File:IllustrationCentralTheorem.png · Wikimedia Commons · See Wikimedia Commons
Key facts
- Type
- Theorem
- Field
- Probability theory
- Statement
- The scaled sum of a sequence of i.i.d. random variables with finite positive variance converges in distribution to the normal distribution .
- Generalizations
- Lindeberg's CLT
via Wikipedia infobox
Wikidata facts
- Image
- CLTBinomConvergence.svg
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- short name
- CLT
- Commons category
- Central limit theorem
Sources (3)
via Wikidata · CC0
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Article
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard normal distribution. This holds even if the original variables themselves are not normally distributed. There are several versions of the CLT, each applying in the context of different conditions.
The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions.
Gallery (3)
Connections
convergence of random variables
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median
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independent and identically distributed random variables
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resampling
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random variable
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probability distribution
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expectation
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law of large numbers
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probability density function
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statistical population
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dependent and independent variables
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Pearson product-moment correlation coefficient
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Sergei Natanovich Bernstein
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power of a test
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errors and residuals
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trend estimation
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demographic statistics
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statistics
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Alan Turing
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International Standard Book Number
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