Returns the sample median of absolute deviation (MAD).

## Syntax

**MAD**(**X**)

- X
- is the input data sample (one/two-dimensional array of cells (e.g., rows or columns))

## Remarks

- 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.
- The median of absolute deviation (MAD) is defined as follows:

$$\operatorname{MAD} = \operatorname{median}_{i}\left(\ \left| X_{i} - \operatorname{median}_{j} (X_{j}) \right|\ \right)$$ - In short, starting with the deviations from the data's median, the MAD is the median of their absolute values.
- The median of absolute deviation (MAD) is a measure of statistical dispersion.
- MAD is a more robust estimator of scale than the sample variance or standard deviation.
- MAD is especially useful with distributions that have neither mean nor variance (e.g., the
**Cauchy distribution**). - MAD is a robust statistic because it is less sensitive to outliers in a data series than the standard deviation.

## Files Examples

## Related Links

## 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.

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