Central Limit Theorem

Initial Publication Date: December 21, 2006

These figures were created by the "Central Limit Theorem" applet from Statistical JAVA discussed below.

For increasing sample size, n, the distribution of sample means approaches a normal distribution centered on the population mean with a decreasing variance (proportional to 1/n). This is true regardless of how values are distributed within a population and is the essence of the central limit theorem (more info) . The two figures above were created by the central limit theorem applet found at Statistical JAVA. Both figures show the distribution of the sample mean for a uniform distribution using 2000 samples. The sample size at left is n=1 and the sample size on the right is n=100. Having students use these applets can help them better understand how the central limit theorm applies to a population of arbitrary distribution. Click on either figure to enlarge.

The Law of large numbers is discussed in relation to the central limit theorem at Random Samples.