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Statistics vocabulary · Probability Distributions

Central limit theorem

Meaning in statistics, with examples

nounCommon term

In statistics, central limit theorem means: The result that the distribution of sample means gets closer to a normal distribution as the sample size grows, whatever the shape of the population distribution, as long as its variance is finite.

In Turkish: merkezi limit teoremi, merkezi limit kuramı

How it is used

Abbreviated CLT. It explains why normal-based methods such as t-tests and confidence intervals work well for means even with non-normal data, once samples are reasonably large. Textbooks often give n ≥ 30 as a rough rule, though very skewed data need more.

Example sentences

  1. Thanks to the central limit theorem, the mean of 200 waiting times is approximately normal, even though the times themselves are skewed.

  2. Can someone explain the central limit theorem without formulas?

Common collocations

  • by the central limit theorem
  • apply the central limit theorem
  • the CLT holds
  • large-sample approximation
  • sampling distributionThe distribution of a statistic, such as the sample mean, that you would get if you took many samples of the same size from the same population.
  • normal distributionA symmetric, bell-shaped distribution in which most values cluster around the mean and become rarer further away from it; its mean, median and mode are equal.
  • sample sizeThe number of observations or participants included in a study, usually written as n (or N for the total).
  • standard errorThe standard deviation of an estimate, such as a sample mean, across repeated samples; it shows how precise the estimate is likely to be.

More terms: Probability Distributions

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