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Why the Normal Distribution has a "Bell-Curve" Shape

Why the Normal Distribution has a "Bell-Curve" Shape

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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Simple Explanation of the Central Limit Theorem

Simple Explanation of the Central Limit Theorem

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 Evolution of Normal Distribution

The Evolution of Normal Distribution

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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Simple Explanation of the Central Limit Theorem

Simple Explanation of the Central Limit Theorem

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

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A Galton Board Demonstration of Why All Statistical Models are Misspecified

A Galton Board Demonstration of Why All Statistical Models are Misspecified

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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The Kids Should See This

The Kids Should See This

Math in Motion: Playing with a desktop Galton Board

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Tools & Toys

Tools & Toys

The Galton Board — A Desktop Probability Machine.

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Learning Statistics Through Guided Block Play: A Precurriculum in Statitical Literacy

Learning Statistics Through Guided Block Play: A Precurriculum in Statitical Literacy

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Results of Simulations of a Model of the Galton Board for Various Degrees of Elasticity of the Ball-to-Nail Collision

Results of Simulations of a Model of the Galton Board for Various Degrees of Elasticity of the Ball-to-Nail Collision

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Bean Machine: A Declarative Probabilistic Programming Language For Efficient Programmable Inference

Bean Machine: A Declarative Probabilistic Programming Language For Efficient Programmable Inference

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Introducing Bean Machine

Introducing Bean Machine

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What If God Were A Giant Game Of Plinko?

What If God Were A Giant Game Of Plinko?

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DE MOIVRE ON THE LAW OF NORMAL PROBABILITY

DE MOIVRE ON THE LAW OF NORMAL PROBABILITY

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Engraved Portraits of Gauss for sale by Acme Klein Bottle!

Engraved Portraits of Gauss for sale by Acme Klein Bottle!

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Fine Art Maths Centre - The Quincunx

Fine Art Maths Centre - The Quincunx

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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3D Printed Galton Board

3D Printed Galton Board

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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Deborah R. Fowler - Galton Board

Deborah R. Fowler - Galton Board

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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Galton Board / Quincunx

Galton Board / Quincunx

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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Random Walk in Stock Market Prices

Random Walk in Stock Market Prices

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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Introduction to the Normal Distribution (Bell Curve)

Introduction to the Normal Distribution (Bell Curve)

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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Bean Machine and The Central Limit Theorem

Bean Machine and The Central Limit Theorem

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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Normal Distribution in Statistics

Normal Distribution in Statistics

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

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Dice for Statistical Experiments

Dice for Statistical Experiments

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

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Bagatelle as the inspiration for Galton’s Quincunx

Bagatelle as the inspiration for Galton’s Quincunx

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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Numerical Study of Galton Board Experiment via Discrete Element Method Simulation

Numerical Study of Galton Board Experiment via Discrete Element Method Simulation

Random walk can be described as certain simplification of phenomena commonly observed in, for example, chemistry and physics.

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A Brief History of Statistics in Three and One-Half Chapters: A Review Essay

A Brief History of Statistics in Three and One-Half Chapters: A Review Essay

This article by Stephen Fienberg reviews the last three and one-half centuries of statistics and probability largely through the author's overview and synthesis of seven recent books on the topic.

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APSU statistics instructor Sam Ligo builds Real-World models to help Students grasp Math Concepts

APSU statistics instructor Sam Ligo builds Real-World models to help Students grasp Math Concepts

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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Beyond the Quintessential Quincunx

Beyond the Quintessential Quincunx

The quincunx, a contraption with balls rolling through a triangle-shaped arrangement of nails, was invented to illustrate the binomial distribution and the central limit theorem for Bernoulli random variables

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The Quincunx: History and Mathematics

The Quincunx: History and Mathematics

The quincunx was invented by Sir Francis Galton in 1873 to demonstrate binomial distributions. During the last 125 years it has been used to illustrate the laws of the binomial and the normal distribution.