Median Absolute Deviation

In Chapter 3 we learned that if we wanted to make the absolute errors (the distance between the representative or model value and each data value) as small as possible, we should use the median to represent the data. Those errors, that is, those deviations of the data from the model value, can help us describe the spread. The graphs below display the deviations for both Sets A and B. Does it appear that there is more error or deviation for one of the two sets?

In the graphs of each set below, the model line has been set at the median. Note how the deviations from the model or errors, represented by the red lines, are much greater for Set B than for Set A.

Let's take a closer look at the deviations themselves. In the table below, the "Deviation" column is the absolute difference between the data value and the median. The deviation is the length of the red bar in the graph above when the model line is at the median.

Set A Set B

Data Median Deviation Data Median Deviation

10 12 2 4 12 8

14 12 2 20 12 8

9 12 3 3 12 9

13 12 1 19 12 7

8 12 4 2 12 10

12 12 0 12 12 0

13 12 1 19 12 7

12 12 0 18 12 6

7 12 5 1 12 11

14 12 2 20 12 8

13 12 1 19 12 7

14 12 2 20 12 8

12 12 0 6 12 6

11 12 1 5 12 7

11 12 1 5 12 7

Just as we wanted to know in Chapter 3 what the typical data value was, here we want to know what the typical deviation is. On the next page we will find the typical deviation for Set A and for Set B.