*is*what the word normal means, but there’s a little bit more to it.

In mathematics—or more specifically, statistics—the word normal refers to a type of

**probability distribution**: a way to calculate the chances that a specific event will occur using mathematical equations (click here for more information about probability). It also describes the way these events look on a graph. Here is a simple example: imagine a 10 mile stretch of a very busy road. All 10 miles of road was constructed at the same time and is therefore the same age, and gets the same wear. The engineers who built this road know that at some point in the next year, the road will develop a crack.

**uniform distribution**.

The normal distribution is also a probability distribution, but in this case not all of the possible outcomes have equal probability. In the normal distribution, there is one outcome value which is the average of all the possible values, and this value has the highest probability. All values higher and lower than this value have lower and lower probabilities the farther they are from the average. For example, think about the height of men in the United States. McDowell reports that the average height for men over 20 years old in the US is 5 feet, 9.5 inches (1). However, we know there are men that are shorter and men that are taller: currently the tallest man in the world is 8 feet, 3 inches tall (2); the shortest man in the world is only 1 foot, 9.5 inches tall (3)! The probability of anyone being this tall (or this short) is very, very low. If we could measure the height of 1000 men from all over the US, and we could plot this information on a graph with number of men on the vertical axis and height measured (in feet) on the horizontal axis, it would look like this:

**mean**(that is, at an average) of 5.79 feet which is 5 feet, 9.5 inches—the average height for men over 20 years old in the US. This means men from our sample have a high probability of being around this height. As the heights get taller or shorter, the probability of finding a man in our sample of this height goes down. This makes the curve look like a bell, which is why it is often called the “bell curve”. So when we say something is “normal”, it really does mean that it has a high probability of being similar to the average!

TRY THIS!

Here’s what you’ll need:

1) A pen or pencil

2) A piece of paper

3) A computer with a spreadsheet program installed, such as Microsoft Excel®

4) At least 30 individuals of around the same age (50 is even better). If you are in school now, you can use your classmates!

5) A tape measure at least 10 feet long.

Here’s what you need to do:

1) Make a table on your piece of paper with height (in feet) in one column, and number of individuals in another. In the height column, write numbers ranging from 3-7 in increments of 0.5, as in the following example:

3) As each individual tells you their height, make a mark in the other column across from the height range they fall into. Here is some example data:

When we use our sample numbers, this is what our graph looks like:

What does your chart look like? If you connect the tops of all the columns, what shape does it look like? Is the highest point roughly in the middle? Print out this graph and save it with your notes!

CHALLENGE YOURSELF!

What else do you think might have a normal distribution? Try measuring the weight of each nail in a box, or count the number of seeds in a bunch of identical seed packages. Be sure to use at least 30 nails or seed packages, or more if you can;

**the more you use for your testing (that is, the larger your sample size) the better you will be able to see the probability distribution**. Be sure you keep track of you numbers the same way as before, and use a spreadsheet program to graph all the numbers (weight or number of seeds on the horizontal axis, and number of observations within a certain range on the vertical axis). This way you can get an idea of what the probability distribution might look like.

References:

1) McDowell, Margaret A.

*et al.*(October 22, 2008). "Anthropometric Reference Data for Children and Adults: United States, 2003–2006".

*National Health Statistics Reports,*

**10.**

2) “World’s Tallest Man—Living”

*. Guinness Book of World Records*. Accessed 8/21/14. Last updated 2/8/2011.

3) Sheridan, Michael. (February 26, 2012). “Chandra Bahadur Dangi is world’s shortest living man: Guinness World Records.”

*New York Daily News*. www.nydailynews.com.