Galton board

Thomas Bayes


The Galton board is a physical model of the binomial distribution which beautifully illustrates the central limit theorem

Galtonboard is also known as:

  • Galtonbrett Simulation,
  • quincunx
  • bean machine
  • or Galton

The Galtonboard is a device invented by Sir Francis Galton to demonstrate the central limit theorem, in particular that the normal distribution is a good approximate to the binomial distribution.

The ball is not the variable. The variable is whether it goes left or right. Every ball is randomly pushed left and right.

The galtonboard demonstrates that the binomial distribution is approximately a normal distribution.

Invented by Sir Francis Galton (1822-1911), the Galton board is a vertically placed rectangular board with evenly spaced pegs or nails.


See also pascal triangle


Gaussian Column First There's only one way for a ball to reach the first column
Gaussian Column Second There are four ways to reach the second column
Gaussian Column Third There are six ways to reach the third column
Gaussian Total Because the machine is symetrical, after some time it will look like a gaussian distribution

See also: Pascal Triangle

Documentation / Reference

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