In statistics the absolute deviation is a measure of how much a particular sample deviates from the average sample.
First we must find the average sample. There are three different ways this can be done. The first is by finding the mean. To find the mean add together all of the samples and divide by the number of samples. For example if your samples are 2, 2, 4, 5, 5, 5, 9, 10, 12 you would add them and get a total of 54. Then divide by the number of samples (9) and you would calculate a mean of 6.
The second method of calculating the average is by using median. Arrange the samples in order from lowest to highest, and find the middle number. From the sample above it would be 5.
The third method of calculating the average sample is by finding the mode. The mode is which ever sample occurs most. In the original case 5 occurs 3 times making it the mode.
Now we can calculate the absolute deviation. If we go to calculate the absolute deviation from the mean we take the mean average (6) and find the difference between it and a sample. If we take the first sample (2) and calculate the absolute deviation the result would be 4. For the last sample (12) the absolute deviation is 6. Note that it is always positive.
You can calculate the Average Absolute Deviation by finding the absolute deviation of each sample and averaging them.
If we take the original series: 2, 2, 4, 5, 5, 5, 9, 10, 12 we can calculate the absolute deviation from the mean for each sample since we know that the mean is 6. In the same order the absolute deviations of our samples would be 4,4,2,1,1,1,3,4,6. We can then take the average of these numbers and calculate the average absolute deviation as 2.888 . Which means the average sample is 2.888 from the mean.