>
>Feel free to disagree, but for me averaging is a way to combine a number
>of data points in such a way that (among other things) small variations
>are removed. So it makes (much) more sense to average NW and NE together
>to N than to S. Or think about a boat that is drifting in the wind.
>After an hour of NW wind and an hour of NE wind the total effect is more
>likely to resemble that of two hours N wind than of two hours S wind.

Two hours of less potent north wind, though not really. 
When I've been out storm spotting, I've had winds from both sides, strong enough to roll a lesser vehicle, and that wouldn't average out to "sitting upright" :)

The vector method solves the averaging for circles, and automatically resolves the inside angle, but it still comes down to wether the thing you're looking at is primarily a cycle, like a heading, or a line, like time (in the absolute sense) or a calendar in the cyclic sense of seasons..

I can see time represented as a grid (calendar), a line, a circle, or a spiral, and there are probably other ways.. 

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