Hide
The Teaching Quantitative Skills in the Geosciences website has not been significantly updated since 2011. We are preserving the web pages here because they still contain useful ideas and content. But be aware that the site may have out of date information.
You can find more recent and extensive resources on the Teach the Earth website.

Central Limit Theorem

Initial Publication Date: December 21, 2006
Central Limit Theorm Figure from Statistical JAVA
Central Limit Theorm Figure from Statistical JAVA

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.