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 standard deviation.
Examples
Example 1:
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Formula | Description (Result) |
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=MAD($B$2:$B$30) | Median of absolute deviation (1) |
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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