# Central Limit Theorem Applet

This applet demonstrates the central limit theorem using simulated dice-rolling experiments. An "experiment" consists of rolling a certain number of dice (1-5 dice are available in this applet) and adding the number of spots showing. This experiment is "performed" repeatedly, keeping track of the number of times each outcome is observed. These outcomes are plotted in the form of a histogram. According to the Central Limit Theorem, if the number of dice rolled is not too small, the histogram's shape should resemble that of the "bell-shaped curve" when the experiment is repeated many times.

To speed up the convergence, it is possible to set the applet to repeat the experiment many times for each mouse click. Note that 10,000 rolls can be done at once -- this may take some time, depending on how fast your machine is. It might be more educational to use a smaller number of simultaneous rolls, so that you can watch the histogram converge to a bell-shaped curve.

If only one die is being rolled, the histogram should look flat. For two dice, the histogram should look like the top of a witch's hat. For three and more dice, the histogram will be more bell-shaped looking.

Note that the distribution of a single die (the "discrete uniform") is symmetric and light tailed, so the convergence of the sum of dice to normality is quite fast. Skewed and/or heavy tailed distributions will converge much more slowly.

by R. Todd Ogden, Dept. of Statistics, Univ. of South Carolina
ogden@stat.sc.edu