# The Galton Board: A Device Invented to Demonstrate the Normal Distribution

### Galton boards are designed to bring to life the statistical concept of normal distribution

As you rotate the Galton Board on its axis, you set into motion a flow of steel beads that bounce with equal probability to the left or right through several rows of pegs.

As the beads accumulate in the bins, they approximate the bell curve, as shown by the yellow line on the front of the Galton board.

This hands-on Galton Board allows you to visualize the order embedded in the chaos of randomness.

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The Galton Board is a 7.5” by 4.5” desktop probability machine. This delightful little device brings to life the statistical concept of normal distribution. As you rotate the Galton Board on its axis, you set into motion a flow of steel beads that bounce with equal probability to the left or right through several rows of pegs.

Measuring 7.5 inch by 4.5 inch, this desktop probability machine is the perfect gift for physics lovers or just as a uniquer desktop toy.

IMPORTANT: Due to an anti-static additive, the opacity of the board may on rare occasions vary slightly

The Galton Board demonstrates centuries-old mathematical concepts in an innovative desktop device. It incorporates Sir Francis Galton’s (1822-1911) illustration of the binomial distribution, which for a large number of beads approximates the normal distribution. 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. The number at each peg represents the number of different paths a bead could travel from the top peg to that peg. The Fibonacci numbers (Leonardo Fibonacci, 1175-1250), can also be found as the sums of specific diagonals in the triangle. The Galton Board is approved for STEM educational activities.

When rotated on its axis, the 3,000 beads cascade through rows of symmetrically placed pegs in the desktop-sized Galton Board. When the device is level, each bead bounces off the pegs with equal probability of moving to the left or right. As the beads settle into the bins at the bottom of the board, they accumulate to approximate a bell-shaped curve. Printed on the board are the bell curve, as well as the average and standard deviation lines. The bell curve, also known as the Gaussian distribution (Carl Friedrich Gauss, 1777-1855), is important in statistics and probability theory. It is used in the natural and social sciences to represent random variables, like the beads in the Galton Board.

##### NORMAL DISTRIBUTION AND STANDARD DEVIATION

The normal distribution, often referred to as the “bell curve”, is the most widely known and used of all probability distributions. Because the normal distribution approximates many natural phenomena so well, it has developed into a standard of reference for numerous probability problems. 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.

As demonstrated by the Galton Board, the random path of 3,000 beads approximates a bell curve every time.

The standard deviation (σ) is a measure of how closely all of the data points are gathered around the average. The shape of a normal distribution is determined by the average and the standard deviation. The more narrow the bell curve, the smaller the standard deviation. When the bell curve is wide, the standard deviation is large.

As seen in the graphic, about two-thirds of the data in a bell curve fall within one standard deviation of the average. About 95% of the data falls within two standard deviations and about 99.7% within three standard deviations.