Chapter 1. The Central Limit Theorem

Introduction

The Central Limit Theorem says that the distribution of sample means of n observations from any population with finite variance gets closer and closer to a Normal distribution as n increases. More specifically, for a population of individual observations with mean μ and standard deviation σ, the Central Limit Threorem says that the means of samples of size n drawn from this population will approximate a Normal distribution whose mean is also μ and whose standard deviation is .

This applet illustrates the Central Limit Theorem by allowing you to generate thousands of samples with various sizes n from a exponential, uniform, or Normal population distribution. You can then compare the distribution of sample means against the Normal distribution with the standard deviation predicted by the Central Limit Theorem.