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:

average

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 5 = 12 5 = 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 and Harmonic Mean.

691, 1453, 1454, 692, 1455, 1456, 2179, 2180, 3053, 3054