What does mean absolute deviation (mad) measure? explain how to find the mad for a set of data.

Mean Absolute Deviation is a quantity of measurement that gives you an idea how far, on average, are the data points deviating from the mean. Its equation is

MAD = ∑|x - μ| /  N, where

x is a single data point
μ is the mean of the data set
N is the total number of data points

Suppose, a data set consist of the following: 4, 7, 5, 9, 6, 7, 7, 4. Let's solve first for the mean:

μ = (4+7+5+9+6+7+7+4)/8 = 6.125

Then, the MAD is equal to:

MAD = (|4 - 6.125| + |7 - 6.125| +|5 - 6.125| +|9 - 6.125| +|6 - 6.125| +|7 - 6.125| +|7 - 6.125| +|4 - 6.125|) ÷ 8
MAD = 11/8
MAD = 1.375