4K | Galton Board & The Bell Distribution Explained | Math

This clip demonstrates and explains the Galton Board and The Bell Curve within the fields of probability and statistics.

Curiously, the Galton board is also known under several other names: the Quincunx (due to the geometrix pattern of five points arranged in across which is repeated on the board) , a Bean machine , and a Binostat . The many different names may contribute to some confusion about the device, but as William Shakespeare said: a rose any other name would smell as sweet ...

The Normal Distribution
If you have studied probability and statistics at any meaningful level you will have come across the concept of the "normal distribution", the "binomial distribution" and the so-called "bell curve" within the fields of statistics and probability theory. The bell curve appears in many aspects of science and mathematics, and it also frequently appears in daily life and nature in surprising ways. But did you ever wonder how the bell curve originates?

The Galton Board
The Galton board, invented by Sir Francis Galton (1822-1911) illustrates the binomial distribution which is pretty good approximation of the normal distribution. It uses 3000 small metal balls and uses 12 rows of pegs to separate them into one of 28 separate bins where the balls accumulate and stack up. But how does this illustrate the normal distribution?

When a ball reaches a peg it has an approximately 50% chance of going left and 50% chance of going right. The chance of going either left or right on all 12 rows of pegs is much smaller than the chance of going left and right roughly the same amount of times. This means that the majority of the balls end up in the middle bins, with fewer and fewer balls reaching the outer bins because the chance of hitting the required number of "rights" or "lefts" is much lower. Thus producing the well-known bell curve.

The video clip is 60 fps and replayed at half speed.

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