Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Univariate Data Distributions Central Limit Theorem  
See also: distributions, Normal Distribution, Mean, TimeAveraging  
Central Limit TheoremGenerally speaking, central limit theorems are a set of weakconvergence results in probability theory. Intuitively, they all express the fact that any sum of many independent identically distributed random variables will tend to be distributed according to a particular "attractor distribution". The most important and famous result is simply called the Central Limit Theorem which states that if the (independent) variables have a finite variance then the sum of these variables will show a normal distribution. Since many real processes yield distributions with finite variance, this explains the ubiquity of the normal distribution.
This simulation shows the consequences of the central limit theorem, which is considered to be one of the most important results in statistical theory:


Home Univariate Data Distributions Central Limit Theorem 