The ComPADRE Collections

Central Limit Theorem


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.