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

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

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 − 25 = 125 = 2.4

Try it yourself!

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.