Conceptual Overview: Explore how the sampling means tend to have a normal distribution regardless of the distribution of the individual observations.

In the graphic below, under the "Roll 1 Die" column click on the "Roll 1 Set"button to roll the die. Its value will be displayed near the top, and a histogram of the resulting value will be displayed beneath it. Click on the "Roll 1 Set" button several times and observe how the histogram is updated.

Next, click on the "Roll 100 Sets" button to perform 100 individual rolls of one die at once. The statistics for the resulting distribution are displayed above the histogram. Select at least 1,000 samples this way to get a sense of the distribution of a single roll of the die.

In this case, it is a "loaded" die so the histogram columns will not have the same height.

Then do the same thing for the "Roll 3 Dice" column. Now the data recorded in the histogram are the means of three rolls of the die. Finally, do the same thing for the "Roll 12 Dice" column. Despite starting with a non-normal distribution, the sampling distributions for means of 3 dice and the means of 12 dice approach a normal distribution.