Mean Absolute Deviation

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

We've already looked a one measure of spread, the range, which is the difference between the highest and lowest 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 the scores and the mean. 

 

Calculating the MAD of a data set

Let's use an example to help explain this.

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

1. Find the mean.

$Mean=\frac{23+18+31+28+20}{5}$Mean=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

3. 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

Find the mean of these differences.

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

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

 

Worked Examples

Question 1

Which of the following is true concerning the mean absolute deviation of a set of data? 

A) It describes the average distance between each data value and the mean.

B) It describes the variation of the data values around the median.

C) It describes the absolute value of the mean.

D) It describes the variation of the data values around the mode.

Think: Deviation is a measure of how different something is compared to something else. 

Do: A) It describes the average distance between each data value and the mean.

 

Question 2

Question 3