The average value of a function over a region provides the "most common" value of the function over that region. Typically this is calculated using integrals, the equation is a generalization of the mean for a uniform distribution as each value in the range is equally likely.

Generally given a function and a region the average value can be calculated as

For a single dimensions the function over a region can be calculated as

or for three dimensions the function over a region can be calculated as