> If I take 1000 samples and 498 are due 
> south and 498 are due north and 2 are due east then I can say that, by 
> adding the vectors, the average wind direction was due east :-). If I do the 
> same the next month and the results are much the same except that the 2 
> samples are North by East (just a tad East of North) then adding the two 
> months tells me that the mean wind direction was North East. It wasn't. It 
> was South or North almost without exception. There was no truly 
> representative direction. The question does not allow the data to tell the 
> truth :-)

If you take an average, you usually need the variance, too, in order to get
something significant -- unless you know that it will be in a certain
range. In your examples, the variance would tell that the average is not a
good one.

Gerhard
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