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FIND MEAN ABSOLUTE DEVIATION

You have used range and the interquartile range to describe the spread of a set of data. You can also use the mean absolute deviation. The mean absolute deviation of a set of data is the average distance between each data value and the mean.

EXAMPLE

The Table shows the maximum speeds of eight roller coasters. Find the mean absolute deviation of the set of data. Describe what the mean absolute deviation represents.

Maximum speeds of roller coaster (MPH)

58 88 40 60

72 66 80 48

STEP 1

Find the mean = = 64

STEP 2

Find the absolute value of the difference between each value in the data set and the mean. (How far each number or piece of data is from the mean.)

This gives us the absolute value (how far each number is from the mean)

Mind the absolute value

64 – 58 = 88 – 64 = 64 – 40 = 64 – 60 =

72 – 64 = 66 – 64 = 80 – 64 = 64 – 48 =

Absolute Value

6 24 24 4

8 2 16 16

STEP 3

Find the average of the absolute values of the differences between each value in the data set and the mean.

= 12.5The mean absolute deviation is 12.5.

STEP 4 (DESCRIBE OR INTERPRET DATA)

This means that the average distance each data value is from the mean is 12.5 miles per hour.

YOUR TURN

The table shows speeds of ten birds. Find the mean absolute deviation of the data. Round to the nearest whole number. Describe what the mean absolute deviation represents.

What is the first Step?

Speeds of Top Ten Fastest Birds (mph)

88 77 65 70 65

72 95 80 106 68

STEP 1 FIND THE MEAN

=

=

The mean is 78.8

or 79

What is the next step?

STEP 2 FIND THE ABSOLUTE VALUE

Find the absolute value of the difference between each value in the data set and the mean. (How far each number or piece of data is from the mean.)

What is the next step?

Absolute Value

88 – 79 = 9 79 – 77 = 2 79 – 65 = 14

79 – 70 = 9 79 – 65 = 14

79 – 72 = 7 95 – 79 = 16

79 – 80 = 19

106 – 79 = 27

79 – 68 =11

STEP 3 FIND THE MEAN ABSOLUTE DEVIATIONFind the average of the absolute values of the differences

between each value in the data set and the mean.

=

12.2 or

The mean absolute deviation is 12