1. Statistics
Mean Absolute
Deviation

2. Vocabulary Mean Absolute Deviation (MAD)
the average distance of data values from the mean

3. What is the Mean Absolute Deviation
of the data set:
3, 7, 10, 13, 17
Step 1: Find the mean of the data:
( ) / 5 = 10
Mean of these numbers = 10

4. Step 2: Find the deviations (distance)
of each value to the mean of the data:
Value
Mean
Deviation 3 7 10 13 17 10 7 10 3 10 10 3 10 7

5. Step 3: Find the mean (average) of the deviations:
Value
Mean
Deviation 3 7 10 13 17 10 7 10 3 10 10 3 10 7
= 20 ÷ 5 = 4

6. All the values, are, on average, 4 away from the mean
Step 4: Analysis
Mean Absolute Deviation = 4
All the values, are, on average, 4 away from the mean

7. What is the Mean Absolute Deviation
of the data set:
0, 1, 5, 7, 11, 12, 20
Step 1: Find the mean of the data:
( ) ÷ 7 = 8
Mean of these numbers = 8

8. Step 2: Find the deviations (distance)
of each value to the mean of the data:
Value
Mean
Deviation 1 5 7 11 12 20 8 8 8 7 8 3 8 1 8 3 8 4 8 12

9. Step 3: Find the mean (average) of the deviations:
Value
Mean
Deviation 1 5 7 11 12 20 8 8 8 7 8 3 8 1 8 3 8 4 8 12
= 38 ÷ 7 = 5.4

10. All the values, are, on average, 5.4 away from the mean
Step 4: Analysis
Mean Absolute Deviation = 5.4
All the values, are, on average, 5.4 away from the mean

11. The owner of a basketball team wants to trade for a player that is consistent. The average points per game scored by 2 players over the last season are listed below. Which player should the owner choose?
Oct
Nov
Dec
Jan
Mar
Apr
Player A 25 22 24 28 30 27
Player B 20 32 29 11

12. Step 1 – Find the mean of both data sets
Oct
Nov
Dec
Jan
Mar
Apr
Player A 25 22 24 28 30 27
Player B 20 32 29
Player A: =
156
÷6 = 26
Player B: =
156
÷6 = 26 12

13. Step 2 – Subtract each time from the Mean.
Player A
Player B
Avg Pts
Mean
Deviation 25 26 22 24 28 30 27
Avg Pts
Mean
Deviation 22 26 20 25 28 32 29 1 4 4 6 2 1 2 2 4 6 1 3 13

14. Step 3: Find the mean of the Deviations
Player A
Player B
Deviation
Deviation 4 1 6 4 2 1 2 2 6 4 1 3 14
÷ 6
= 2.3 22
÷ 6
= 3.7 14

15. Player A MAD = 2.3 MAD = 3.7 Step 4 – Analysis Player B Player A
Which player
Should he
choose?
Player A
MAD = 2.3
MAD = 3.7 15

16. Which city should she pick?
Maria has a condition where large swings in temperature are detrimental to her health. She is trying to decide what would be the perfect city for her to move to. Below are the average temperatures for September through May for 2 different cities:
Sept
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
City A 65 61 50 35 23 29 39 52
City B 72 70 60 54 58 59 63 67
Which city should she pick?

17. Step 1 – Find the mean of both data sets
City A 65 61 50 35 23 29 39 52
City B 72 70 60 54 58 59 63 67
City A: =
419
÷9 =
46.6
City B: =
573
÷9 =
63.7 17

18. Step 2 – Subtract each time from the Mean.
City A
City B
Temp
Mean
Deviation 65
46.6 61 50 35 23 29 39 52
Temp
Mean
Deviation 72
63.7 70 60 54 58 59 63 67
18.4
8.3
14.4
6.3
3.4
3.7
11.6
9.7
23.6
5.7
17.6
4.7
7.6
0.7
5.4
3.3
18.4
6.3 18

19. Step 3: Find the mean of the Deviations
City A
City B
Deviation
Deviation
8.3
18.4
6.3
14.4
3.4
3.7
11.6
9.7
23.6
5.7
17.6
4.7
7.6
0.7
5.4
3.3
18.4
6.3
120.4
÷ 9
= 13.4
48.7
÷ 9
= 5.4 19

20. City B MAD = 13.4 MAD = 5.4 Step 4 – Analysis City A City B Which city
should
Maria choose?
City A
City B
City B
MAD = 13.4
MAD = 5.4 20