One way of stating the central limit theorem is "The arithmetic mean (aka "average") of a random sample is normally distributed with he same mean as the population and a standard deviation that is smaller than the standard deviation of individual scores by a factor of the squareroot of sample size.
This result holds true for whatever population the samples are drawn from.
Shown below are several animations from the RippleSoft Software "Statistics Tool" application illustrating this theorem. There is a lot of information on the animation screen.
|The Central Limit Theorem Illustrated Screen contains a lot of information. Click here to open another window describing the areas of the screen.|
©2006 by Burrton Woodruff. All rights reserved. Modified