Mean Absolute Deviation

1. Mean Absolute Deviation Otherwise known as MAD

2. MAD—what is it? • Mean Absolute Deviation is used to find out how much data varies from the mean of that data set. • So its not just finding the mean once, its kind of like finding the mean of the mean (you’ll see what this means in a second). • The answer will always be one number. • Outliers do not have a big impact on the MAD.

3. MAD-what does it mean? • The higher the MAD, the greater variability there is in the data (variability is how spread out or how clustered a group of data is). • High variability means the data is really spread out. • Low variability means the data is really close together.

4. MAD-how do you find it? • This calculation has 3 steps to it. • We will slowly walk you through each step using this problem: • Sara took 6 tests last quarter. Her 6 test scores are 93, 84, 72, 65, 77, and 89 percents.

5. Sara took 6 tests last quarter. Her 6 test scores are 93, 84, 72, 65, 77, and 89 percents. • Step 1.) Find the mean of the data. • Add up 93 + 84 + 72 + 65 + 77 + 89 • You should get 480 • Divide 480 by 6 since there are 6 tests. • You should get 80. • So the 1st mean is 8o. Don’t forget this!

6. Sara took 6 tests last quarter. Her 6 test scores are 93, 84, 72, 65, 77, and 89 percents. • Step 2.) Find out how far away each piece of data is from the 1st mean (which was 80, remember?) Hint: You can do this step by using subtraction!

7. Sara took 6 tests last quarter. Her 6 test scores are 93, 84, 72, 65, 77, and 89 percents. • Last step…finally!  • Now you find the mean AGAIN, this time of the new numbers from step 2. Find Mean

8. You are done! • So the Mean Absolute Deviation of Sara’s test scores is 8.67. • This means (no pun intended) that the average distance each of Sara’s test scores is away from the original mean of 80 is 8.67 percentage points.

9. Your turn…  • Use the chart we provided to help you organize your work when finding the MAD of your Graph It survey data.