central limit theorem
The 'central limit theorem' is a key principle in statistics and probability theory, essential for understanding the behavior of sample means.
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Definition
C1Statistics
(technical, academic)The principle that the distribution of the sample mean of a large number of independent, identically distributed variables will approximate a normal distribution, regardless of the original distribution.
Example
- According to the central limit theorem, the average height of a large group of people will form a normal distribution, even if individual heights do not.
C1Probability Theory
(technical, academic)A theorem stating that the sum of a large number of independent, identically distributed random variables will be normally distributed, given a finite variance.
Example
- The central limit theorem allows statisticians to use normal distribution models in various applications, despite the underlying data distribution.