Definition:Mean Absolute Deviation

Definition

Let $S = \set {x_1, x_2, \ldots, x_n}$ be a set of observations.

Let $\bar x$ denote a measure of central tendency of $S$.

The mean absolute deviation with respect to $\bar x$ of $S$ is defined as the arithmetic mean of the absolute values of the deviation of the elements of $S$ from $\bar x$ :

$\ds \sum_{i \mathop = 1}^n \dfrac 1 n \size {x_i - \bar x}$

Discrete Random Variable

Let $X$ be a discrete random variable.

Let $\bar x$ denote a measure of central tendency of $X$.

The mean absolute deviation of $X$ is the first absolute moment of $X$ about $\bar x$.

Continuous Random Variable

Let $X$ be a continuous random variable.

Let $m$ denote the median of $X$.

Let the frequency function of $X$ be $f$.

The mean absolute deviation of $X$ is defined as:

$\ds \int_{-\infty}^{+\infty} \size {x - m} \map f x \rd x$

Also see

• Results about mean absolute deviation can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): mean absolute deviation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): mean absolute deviation