Galton Board and the Binomial Distribution
Random journeys build an orderly peak
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Summary
The Galton board: balls passing through rows of pegs bounce left or right with a 50% chance each time. Drop thousands of balls and the distribution of their final positions forms a bell curve (the normal distribution). It is a visual proof of the central limit theorem.
In depth
In the 19th century Sir Francis Galton built a device in which balls poured in at the top bounce off evenly spaced pins (pegs) and fall into boxes (bins) along the bottom. If at each pin the ball goes left or right with equal probability, balls passing through N pins follow the binomial distribution B(N, 0.5). As N grows, this distribution approaches the bell curve, one of the most fundamental results in statistics. As a physical device, the Galton board shows how abstract ideas of probability play out in the real world. The same principle holds everywhere, from random molecular collisions in your body to daily swings in financial markets and measurement errors in scientific experiments.
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