Nothing is Sacred

Explanations exist; they have existed for all time;there is always a well-known solution to every human problem — neat, plausible, and wrong. –H L Mencken

“Half of all programmers are below average ability.”

This saying - or something close to it - is repeated from time to time.  It sounds plausible.  But you must consider the probability distribution involved.   If the population of programmers is measured by ability (however one might do that), and that population is unimodal and symmetric about its mean, then sure, the saying “half of everyone is below average” is not just plausible, but correct.

But it seems to me that the implied sample (or population) that goes with the saying, could very well come from a sample / population that is greatly skewed one way or another.

Say you are in a workgroup with one really experienced programmer, one mid-experience programmer, and a dozen relatively inexperienced programmers.   In this sample, many more than half of the programmers will be less than the arithmetic mean level of experience.  The outliers will drag the mean above the median.

Probably the saying should be revised to “half of all programmers have less than the median level of ability.”  That’s true by definition, and stretches to work with whatever sample or population you have explicitly identified, or implicitly intended.

. . . not that this bit of statistical nit-picking will change anyone’s mind.  To complain that the mean is not universally appropriate for sayings like this, but that the median is, is to invite eye-rolls along with “you know what I meant, you raisin-crapper”.

There is a pestilence upon this land! nothing is sacred. – Roger the Shrubber, Monty Python and the Holy Grail

Nothing is sacred, including a grasp of basic statistics and probability…