Mean Absolute Deviation

Global Algorithm - One-Dimensional Algorithm

Mean Absolute Deviationalgorithm is commonly used as a robust measure of the variability of data. The basic formulat is stated as follows:

$$\text{MAD} = \text{Median}[(|Y_1-\text{Median}(Y)|, |Y_2-\text{Median}(Y)|, \ldots, |Y_N-\text{Median}(Y)|)^T \, \text{,}$$

where $Y_i$ denotes the $i$th element of the input data vector $Y$. $|\cdot|$ returns the absolute value and $T$ denotes the transpose of the vector. Median algorithm returns the Median value of $Y$.

Input Parameters

Parameter	Type	Constraint	Description	Remarks
$Y$	$Y \in \mathbb R^N$	$N \in \mathbb{N}$	Input data vector of length $N$

Output Parameters

Parameter	Type	Constraint	Description	Remarks
$\text{MAD}$	$\text{MAD} \in \mathbb R$

Tool Support

• Matlab

  For details refer to the online documentation of the function ‘mad’.

Single Steps using the Algorithm

• Variance Estimation with Mean Absolute Deviation (MAD)

References

• F. Mosteller, J. Tukey, Data Analysis and Regression, Upper Saddle River, NJ: Addison-Wesley, 1977.
• L. Sachs, Applied Statistics: A Handbook of Techniques, New York: Springer-Verlag, 1984.