MAD - Median of Absolute Deviation

1. The input data series may include missing values (e.g. #N/A, #VALUE!, #NUM!, empty cell), but they will not be included in the calculations.
2. The median of absolute deviation (MAD) is defined as follows:
   
   $$\operatorname{MAD} = \operatorname{median}_{i}\left(\ \left| X_{i} - \operatorname{median}_{j} (X_{j}) \right|\ \right)$$
3. In short, starting with the deviations from the data's median, the MAD is the median of their absolute values.
4. The median of absolute deviation (MAD) is a measure of statistical dispersion.
5. MAD is a more robust estimator of scale than the sample variance or standard deviation.
6. MAD is especially useful with distributions that have neither mean nor variance (e.g. the Cauchy distribution.)
7. MAD is a robust statistic because it is less sensitive to outliers in a data series than standard deviation.

Example 1:

Related Links

• Wikepedia - Median absolute deviation

References

• Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740