# Mean Deviation

## Mean Deviation

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.