r o l l   t h e   d i c e !

This interactive lab illustrates one of the most profound and magical facts of statistics, known as the "Central Limit Theorem". Roughly stated, the Central Limit Theorem says that, if each of the results of a large number of independent random events has the same distribution as the others, then, as the number of events gets large, the distribution of the sum of their results tends toward a bell-shaped curve (statisticians call this a "normal" distribution). Amazingly, this fact doesn’t depend on the distribution of the underlying events!

In this illustration, the number on the top of each rolled die is an independent random event. Independent because the result of each die roll does not depend on the result of any previous roll, and random because, assuming that the die is "fair", the value on the top of the rolled die cannot be predicted in advance. The sum of their results is the total number of dots on the tops of all the rolled dice. The bar chart illustrates the distribution of the sum. The distribution of each independent die roll is flat, not bell-shaped. See for yourself. Roll one die a bunch of times and watch the bar chart evolve. The distribution of the sum of two independent die rolls is triangular. Try it and see. What about five dice? What about ten?

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