Arithmetic mean of the deviations from the mean of the data in a distribution of a statistical variable.

### Notation

The mean deviation of a statistical distribution is generally noted as: **MD**.

### Formules

- In a statistical distribution of
*n*data (sample) with a mean of \(\overline{x}\), the mean deviation MD is given by:

MD \(\dfrac{\Sigma |x_i − \overline{x} |}{n}\).

- In a statistical distribution with
*N*data values representing an entire population in which the mean is \(μ\), the mean deviation MD is given by:

MD = \(\dfrac{\Sigma |x_i − μ |}{N}\).

### Example

Consider this data set: {3, 5, 9, 11, 12}.

The mean is 8 and the number of results is 5.

Therefore: (8 – 3) + (8 – 5) + (9 – 8) + (11 – 8) + (12 – 8) = 16 and 16 ÷ 5 = 3.2.

The mean deviation is: MD = 3.2.