# MAD - Median of Absolute Deviation

Returns the sample median of absolute deviation (MAD).

## Syntax

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

## Remarks

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.

## Examples

Example 1:

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A B
Date Data
1/1/2008 #N/A
1/2/2008 -1.28
1/3/2008 0.24
1/4/2008 1.28
1/5/2008 1.20
1/6/2008 1.73
1/7/2008 -2.18
1/8/2008 -0.23
1/9/2008 1.10
1/10/2008 -1.09
1/11/2008 -0.69
1/12/2008 -1.69
1/13/2008 -1.85
1/14/2008 -0.98
1/15/2008 -0.77
1/16/2008 -0.30
1/17/2008 -1.28
1/18/2008 0.24
1/19/2008 1.28
1/20/2008 1.20
1/21/2008 1.73
1/22/2008 -2.18
1/23/2008 -0.23
1/24/2008 1.10
1/25/2008 -1.09
1/26/2008 -0.69
1/27/2008 -1.69
1/28/2008 -1.85
1/29/2008 -0.98

Formula Description (Result)
=MAD($B$2:$B$30) Median of absolute deviation (1)