scipy.stats.median_absolute_deviation

scipy.stats.median_absolute_deviation(x, axis=0, center=<function median>, scale=1.4826, nan_policy='propagate')

Compute the median absolute deviation of the data along the given axis.

The median absolute deviation (MAD, [1]) computes the median over the absolute deviations from the median. It is a measure of dispersion similar to the standard deviation, but is more robust to outliers [2].

The MAD of an empty array is np.nan.

New in version 1.3.0.

Parameters

xarray_like

Input array or object that can be converted to an array.

axisint or None, optional

Axis along which the range is computed. Default is 0. If None, compute the MAD over the entire array.

centercallable, optional

A function that will return the central value. The default is to use np.median. Any user defined function used will need to have the function signature func(arr, axis).

scaleint, optional

The scaling factor applied to the MAD. The default scale (1.4826) ensures consistency with the standard deviation for normally distributed data.

nan_policy{‘propagate’, ‘raise’, ‘omit’}, optional

Defines how to handle when input contains nan. ‘propagate’ returns nan, ‘raise’ throws an error, ‘omit’ performs the calculations ignoring nan values. Default is ‘propagate’.

Returns

madscalar or ndarray

If axis=None, a scalar is returned. If the input contains integers or floats of smaller precision than np.float64, then the output data-type is np.float64. Otherwise, the output data-type is the same as that of the input.

See also

numpy.std, numpy.var, numpy.median, scipy.stats.iqr, scipy.stats.tmean, scipy.stats.tstd, scipy.stats.tvar

Notes

The center argument only affects the calculation of the central value around which the MAD is calculated. That is, passing in center=np.mean will calculate the MAD around the mean - it will not calculate the mean absolute deviation.

References

1(1,2)

“Median absolute deviation” https://en.wikipedia.org/wiki/Median_absolute_deviation

2(1,2)

“Robust measures of scale” https://en.wikipedia.org/wiki/Robust_measures_of_scale

Examples

When comparing the behavior of median_absolute_deviation with np.std, the latter is affected when we change a single value of an array to have an outlier value while the MAD hardly changes:

>>> from scipy import stats
>>> x = stats.norm.rvs(size=100, scale=1, random_state=123456)
>>> x.std()
0.9973906394005013
>>> stats.median_absolute_deviation(x)
1.2280762773108278
>>> x[0] = 345.6
>>> x.std()
34.42304872314415
>>> stats.median_absolute_deviation(x)
1.2340335571164334

Axis handling example:

>>> x = np.array([[10, 7, 4], [3, 2, 1]])
>>> x
array([[10,  7,  4],
       [ 3,  2,  1]])
>>> stats.median_absolute_deviation(x)
array([5.1891, 3.7065, 2.2239])
>>> stats.median_absolute_deviation(x, axis=None)
2.9652