# spacepy.toolbox.medAbsDev¶

`spacepy.toolbox.``medAbsDev`(series, scale=False)[source]

Calculate median absolute deviation of a given input series

Median absolute deviation (MAD) is a robust and resistant measure of the spread of a sample (same purpose as standard deviation). The MAD is preferred to the inter-quartile range as the inter-quartile range only shows 50% of the data whereas the MAD uses all data but remains robust and resistant. See e.g. Wilks, Statistical methods for the Atmospheric Sciences, 1995, Ch. 3. For additional details on the scaling, see Rousseeuw and Croux, J. Amer. Stat. Assoc., 88 (424), pp. 1273-1283, 1993.

Parameters
seriesarray_like

the input data series

Returns
outfloat

the median absolute deviation

Other Parameters
scalebool

if True (default: False), scale to standard deviation of a normal distribution

Examples

Find the median absolute deviation of a data set. Here we use the log- normal distribution fitted to the population of sawtooth intervals, see Morley and Henderson, Comment, Geophysical Research Letters, 2009.

```>>> import numpy
>>> import spacepy.toolbox as tb
>>> numpy.random.seed(8675301)
>>> data = numpy.random.lognormal(mean=5.1458, sigma=0.302313, size=30)
>>> print data
array([ 181.28078923,  131.18152745, ... , 141.15455416, 160.88972791])
>>> tb.medAbsDev(data)
28.346646721370192
```

note This implementation is robust to presence of NaNs