Mean Absolute Deviation

You  will  learn  how  to  calculate  the  Mean  Absolute  Deviation  (MAD)  of  a  Data  Set  

 http://www.mathsisfun.com/data/mean-­‐deviation.html    

The mean absolute deviation is a measure that indicates by how much each data point in a data set differs from the mean of the data set.

Class 1 Class 2 100 100 100 90 100 90 100 85 90 80 60 75 60 70 60 70 50 60 50 50

Class 1 Class 2 100 100 100 90 100 90 100 85 90 80 60 75 60 70 60 70 50 60 50 50

What is the sum of class 1?

What is the mean for class 1?

What is the sum of class 2?

How many kids are in each class?

What is the mean for class 2?

10

770

770

77

77

Class 1 Class 2 100 100 100 90 100 90 100 85 90 80 60 75 60 70 60 70 50 60 50 50

What is the range of class 1?

What is the median of class 2

What is the median of class 1?

What is the range for class 1?

What is the mode for class 1?

50

50

75

77.5

100 What is the mode for class 2? 70 & 90

x

x

x x

x x x

x x x x

x x

x x x x x x x x 50  60 70 80 90 100

Class 1 50  60 70 80 90 100

Class 2

Let’s compare the line plots & data. Talk in your prides about what’s happening in both line plots!

Mean = 77 Range = 50

Mean = 77 Range = 50

X

X

X X

X X X

X X X X

Even though their means and ranges are equal, the distributions of scores in Classes 1 and 2 are quite different.

50  60 70 80 90 100

Class 1

Most of the scores in Class 1 are either much higher or much lower than the mean.

In contrast, most of the scores in Class 2 are closer to the mean

A measure that shows the difference between these distributions is called the Mean Absolute Deviation a.k.a. MAD.

x x

x x x x x x x x

50  60 70 80 90 100

Class 2

Class 1 100 100 100 100 90 60 60 60 50 50

1) Calculate the mean for class 1… 77.

2) Subtract the mean from each data point. This number is the deviation. 100-77=23 100 – 77 = 23 90 – 77 = 60 – 77 = 50 – 77 =

To find the MAD, subtract the mean from the value and use the absolute value because distance cannot be negative.

13 -17 -27

Class 1 100 100 100 100 90 60 60 60 50 50

3. Take the absolute value of each number from step 2. This is called the absolute deviation.

100 – 77 = 90 – 77 = 60 – 77 = 50 – 77 =

|13| |-17| |-27|

|23|

The distance of a number from zero. Distance can NEVER be negative.

= 23 = 13 = 17 = 27

What is absolute value?

4. Calculate the mean (average) of the numbers found in step 3. This is the mean absolute deviation aka MAD.

Class 1 Absolute Deviation

100 23 100 23 100 23 100 23 90 13 60 17 60 17 60 17 50 27 50 27

Mean: 77 Mean: 21 = MAD

Data sets with small variations have a low MAD. Data sets with large variations have a higher MAD.

Find  the  mean  absolute  deviation  of  the  following  data  set:  

Bowling  scores:    90,    85,    95  

3550 ++

Mean = 90+85+ 953

= 90

Deviations: Absolute Deviation: Mean Absolute Deviation

90 – 90 = 0 = |0| 0 MAD = 10 ÷ 3 =

85 – 90 = -5 = |-5| 5

95 – 90 = 5 = |5| 5

313