Mean Absolute Value

The mean absolute value of real data , ..., is the arithmetic mean of their absolute values,

(1)

for . It is also called the average rectified value (Aarts 2021, p. 87).

For a real random variable , the mean absolute value is the first absolute moment about zero,

(2)

provided this expectation value is finite (Geary 1947, p. 219). The mean deviation is obtained by first subtracting the mean from . These quantities agree when the mean is zero.

For a real function on an interval with , the mean absolute value is

(3)

when the integral is finite. The ratio of the root-mean-square to the mean absolute value is the form factor.