The mean absolute deviation (MAD) is a way to measure how spread out the values are in a set of data. It tells us on average how far each data value is from the average of all the data values.
To find the MAD, we take the absolute value (ignoring negative or positive signs) of each difference between a data value and the average, and then we take the average of those absolute differences.
For example, let’s say we have a set of data on the number of hours students study for a test: 4, 5, 6, 7, 8. The average is 6, so we subtract 6 from each data value to find the difference: -2, -1, 0, 1, 2. Then, we take the absolute value of each difference: 2, 1, 0, 1, 2. The average of those absolute differences is the MAD, which in this case is 1.2.
The MAD is useful because it gives us an idea of how spread out the data values are from the average. A small MAD means the data values are closer together, while a large MAD means the data values are farther apart.