14.5 Mean Absolute Deviation AKA “MAD”

Mean Absolute Deviation…. The MAD is the average deviation from the mean. It is found by subtracting the mean from each value in the data set, taking the absolute value of those differences and then averaging all those positive differences. M - mean or average A – absolute value (positive numbers only) D – deviation means “difference between”

Step One – Find the Mean = 440/5=88 Data points Subtract the mean from each point Value - Mean= Take the absolute value of each number in previous column (make them all positive) 100 85 95 90 70 Find mean. = 440/5=88

Step Two – Find the difference between each data point and the mean Data points Subtract the mean from each point Value - Mean= Take the absolute value of each number in previous column (make them all positive) 100 100 – 88 = 85 85 – 88 = 95 95 – 88= 90 90 – 88 = 70 70 – 88 = Find mean. = 440/5=88 12 - 3 7 2 - 18

Step Three – Find the absolute value of each one of the differences. Data points Subtract the mean from each point Value - Mean= Take the absolute value of each number in previous column (make them all positive) 100 100 – 88 = 12 12 85 85 – 88 = - 3 3 95 95 – 88 = 7 7 90 90 – 88 = 2 2 70 70 – 88 = -18 18 Find mean. = 440/5=88

Step Four – Average those positive differences…. Data points Subtract the mean from each point Value - Mean= Take the absolute value of each number in previous column (make them all positive) 100 100 – 88=12 12 85 85 – 88 =-3 3 95 95 – 88 =7 7 90 90 – 88 = 2 2 70 70 – 88 = -18 18 Find mean. = 440/5=88 MAD = (12+3+7+2+18)/5 = 42/5 = 8.4

Now you try one… Find the MAD of the following set of data: 12, 11, 14, 17, 16, 22, 14, 10 Find the mean: Mean = 14.5 Subtract the mean from each number above: -2.5, -3.5, -0.5, 2.5, 1.5, 7.5, -0.5, -4.5 Take the absolute value of each number above: 2.5, 3.5, 0.5, 2.5, 1.5, 7.5, 0.5, 4.5 Find the mean of those numbers: 23/8 = 2.875 Mean Absolute Deviation