# How to Find the Mean

The mean is the **average** of the numbers.

It is easy to calculate: **add up** all the numbers, then **divide by how many** numbers there are.

In other words it is the **sum** divided by the **count**.

### Example 1: What is the Mean of these numbers?

6, 11, 7

- Add the numbers:
**6 + 11 + 7 = 24** - Divide by
*how many*numbers (there are 3 numbers):**24 / 3 = 8**

**The Mean is 8**

## Why Does This Work?

It is because 6, 11 and 7 added together is the same as 3 lots of 8:

It is like you are "flattening out" the numbers

### Example 2: Look at these numbers:

3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

The sum of these numbers is 330

There are fifteen numbers.

The mean is equal to 330 / 15 = 22

**The mean of the above numbers is 22**

## Negative Numbers

How do you handle negative numbers? Adding a negative number is the same as subtracting the number (without the negative). For example 3 + (−2) = 3−2 = 1.

Knowing this, let us try an example:

### Example 3: Find the mean of these numbers:

3, −7, 5, 13, −2

- The sum of these numbers is
**3 − 7 + 5 + 13 − 2 = 12** - There are
**5**numbers. - The mean is equal to
**12 ÷ 5 = 2.4**

**The mean of the above numbers is 2.4**

Here is how to do it one line:

Mean = | 3 − 7 + 5 + 13 − 2 | = | 12 | = 2.4 |

5 | 5 |

Now have a look at The Mean Machine.

*Advanced Topic: the mean we have just looked at is also called the "Arithmetic Mean", because there are other means such as the Geometric Mean.*