GALTON BOARD ARTICLES

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The normal distribution certainly has a beautiful shape. And in our dataful world, it's everywhere. Heights, weights, neurons firing, the apparent brightness of stars... they all mysteriously fall into line on the "bell curve".

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Statistics is the most widely applied of all mathematical disciplines and at the center of statistics lies the normal distribution, known to millions of people as the bell curve, or the bell-shaped curve.

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The central limit theorem (CLT) says that for sufficiently large random samples, the sample means will be approximately normally distributed.

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The Galton board or quincunx is a fascinating device that provides a compelling demonstration of one the main laws of statistics.

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Math in Motion: Playing with a desktop Galton Board

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The Galton Board — A Desktop Probability Machine.

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Austin Peay State University statistics instructor Sam Ligo for years has used his woodworking skills and engineering know-how to build mathematical models – real-world 3D representations of the math – to help his students learn.

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The word “quincunx” refers to a pattern of four objects arranged in a square with a fifth in the centre, like the spots on a dice.

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A Galton board (AKA a bean machine) demonstrates probability by allowing balls to drop through an array of pegs through which they have a 50/50 chance of going left or right at each point.

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The idea of a Galton board is to demonstrate the bell curve. Dropping balls on pegs arranged in a way such that when the ball is dropped it has a 50/50 chance of going left or right. Generally speaking there are more paths going toward the middle and thus produces the bell curve, or binomial distribution, or normal distribution of balls in the slots below the pegs.

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The Galton board (also called a Quincunx) is a physical model of the binomial distribution which beautifully illustrates the central limit theorem.

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FOR MANY YEARS economists, statisticians, and teachers of finance have been interested in developing and testing models of stock price behavior. One important model that has evolved from this research is the theory of random walks.

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The normal distribution is a continuous probability distribution that is symmetrical on both sides of the mean, so the right side of the center is a mirror image of the left side.

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While I was studying Statistical Physics at the university, I was fascinated by the ability of statistics to simplify and explain the chaotic processes in a smart approach.

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The normal distribution is the most important probability distribution in statistics because it fits many natural phenomena.

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Every statistician wants now and then to test the practical value of some theoretical process...

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This paper considers the question of how Francis Galton came to devise the quincunx, a pin-board that simulates the effect of a large number of Bernoulli trials to yield an empirical normal curve.

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