## What is an Average?

The word “average” is used in everyday life to describe where the **middle number of a data set** is. It’s the typical number you would expect to find in a series of numbers. In statistics, the average is called the “arithmetic mean,” usually just shortened to *the mean*. Both the average and the mean use the same formula:

**avg = total sum of all the numbers / number of items in the set. **

In other words, to find the average, add up all of the numbers in the set, and then divide by however many items you have. Let’s say you have 5,10, and 15. Add them all up to get 5 + 10 + 15 = 30, then divide by 3(the number of items). The answer is 30 / 3 = 10.

## How to Calculate Average: Examples

**Example 1:** You earned $129, $139, $155 and $176 over the last 4 weeks. What is your average pay?

Step 1: Add up all of the numbers in the set. $129 + $139 + $155 + $176 = $599.

Step 2: Divide Step 1 by the total number of items in the set. There are 4 items in the set, so $599 / 4 = $149.75.

**Example 2:** You have semester grades of B, C, D, A, B and B. What is your average grade?

Step 1: Add up all of the numbers in the set. You have grades here, so you need to convert them on a 4.0 scale:

B = 3.0

C = 2.0

D = 1.0

A = 4.0

B = 3.0

B = 3.0

So we have: 3.0 + 2.0 + 1.0 + 4.0 + 3.0 + 3.0 = 16.0.

Step 2: Divide Step 1 by the total number of items in the set. There are 6 items in the set, so 16.0/6 = 2.66.

## A More Formal Definition

In probability and statistics, you’ll see the following formula used:

Don’t let the formula scare you! The summation sign (Σ) just means to “add up” and the letter *n *stands for the number of items in the set. Taking example 1 from above, the formula could be used to find the same answer:

AM = 1/4 * ($129 + $139 + $155 + $176 = $599.

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