Introduction to the Mean Absolute Deviation

Sibling Survey Kyan surveyed two groups of people. He asked them how many siblings they each had. Average (mean) number of siblings from the 1st group: Average (mean) number of siblings from the 2nd group : So was the data basically the same? 2 2

We’ll have to look at the data to be sure. Data from 1st group: 1, 2, 3, 2, 1, 2, 3, 2 Data from 2nd group: 0, 0, 5, 1, 4, 6, 0, 0 So was the data basically the same? No! The data from 2nd group was much more spread out from the mean.

The Mean Absolute Deviation (M. A. D The Mean Absolute Deviation (M.A.D.) is a measure of how spread out the data is from the mean. We call it a measure of variation, since it tells how much the data varies. mean mean mean mean

If there is a large variety of data, which is very spread out over a large range, the M.A.D. will be a greater number. Data with little variety, which isn’t as spread out, will have a lesser M.A.D. M.A.D. = 1.75 M.A.D. = 0.5

When you place Kyan’s sibling data on a dot plot, you get a visual representation of how the data varies. 1st Group 2nd Group mean mean

So, the 2nd group will have a greater M. A. D So, the 2nd group will have a greater M.A.D., which tells that the data is more spread out from the mean. 1st Group 2nd Group mean mean

So, how do we calculate the M.A.D.? Step 1: Step 2: Step 3: Find the mean. 1st group: 1 + 2 + 3 + 2 + 1 + 2 + 3 + 2 = 16 16 ÷ 8 = 2 Find each absolute distance from the mean. mean 0 steps 1 step 1 step 1 step 1 step Find the mean (average) of those distances. 1 + 1 + 0 + 0 + 0 + 0 + 1 + 1 = 4 4 ÷ 8 = 0.5 is the M.A.D.

What is the M.A.D. for the 2nd group? Step 1: Step 2: Step 3: Find the mean. 2nd group: 0 + 0 + 5 + 1 + 4 + 6 + 0 + 0 = 16 16 ÷ 8 = 2 Find each absolute distance from the mean. mean 2 steps 2 steps 2 steps 2 steps 1 step 2 steps 3 steps 4 steps Find the mean (average) of those distances. 2 + 2 + 2 + 2 + 1 + 2 + 3 + 4 = 18 18 ÷ 8 = 2.25 is the M.A.D.

So the 1st group had less variation, and we can calculate the M. A. D So the 1st group had less variation, and we can calculate the M.A.D. value of 0.5 to represent the variation of the data points compared to the mean. The 2nd group had more variation, and we can calculate the M.A.D. value of 2.25 to represent the variation of the data points compared to the mean.

Try one more… Calculate the Mean Absolute Deviation of this data set: Step 1: Find the mean. Tickets Purchased 3 9 2 4 8 6 5 3 + 9 + 2 + 3 + 4 + 8 + 6 + 5 = 40 40 ÷ 8 = 5

Step 2: Find each absolute distance from the mean. 2 steps 3 steps 2 steps 1 step 0 steps 1 step 3 steps 4 steps

Step 3: Find the mean (average) of those distances. 3 + 2 + 2 + 1 + 0 + 1 + 3 + 4 + = 16 16 ÷ 8 = 2

Now you know how to calculate the Mean Absolute Deviation! It’s a measure of variation, which tells how spread out the data is from the mean.

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