1. Using Mean Absolute Deviation
Comparing Sets of Data
Using Mean Absolute Deviation
UNIT EQ: What inferences can be made from data collection?

2. Mean Absolute Deviation
The mean absolute deviation, or MAD,
of a numerical data set is the average
deviation of the data from the mean.

3. What does Mean Absolute Deviation (MAD) tell us about a data set?
How spread out the data is
How far the numbers in a data set are from the mean
If a data set has an outlier
If the mean is relevant for the data set

4. What can I infer about Terry MS’s book club?
Look at this dot plot. 6 6 6
What can I infer about Terry MS’s book club?

5. Now, look at this dot plot.6 6 6
What can we infer about Lamar MS’s book club? Does it look the same as Terry MS’s data?

6. 6 6 6 MAD= .6 What does the MAD tell about a set of data? 1 1 1 1 1 11 1 1 6 6 6
MAD= .6
Draw a line through the plots that represent the mean.
Above each data point write the deviation from the mean.
Find the mean of the deviations.

7. Draw a line through the plots that represent the mean.
Do you think the MAD will be larger or smaller for this set of data? Why? 7 6 4 5 3 6 3 6 6 6
MAD = 3.4
Draw a line through the plots that represent the mean.
Above each data point write the deviation from the mean.
Find the mean of the deviations.

8. What does MAD tell us?
The MAD can tell us if the mean is relevant for a set of data.
A LARGE MAD indicates the mean is NOT relevant.
The items in the data set are farther away from the mean.
The items in the data set are MORE spread out.
A SMALL MAD indicates the mean IS relevant.
The items in the data set are closer to the mean.
The items in the data set are LESS spread out.

9. Finding Mean Absolute Deviation
1. Find the mean of the data.
Subtract the mean from each value –
the result is called the deviation from
the mean.
Take the absolute value of each
deviation from the mean.
4. Find the sum of the absolute values.
5. Divide the total by the number of items.

10. Find the mean absolute deviation:
Test scores for 6 students were : 85, 92, 88, 80, 91 and 20.
Find the mean:
( )/6=76
2. Find the deviation from the mean:
85-76= = =12
80-76= = =-56

11. Find the mean absolute deviation:
Test scores for 6 students were :
85, 92, 88, 80, 91 and 20.
3. Find the absolute value of each deviation from the mean:

12. Find the mean absolute deviation
Test scores for 6 students were :
85, 92, 88, 80, 91 and 20.
4. Find the sum of the absolute values:
= 112
5. Divide the sum by the number of data items:
112/6 = 18.7
The mean absolute deviation is 18.7.

13. Find the mean absolute deviation
Test scores for 6 students were : 85, 92, 88, 80, 91 and 74.
Find the mean:
( )/6=85
2. Find the deviation from the mean:
85-85= = =3
80-85= = =-11

14. Find the mean absolute deviation
Test scores for 6 students were :
85, 92, 88, 80, 91 and 74.
3. Find the absolute value of each deviation from the mean:

15. Find the mean absolute deviation
Test scores for 6 students were :
85, 92, 88, 80, 91 and 74.
4. Find the sum of the absolute values:
= 32
5. Divide the sum by the number of
data items:
32/6 = 5.3
The mean absolute deviation is 5.3.

16. Which girl had the greater mean deviation for her scores?
Emma and Sara play 5 games on a handheld video game and record their scores in this table.
Game
Emma
Sara 1 30 15 2 20 25 3 10 4 5
Which girl had the greater mean deviation for her scores?

17. First, let’s look at Emma’s scores
Game
Emma 1 30 2 20 3 10 4 5
Find the mean
Find the deviation form the mean
Take the absolute value of each deviation
Find the sum of the absolute values
Divide the sum but the number or items

18. Now, Let’s look at Sara’s Scores
Find the mean
Find the deviation form the mean
Take the absolute value of each deviation
Find the sum of the absolute values
Divide the sum by the number or items
Game
Sara 1 15 2 25 3 20 4 5

19. Now let’s compare the deviations:
What was the MAD of Emma’s scores?
What was the MAD of Sara’s scores?
What do the MAD’s tell us about Emma’s & Sara’s scores?
For which girls’ scores was the mean MOST relevant?
Which girl had the most consistent scores?
Which girls’ scores had the greatest variability?

20. Your turn: Daily Tips
Two friends, Greg and Trent, work at different restaurants.
They have compared their average incomes and feel that they are very similar.
Greg
Trent
$15
$20
$24
$22
$26
$18
$17
What is Greg’s mean tip money?
What is Trent’s mean tip money?
What is the mean of the combined tip money?
Your task is to examine the Mean Absolute Deviation
of each set of data and decide which restaurant would
likely yield the most consistent tips.

21. Daily Tips What is MAD of the combined tip money? What is Trent’s MAD?
What is Greg’s MAD?
Greg
Trent
$15
$20
$24
$22
$26
$18
$17

22. Daily Tips Whose MAD is closer to the MAD of the combined tip money?
What does this piece of information tell us?
Greg
Trent
$15
$20
$24
$22
$26
$18
$17