Mean Absolute Deviation

The mean absolute deviation provides the absolute value of the average difference between the data values and the mean.

It is calculated as the sum of the absolute deviations from the mean divided by the sample size.

For example, three students have three, five, and seven cookies in their lunch boxes. The deviations in the number of cookies from the mean of five cookies are minus 2, zero, and two.

If one adds these deviations, the positive and negative values cancel each other out, giving a zero mean deviation, which is unhelpful. If the absolute values are added, one obtains a single non-zero value instead.

This value, when divided by the sample size, gives the mean absolute deviation.

Calculating the mean absolute deviation involves a non-algebraic modulus operation, while the standard deviation uses algebraic operations. Therefore it is not suitable for inferential statistics.

It is also a biased statistic, as the calculated mean absolute deviation of a sample does not adequately represent the population mean absolute deviation.