Mean Absolute Deviation Otherwise known as MAD

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.

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.

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.

So the 1st mean is 8o. Don’t forget this! 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!

Sara took 6 tests last quarter 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?) Original Test Score Distance Away from 80 93 13 84 4 72 8 65 15 77 3 89 9 Hint: You can do this step by using subtraction!

Sara took 6 tests last quarter 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. Add up 13+4+8+15+3+9 This equals 52 Divide 52 by 6 since there are 6 numbers This equals 8.67 (rounded) Distance Away from 80: 13 4 8 15 3 9 Find Mean

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.

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