**Mean absolute deviation** is a measure of how a set of numbers varies.

To calculate the mean absolute deviation, we work out the average of the absolute differences from the mean as follows:

**Step 1**

Work out the mean.

**Step 2**

For each number, subtract the mean and write down its absolute (positive size).

**Step 3**

Work out the mean of these absolute values.

**Example**

Over the course of five days, there were the following number of empty seats at a theatre.

14 seats | 18 seats | 12 seats | 20 seats | 21 seats |

Calculate the mean absolute deviation in the number of empty seats.

**Answer**

**Step 1**

Mean = (14 + 18 + 12 + 20 + 21) ÷ 5 = 85 ÷ 5 = 17

**Step 2**

|14 - 17| = |-3| = 3

|18 - 17| = |1| = 1

|12 - 17| = |-5| = 5

|20 - 17| = |3| = 3

|21 - 17| = |4| = 4

**Step 3**

Mean of 3, 1, 5, 3 and 4 = (3 + 1 + 5 + 3 + 4) ÷ 5 = 16 ÷ 5 = 3.2

Mean absolute deviation = **3.2**