Mean Absolute Deviation

Mean Absolute Deviation

FIRST, LETS PRACTICE FINDING A MEAN!

Poll

What is the average (mean) of these 3 numbers?

5, 78, 24

• 107

• 35.666

• 37.42

Poll

What is the average (mean) of these 3 numbers?

58, 3, 94

• 51.666

• 64

• 59.333

Poll

What is the average of these 5 numbers?

3, 7, 1, 6, 8

• 6

• 6.2

• 5

Poll

What is the mean??

10, 20, 30, 40, 50, 60, 70

• 30

• 40

• 50

Now lets talk about Mean Absolute Deviation

Why??

• Think about our last test... What was your grade? What was the class average? How far away from the class average was your score? How far away from the class average was everyone else?

MAD MEASURES CENTRAL TENDENCY

MAD helps us to measure central tendency. In other words, how likely a number is to being close to the mean of the set. If the MAD is small, then most people in the class will get around the same score. For example, everyone scoring around an 80. If MAD is larger, then the scores are spread across a larger range. Some people in the class may have failed. Others may have gotten all of them right.

To find mean absolute deviation:

• Calculate the mean of the set

• Find the distance that each number in the set is from the mean and write the differences (deviations) in a list.                                                                                                                                                                  *NOTE- This value needs to be positive because it is the absolute value of the deviation. It does not matter if the values are above or below the mean. This distance will always be postive.                                                             

• Calculate the mean of the deviations.

  
  
  
  

An example:  Find the mean standard deviation of this number set-   4, 9, 12

• Step 1- Find the mean of the number set

• Step 2- Go through each number and find how far away each one is from the mean by subtracting. List them. This is called deviation.
  

• Step 3- Take the mean of the deviations

• Answer- Approximately 2.87

Multiple Choice

Find the mean standard deviation of the following number set:

60, 58, 54, 56, 63, 65

• 3.54

• 6.87

• 2.54

• 3.33