I don't know if there's a 'correct' or 'standard' way, but typically 
I've handled such cases by making a scale that's twice as large as what 
I'm measuring, and keeping the average away from the edges.

0-360 degrees becomes -360 to 360.  When the average gets close to the 
edge, perhaps 100 degrees away from either edge then I add or subtract 
360 degrees depending on the edge.

The input and output have to be changed into the correct range.  If the 
average is below 0 then subtract 360 from the input before adding to the 
average, and add 360 to the average to get the output.

There is an interesting corner case at 0, however, which may need some 
careful thought depending on the application.  In this case, if the 
average is 0, then look at the input - if the input is above 180 then 
subtract 360 from the input.  If below 180 then do not modify.  In 
either case the average will have moved from 0 so the output equations 
can remain the same.  If the input is at 360 or zero then the average 
remains the same, and the output is 0 (or 360 if you allow that in your 
system).

Of course, if your input varies by 1/2 a cycle per measurement then 
you've got bigger problems than keeping a correct average - consult 
nyquist.  :-)

-Adam

Wouter van Ooijen wrote:

>Is there a (standard) way to calculate the average of a parameter that
>is cyclic in nature, like the wind direction or the month of the year?
>
>Wouter van Ooijen
>
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