# Arithmetic Mean: Definition, Formula & Example

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• 0:02 What is an Arithmetic Mean?
• 1:03 The Arithmetic Mean Formula
• 1:55 Examples
• 3:54 Lesson Summary
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Lesson Transcript
Instructor: Norair Sarkissian
In this lesson, we will learn about the arithmetic mean, which is a quantity that is used in a wide variety of applications, such as science, engineering, medicine, statistics and finance.

## What is an Arithmetic Mean?

There are six kindergarten classrooms in a small school district in Florida. The class sizes of each of these kindergartens are 26, 20, 25, 18, 20 and 23. A researcher writing a report about schools in her town wants to come up with a figure to describe the typical kindergarten class size in this town. She asks a friend for help and her friend suggests that she calculate the average of these class sizes.

To do this, the researcher finds out that she needs to add the kindergarten class sizes together and then divide this sum by six, which is the total number of schools in the district. Adding the six kindergarten class sizes together gives the researcher a total of 132. If she then divides 132 by six, she gets 22. Therefore, the average kindergarten class size in this school district is 22.

This average is also known as the arithmetic mean of a set of values.

## The Arithmetic Mean Formula

The arithmetic mean of a set of values is the ratio of their sum to the total number of values in the set. Thus, if there are a total of n numbers in a data set whose values are given by a group of x-values, then the arithmetic mean of these values, represented by 'm', can be found using this formula:

In our kindergarten class size example, n is 6, or the number of kindergarten classrooms, while the x-values are given by the class sizes in each of the kindergartens within the school district. If you recall adding the total number of students in the six classrooms gave us 132. We can plug these values into our formula, dividing 132 by six, and find once again that the average class size is 22. Let's take a look at a couple more examples of how to calculate the arithmetic mean of a group of values.

## Examples

A pediatrician has four 9-year-old patients who are boys. Their heights in inches are 54, 57, 53 and 52. She finds out that according to national statistics, the average height of a nine year old boy is 55 inches, or 4 feet and 7 inches. What is the mean or average height of these four boys?

Remember when finding the average, or arithmetic mean, we add together the given values in a data set, then divide by the number of given values. In this example, there four different heights given for four different boys. Since we are considering n = 4 boys, we add the four heights together and divide the result by 4:

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