# Mean Absolute Deviation¶

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

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.