mad_std

astropy.stats.mad_std(data, axis=None)

Calculate a robust standard deviation using the median absolute deviation (MAD).

The standard deviation estimator is given by:

\[\sigma \approx \frac{\textrm{MAD}}{\Phi^{-1}(3/4)} \approx 1.4826 \ \textrm{MAD}\]

where \(\Phi^{-1}(P)\) is the normal inverse cumulative distribution function evaluated at probability \(P = 3/4\).

Parameters:

data : array-like

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

axis : int, optional

Axis along which the medians are computed. The default (axis=None) is to compute the median along a flattened version of the array.

Returns:

result : float

The robust standard deviation of the data.

Examples

>>> from astropy.stats import mad_std
>>> from astropy.utils import NumpyRNGContext
>>> from numpy.random import normal
>>> with NumpyRNGContext(12345):
...     data = normal(5, 2, size=(100, 100))
...     mad_std(data)    
2.02327646594