The Galton board and the Normal distribution

Have you ever watched the show Tipping Point or played on a coin pusher machine? You drop a coin from the top of the machine and is bounces around a series of pegs before landing on a moving platform. People try and predict where they want the coin to land in order to push the most coins down but it’s rigged (arcades surprisingly don’t want you to win money).

The concept shares similarities with a more interesting contraption known as the Galton Board. Invented by Sir Francis Galton, a 19th century polymath from Birmingham, UK, the probability machine stood at 19.05cm by 11.43cm desktop and demonstrated an important probability distribution in real-time known as the Normal distribution.

It works as follows:

As you rotate the Galton Board on its axis, you set into motion a flow of steel beads that bounce with equal probability to the left or right through several rows of pegs. As the beads accumulate in the bins, they approximate the bell curve, as shown by the yellow line [see video below] on the front of the Galton board.

From the chaos of randomness comes a uniform curve seen in everything from physics to finance, rainfall, even the growth of hair, nails and teeth. And all that from some beads bouncing against some pegs.

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