R. Webster West and R. Todd Ogden
University of South Carolina
Journal of Statistics Education v.6, n.3 (1998)
Copyright (c) 1998 by R. Webster West and R. Todd Ogden, all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the authors and advance notification of the editor.
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 the speed of your machine. 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 rolled, the histogram should look flat. For two dice, the histogram should look like the top of a witch's hat. For three or more dice, the histogram will be more bell-shaped.
Note that the distribution of the number on a single die (the discrete uniform) is symmetric and light-tailed, so the convergence to normality of the sum is quite fast. For skewed and/or heavy-tailed distributions, convergence is much slower.
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