7.05 Mean absolute deviation (MAD)

Measures of distribution tell us how far the scores in a data set are spread out.

We've already looked at one measure of spread, the range, which is the difference between the greatest and least score in a data set.

Now we are going to learn about a new measure of spread called the Mean absolute deviation (MAD). The MAD of a set of data is the average distance between each data value and the mean. 

Let's use an example to help explain this.

Worked example

Question 1

Find the mean absolute deviation of $23,18,31,28,20$23,18,31,28,20.

Think/Do:

1. Find the mean.

$\frac{23+18+31+28+20}{5}$23+18+31+28+205​$=$=$24$24

2. Find the difference between each individual score and the mean.

$23-24=-1$23−24=−1

$18-24=-6$18−24=−6

$31-24=7$31−24=7

$28-24=4$28−24=4

$20-24=-4$20−24=−4

Take the absolute value of each difference.

$\left|-1\right|=1$|−1|=1

$\left|-6\right|=6$|−6|=6

$\left|7\right|=7$|7|=7

$\left|4\right|=4$|4|=4

$\left|-4\right|=4$|−4|=4

3. Find the mean of these differences.

$\frac{1+6+7+4+4}{5}$1+6+7+4+45​$=$=$4.4$4.4

Therefore, the mean absolute deviation is $4.4$4.4 units.

Reflect: This means that, on average, scores in this data set are $4.4$4.4 units above or below the mean.

The box below summarizes our steps.

 

Practice questions

Question 2

Question 3