San José State University
Department of Economics

applet-magic.com
Thayer Watkins
Silicon Valley
& Tornado Alley
USA

 The Central Limit Theorem and Sample Statistics

## The Central Limit Theorem

The Central Limit Theorem (CLT) is a powerful and important result of mathematical analysis. In its standard form it says that if a stochastic variable x has a finite variance then the distribution of the sums of n samples of x will approach a normal distribution as the sample size n increases without limit. The CLT provides a basis for some sample statistics having a normal distribution for large samples. This page provides illustrations of the distribution of some sample statistics for samples drawn from a population which has a uniform distribution; i.e., the probability density is constant over a range of values.

Suppose the probability density distribution for z is

#### p(z) = 1 for -0.5≤z≤+0.5 p(z) = 0 for all other values of z

The following cases shows the distributions for several sample statistics

## The Distributions of Sample Statistics

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