CENTRAL LIMIT THEOREM Definition & Meaning

central limit theorem

noun

Statistics.

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.

central limit theorem

noun

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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�y��vlog History and Origins

Origin of central limit theorem¹

First recorded in 1950–55

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Example Sentences

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Then, using tools from probability such as the Central Limit Theorem, it's possible to calculate that in elections with large numbers of voters there is, on average, about a 2% chance that 0.1% random vote corruption changes the outcome of a majority vote.

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Some concepts would have benefited from a deeper treatment: notably, bootstrapping, or estimating the distribution of a statistic on the basis of random resampling; and the central limit theorem, which holds that averages of increasingly large subsets of the data in many sets tend towards a normal distribution.

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It is well known that if you wish to obtain a traditional result with little variance, all you need to do is assemble a large committee; this outcome is guaranteed by the central limit theorem of statistics.

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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.

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