in probability. Originally known as the law of errors, in its classic form it states that the sum of a set of independent random variables will approach a normal distribution regardless of the distribution of the individual variables themselves, given certain general conditions. Further, the mean (*see* mean, median, and mode) of the normal distribution will coincide with the (arithmetic) mean of the (statistical) means of each random variable.

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