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.