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