Galton Board (Physical Model)
A random walk made physical
Summary
A Galton board is a physical device in which balls poured in at the top bounce off pegs and fall into bins at the bottom. It is a visual proof of the binomial distribution (and of the central limit theorem): the counts in the bins form the same bell curve every time.
In depth
Sir Francis Galton (1822–1911), a cousin of Charles Darwin and one of the pioneers of statistics, designed this device in 1873. It is also called the "bean machine" or the "quincunx", a Latin word for a pattern of five points. Each ball poured in at the top bounces left or right at every peg as it passes through N rows of pegs. N independent Bernoulli trials → the total number of steps to the right follows a binomial distribution. Galton's great contribution was to make statistical thinking visible with this physical model. The device is also a concrete demonstration of the central limit theorem: drop thousands of balls and the distribution always approaches the normal curve. The 3D model on this page shows the real mechanical structure of the device: the geometric arrangement of the pegs, the paths of the balls and the symmetry of the bins below.
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