MAD - on average, how far away are the numbers from their average
Mean - average
If we say how far away something is, we are talking about its distance. Distance is always positive so this is where the absolute comes from (remember absolute value?).
Deviation means that if something deviates from the norm then it is not the same as the norm. This goes along with the step for finding the distance of each data value from the mean, where the mean is the norm.
1) Find the average of the data.
2) Find the distance of each of the data values from the average found in step 1. (Use the absolute value to make sure all the answers are positive.)
3) Find the average of the distances found in step 2.
Example: 1, 2, 3, 4, 5, 6
1) Mean is 21/6 = 3.5
2) Distances = 2.5, 1.5, .5, .5, 1.5, 2.5
3) Mean of distances will give the MAD = 9/6 = 1.5
This means that the average distance of the data points from their average is 1.5, which shows that the mean is a good measure of center since the MAD is relatively low.
However, if you have data with an outlier in it, the mean will have a big MAD showing that the mean is not a good measure of center. In these cases you will want to use the median since the median finds the middle of the data and ignores any outliers.