Dice Sample

This applet illustrates the central limit theorem by repeatedly rolling sets of dice. The example below rolls sets of three dice. Click on the "1 Roll" button several times to observe what is happening for a single roll. Then speed up the sampling by clicking on the "10 Rolls" and then the "1000 Rolls" buttons.

Larger Sample Size

An applet that specifies the number of dice in a roll. With a larger sample size (n = 12) in the applet below, the fit to the normal distribution is better and the standard deviation (standard error of the mean) is smaller.

"Loaded" Dice

Another applet <param> allows specification of unequal frequencies for the die faces. The first applet below shows rolls of a single die. Roll the die many times to detemrine the base distribution. Then observe in the second applet how the distribution of the means still converges to a normal distribution when rolling sets of 12 "loaded" dice.

Rolling One "Loaded" Die

Rolling 12 "Loaded" Dice

Skewed Distributions

Similarly, the frequency distribuiton for the dice can have a skewed distribution as in the example below. The first applet rolls a single die so that you may observe the skewed distribution. The second applet rolls sets of 12 dice and again approaches a normal distribution, despite the underlying skewed distribution.

Rolling One Die with Skewed Distribution

Rolling 3 Dice with Skewed Distributions

Rolling 12 Dice with Skewed Distribution