Average of many wind directions

Hi,

I do not think it is just excel question it is more about data representation, or other "pure mathematics" problem.

In your particular case, I'd describe these directions as
-10
10
140
190
40

or (equivalent):
350
370
500
550
400

because this representation leads to lowest standard deviation (ca. 87)
So the average direction would be 74 degrees


Note that any other representationgives higher standard deviation values:

350 350 350 350 350
10 370 370 370 370
140 140 140 500 500
190 190 190 190 550
40 40 400 400 400
SD
135 141 117 112 87

But as we are on Excelforum - you may see how did I checked it in attached file

Is it not:

Formula:

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(assuming equal strength wind in all directions...)

I know that there are special considerations for averaging wind speed and direction, so not only is this probably more math than Excel, but it probably also needs a discussion specific to meteorology.

Here's a brief page from the US government's NOAA: https://www.ndbc.noaa.gov/wndav.shtml Basically it says that the standard approach to averaging wind speed and direction is to get a scalar average of the wind speeds and a unit vector average of the wind direction. This usually boils down to an ATAN() or, better yet, an ATAN2() function.
This page does not claim any meteorological expertise, but he has spreadsheet examples: https://www.scadacore.com/2014/12/19...nd-wind-speed/
The WebMet reference from the previous page: http://www.webmet.com/met_monitoring/622.html

Perhaps those references will help.