What are the units of a medcouple? Let's say I have a distribution of some weights in kg. I want to estimate the skewness of this distribution using a robust statistic, the medcouple [ G. Brys; M. Hubert; A. Struyf (2004). A robust measure of skewness. Journal of Computational and Graphical Statistics  13(4), 996-1017.]
Could you help me with the units of the medcouple measure? In this example, are they kg or 1/kg or kg$^2$ or something else, or does it have no units? 
 A: The medcouple has no units. Certain complications aside, which don't produce an exception to that statement, it is a ratio of quantities on the original scale, so the units cancel. It could hardly be a (useful) measure of skewness otherwise. 
Personally I often value sensitivity in measures of skewness (and kurtosis, which otherwise we will leave on one side here), as they alert me to what may be a problem, or even a feature: high skewness may be one signal that I would be better off working on some transformed scale.
For those in search of alternatives to moment-based skewness: 


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*It's always worth remembering that (mean $−$ median) / SD is bounded in $[−1,1]$ and is easy to explain and calculate. It's not particularly robust, but as a bounded measure it is less explosive than the moment-based measure. 

*L-moments offer a well-based set of ideas. The Wikipedia entry is a fair start, with several key references. 
The thread Robust analogues of Mean, CV and Skewness also touches on these issues. 
