Ball-Dropping Approximation of the Normal Distribution

In lots of different aspects of the natural world we see variation around a central mean. For instance, shoe sizes vary. Most men have shoe sizes that range between size 8 and size 11, and a few men have very large feet or very small feet. Women also have shoe sizes that vary, although their feet tend to be somewhat smaller. The simulation below is meant to illustrate how differences like different shoe sizes can result from a simple mechanism of dropping balls. When a ball hits a pin below, it can either go left or right as it drops. All the balls start at the same point, but as they drop they tend to spread out. Because very few balls tend to consistently drop to the left or to the right, most balls cluster around the middle, giving the distribution its characteristic bell-shaped curve.

The two sets of balls are dropped from slightly different points at the top. This results in a shift in the red distribution to the right. The balls are actually colored marbles, and so if a red an a yellow ball land in the same spot you see an orangish ball. This indicates that the two distributions overlap.

Although the two groups of balls drop from different locations at the top, it is often difficult to tell this fact until lots of balls drop. This is true in experiments as well, where you need lots of observations or trials in order to determine whether two distributions were different. To return to the shoe example above, if you knew nothing about mens and womens shoe sizes, you would have to examine lots of feet before you could be sure that in fact men have larger feet than women.

Orignial ball dropping code by David Krider

Adaptation for two distributions by Tom Busey