On the demise of the Mean

Perhaps I should call this On the demise of the Normal.  More and more these days I encounter distributions where the median is a much better descriptor than the mean.  Of course if things are distributed normally then the median and the mean (and the mode) are all the same number.  But if things are abnormal then those definitions start to point to different parts of the distribution.

My first encounter with non-normal distributions came in graduate school as I was thinking about the distribution of elevations in topographic profiles.  Turns out that those things have a lot in common with power-law distributions.  So does the distribution of sizes of earthquakes.  And all sorts of other things in nature as well.  Then of course there were arguments about the differences between log-normal distributions and power-law distributions and how you might be able to tell in which was which by measuring things.  In the context here, it doesn't matter; neither one in normal.

I have been pondering this lately because I have been trying to write about proxies for the state of the human system part of the Earth system and central tendency indictors and variability around those have come up with considerable strength.  And now I am wondering if that most archetypal of all normal distributions - heights of humans - will stand up as normal over all of Earth.  Or does that example really only work in a suburban middle class classroom in the mid-1970s.

Which in turn makes one wonder whether in fact it is the normal distribution that is abnormal...

(ain't I clever!)