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A simple arrangement of pegs on a board that can be used to illustrate the binomial and normal distributions. A funnel allows a ball to roll down and strike the single peg on the top line. The ball rolls to left or right (ideally, with equal probability) and then falls to strike a peg on the next row and the process is repeated on each row. At the bottom the ball is held in one of a number of channels. When many balls are fed through the system it is found that the central channels will contain more balls than the extreme ones. Sir Francis Galton used a quincunx in his 1874 lecture on the normal distribution at the Royal Institution in London. See diagram.

Quincunx. In the diagram each point represents a peg. A series of small balls is inserted at the top of the quincunx. Each ball hits a sequence of pegs before coming to rest in a channel at the bottom of the quincunx. The distribution of balls in channels will be a realization of a binomial distribution, with n being the number of rows of pegs.

Subjects: Probability and Statistics — Arts and Humanities.

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