Mean Absolute Deviation

To avoid the problem of positive and negative deviations canceling out each other, we can use the Mean Absolute Deviation which is given by

Here

=

if

and

=

Although Mean Absolute Deviation avoids the problem of positive and negative deviations canceling out, it is not popular in practice. This is because it neglects the difference between positive and negative deviations although the positive and negative signs are considered in calculating the mean which in turn is used to calculate the deviations. Further, it is difficult to deal with the quantity   algebraically.