Mean Absolute Deviation Statistics. 2 Vocabulary Mean Absolute Deviation (MAD) – the average...

Mean AbsoluteDeviation

Statistics

2

Vocabulary

Mean Absolute Deviation (MAD) – the average distance of data values from the mean

3

Example

3, 7, 10, 13, 17

What is the Mean Absolute Deviation of the data set:

4

Example

(3+7+10+13+17) / 5 = 10

Mean of these numbers is 10

Step 1: Find the mean of the data:

5

ExampleStep 2: Find the deviations (distance) of each value to the mean of the data:

Value Mean Deviation

3 10

7 10

10 10

13 10

17 10

7

3

0

3

7

6

ExampleStep 3: Find the mean (average) of the deviations:


3 10 7

7 10 3

10 10 0

13 10 3

17 10 7

7 + 3 + 0 + 3 + 7 = 20 / 5 = 4

7

ExampleSo, the Mean Average Deviation

= 4 What does this mean?

All the values, are, on average, 4 away from the mean

8

Example

0, 1, 5, 7, 11, 12, 20

What is the Mean Average Deviation of the data set:

9

Example

(0+1+5+7+11+12+20) = 56 / 7 = 8

Mean of these numbers is 8

Step 1: Find the mean of the data:

10

ExampleStep 2: Find the deviations (distance) of each value to the mean of the data:


0 8

1 8

5 8

7 8

11 8

12 8

20 8

8

7

3

1

3

4

12

11

ExampleStep 3: Find the mean (average) of the deviations:

8+7+3+1+3+4+12 = 38 / 7 = 5.4


0 8 8

1 8 7

5 8 3

7 8 1

11 8 3

12 8 4

20 8 12

12

ExampleSo, the Mean Average Deviation

= 5.4 What does this mean?

All the values, are, on average, 5.4 away from the mean

13Copyright © 2013 by Monica Yuskaitis

Bus Routes


Parents were complaining that their children were getting off the bus at different times every day, so the director decided to collect data to see whose times varied the most. He had two different drivers record the time it took to complete their bus routes for 5 days. Each had the same route but on different days.

Other Things You Should Be Aware of When Displaying Your Data

Copyright © 2013 by Monica Yuskaitis 15

Number of Observations 5

How it was measured Record Time elapsed on Bus route

Unit of Measurement Minutes

Nature of attribute Times to complete bus route

Overall Pattern To be seen


Here were the times in minutes for bus driver A and bus driver B:

A 55 45 60 59 50

B 54 52 51 56 55

Find the mean absolute deviation for each driver and compare as to which

driver’s times varied the most.


Step 1 – Find the mean of both sets of data.

A 55 45 60 59 50

B 54 52 51 56 55A5545605950+

269

B5452515655+

268/ 5 = 54 / 5 = 54


Step 2 – Subtract each time from the Mean. (Make a table to keep track.)

Time Mean Deviation

55 54

45 54

60 54

59 54

50 54

Driver A

1

96

5

4


Step 2 – Subtract each time from the Mean. (Make a table to keep track.)

Time Mean Deviation

54 54

52 54

51 54

56 54

55 54

Driver B

1

2

32

0


Step 3 – Find the mean of the Deviation Values

Deviation

1

9

6

5

4

Driver A Driver BDeviation

0

2

3

2

1

25 /5 = 5 8 = 1.6 /5


Step 4 – Compare the Mean Absolute Deviation Scores

Driver A Driver B

MAD = 5 MAD = 1.6

Which bus driverdid the director

need to reprimand?

Driver A

22Copyright © 2013 by Monica Yuskaitis 22Copyright © 2013 by Monica Yuskaitis

The owner of a drive-in wanted to make sure the customers were getting the same

amounts in their smoothies. So he had the waiters weigh and record the weight of each smoothie they made for 7 times.

Other Things You Should Be Aware of When Displaying Your Data

Copyright © 2013 by Monica Yuskaitis 23

Number of Observations 7 per waiter

How it was measured Weighed

Unit of Measurement Ounces

Nature of attribute Finding the Weight of smoothies

Overall Pattern To be seen

24Copyright © 2013 by Monica Yuskaitis 24Copyright © 2013 by Monica Yuskaitis

Here are the weights of the smoothies in ounces from waiter A and waiter B.

A 16.1 15.9 16 15.8 16.2 16.1 15.8

B 15.7 16.4 15.6 16.5 15.9 16.8 15.3

2525

How to Find the Mean Absolute Deviation

Step 1 – Find the mean weight from each waiter.

A16.115.916. 15.816.216.115.8+

B15.716.4

15.6 16.515.916.815.3+

.9

7)111.9

15.9

7)112.2

1 .16 6 0 16

111 211 .2


26

How to Find the Mean Absolute DeviationStep 2 – Subtract Each Weight from the

Mean. (Make a table to keep track.)Weight Mean Deviation

16.1 16

15.9 16

16 16

15.8 16

16.2 16

16.1 16

15.8 16

Wai

ter

A

.1

.1

0.2.2

.1

.2


27

How to Find the Mean Absolute DeviationStep 2 – Subtract Each Weight from the

Mean. (Make a table to keep track.)Weight Mean Deviation

15.7 16

16.4 16

15.6 16

16.5 16

15.9 16

16.8 16

15.3 16

Wai

ter

B

.3.4

.4

.5.1.8

.7


28

How to Find the Mean Absolute DeviationStep 3 – Find the mean of the deviations

Deviation.1

.1

0

.2

.2

.1

.2Wai

ter

A

Deviation.3

.4

.4

.5

.1

.8

.7Wai

ter

B0.9 /7 = 0.13 3.2 /7 = 0.46


How to Find the Mean Absolute DeviationStep 4 – Compare the Mean Absolute

Deviation scores.Waiter A Waiter B

MAD = .13 MAD = .46

Which waiterhas the leastamount ofvariance inpreparing

smoothies?

Waiter A

Mean Absolute Deviation Statistics. 2 Vocabulary Mean Absolute Deviation (MAD) – the average...

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