Signed Deviation

The signed deviation is defined by

$$\Delta u_i \equiv (u_i - \bar u),$$

so the average deviation is

$$\overline {\Delta u} = \overline {u_i-\bar u} = \overline {u_i}- \bar u = 0.$$

See also Absolute Deviation, Deviation, Dispersion (Statistics), Mean Deviation, Quartile Deviation, Standard Deviation, Variance