# How to Create Bell Curves

Written by stephanie ellen
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The bell curve is a lay term for what statisticians call a normal distribution; it's called a bell curve because the shape of a normal distribution is in the shape of a bell. According to David Stockburger, meritus Professor, Missouri State University, the normal curve isn't a single curve, it's actually "an infinite number of all possible curves." Professor Mark Janeba, Associate Professor of Mathematics at Williametter University, says that many properties of the bell curve were discovered by the German mathematician, Carl Friedrich Gauss. If you look on the back of a 10 Deutschmark bill, you can see a portrait of Gauss, along with a bell curve--sometimes called a Gaussian Distribution.

Skill level:
Moderate

• Pencil
• Paper

## Instructions

1. 1

Draw a horizontal line representing the x-axis.

2. 2

Draw a bell shape above the x-axis. Make sure that the left and right portions of the bell mirror image each other. If you are unsure what is meant by a bell-shape, imagine looking at a church bell head on, with the base of the bell forming the x-axis, and the curve of the bell forming your graph.

3. 3

Place a tick mark in the middle of the x-axis, below the highest point in your bell curve. This tick mark represents the mean.

4. 4

Place three tick marks to the left of the middle tick mark, and three to the right. According to Stockburger, the three tick marks should divide the line into three sections (the tick marks to the far right and the far left will be very, very close to the end of the graph).

5. 5

Label the tick marks in the following order, from left to right: -3, -2, -1, 0, 1, 2, 3. Each tick mark represents one standard deviation from the mean.

#### Tips and warnings

• Create different curves by tailoring the numbers on your x-axis according to your mean and standard deviation. For example, if you have a mean of 10 and a standard deviation of 2.5, place the mean,10, in the centre of your graph. Subtract 2.5 to the left, and add 2.5 to the right, making your tick marks (from left to right) 2.5, 5, 7.5, 10. 12.5, 15, 17.5.

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