![]() ![]() The difference comes in how the group processes the information available to them. But new research suggests that there are group decision dynamics at play where bigger (crowds) may not always be better.Ī recent study by Iain Couzin and Albert Kao at Princeton suggests that in real world situations, where information is more complex and spotty, the benefits of crowd wisdom peaks in groups of 5 to 20 participants and then decreases after that. In other words, if we average the knowledge of many people, we’ll be smarter than any of us would be individually. About 95% of the data falls within two standard deviations and about 99.7% within three standard deviations.Since James Surowiecki published his book “The Wisdom of Crowds”, the common wisdom is – well – that we are commonly wise. When the bell curve is wide, the standard deviation is large.Īs seen in the graphic, about two-thirds of the data in a bell curve fall within one standard deviation of the average. The more narrow the bell curve, the smaller the standard deviation. The shape of a normal distribution is determined by the average and the standard deviation. The standard deviation (σ) is a measure of how closely all of the data points are gathered around the average. Several sets of data follow the normal distribution: for example, the heights of adults the weights of babies classroom test scores returns of the stock market and the beads in the Galton Board.Īs demonstrated by the Galton Board, the random path of 3,000 beads approximates a bell curve every time. Because the normal distribution approximates many natural phenomena so well, it has developed into a standard of reference for numerous probability problems. The normal distribution, often referred to as the "bell curve”, is the most widely known and used of all probability distributions. An even larger Eames probability machine was showcased at IBM’s Pavilion for the 1964 World’s Fair in New York. The Galton Board is reminiscent of Charles and Ray Eames’ groundbreaking 11-foot-tall “Probability Machine,” featured at the 1961 Mathematica exhibit. Those include: prime numbers powers of two Magic 11’s Hockey Stick Pattern triangular numbers square numbers binary numbers Fibonacci’s sequence Catalan numbers binomial expansion fractals Golden Ratio and Sierpinkski’s Triangle. ![]() ![]() Within Pascal’s Triangle, mathematical properties and patterns are evident. In the Galton Board you may see: the Gaussian curve of the normal distribution, or bell-shaped curve the central limit theorem (the de Moivre-Laplace theorem) the binomial distribution (Bernoulli distribution) regression to the mean probabilities such as coin flipping and stock market returns the law of frequency of errors and what Sir Francis Galton referred to as the “law of unreason.” The Galton Board and the superimposed Pascal’s Triangle incorporate many mathematical, statistical and probability concepts. The Galton Board is reminiscent of Charles and Ray Eames’ groundbreaking 11-foot-tall “ Probability Machine,” featured at the 1961 Mathematica exhibit. It is used in the natural and social sciences to represent random variables, like the beads in the Galton Board. The bell curve, also known as the Gaussian distribution (Carl Friedrich Gauss, 1777-1855), is important in statistics and probability theory. Printed on the board are the bell curve, as well as the average and standard deviation lines. As the beads settle into the bins at the bottom of the board, they accumulate to approximate a bell-shaped curve. When the device is level, each bead bounces off the pegs with equal probability of moving to the left or right. When rotated on its axis, the 3,000 beads cascade through rows of symmetrically placed pegs in the desktop-sized Galton Board. The Galton Board is approved for STEM educational activities. ![]() The Fibonacci numbers (Leonardo Fibonacci, 1175-1250), can also be found as the sums of specific diagonals in the triangle. The number at each peg represents the number of different paths a bead could travel from the top peg to that peg. It also has a superimposed Pascal’s Triangle (Blaise Pascal, 1623-1662), which is a triangle of numbers that follows the rule of adding the two numbers above to get the number below. It incorporates Sir Francis Galton’s (1822-1911) illustration of the binomial distribution, which for a large number of beads approximates the normal distribution. The Galton Board demonstrates centuries-old mathematical concepts in an innovative desktop device. ![]()
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