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November 29, 2009

In this exercise, we demonstrate the difference between a random and normal distribution.

Normal Distribution

A Quincunx is a device designed to demonstrate a normal distribution.  The bean machine, Galton Box, Pachinko and Plinko are all common examples: a ball drops down, bouncing off a series of offset pegs, forced right or left.  If enough balls are allowed to drop, they will mostly tend toward the center, where the ball began, but some will fall to the left and right, and a few to the extremes.  This normal distribution, or normal curve, is determined by the combination of independent samples and additive outcomes.

As an alternative illustration, I demonstrate here what it means to be short, of average build, or tall.  The human frame is composed of a combination of elements–simplified here as lower and upper leg joints, torso and head–all of which have short, average and long dimensions:

You have an even chance of getting any one of these elements in any dimension within this range, but the cumulative probability of getting all of them at one end of a distribution at once is fairly small.  The law of large numbers predicts a majority with an average height, with some being all short, and others all tall:

There is a slight bias to the left here due to the fact that I rounded to the nearest inch.  Here’s the Processing sketch:


Random Distribution

As a point of comparison, the following is an illustration of a completely random distribution.  The ball is dropped from a location chosen at random (with Processing’s random() function) across the width of the frame.  It has an even chance of being dropped from any x-coordinate –each sample is independent– but there is no additive function joining the outcomes, so there is no bias to the distribution:

And in Processing:


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