Mean / avg angle calculation and error of incoming values

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Note: i have alteady looked over this thread and helped me the mean angle.

I have a stream of angles in [0, 360) based on I am computing the mean angle in a calibrating step of the code. Let's say during calibration I get values between randomly 340 deg and 30 deg, which means the mean angle should be around 5deg.

After calibration, I want to identify an activity, based on the incoming angle values. Is there any method to calculate this error? Let's say, for the same mean angle of 5deg, if I get a 45deg during readings, the error will clearly be 30deg, but for 335deg the error will not be 30deg anymore.

Also, may it be there any method to store a circular interval, and maybe using simple math operations like modulo or something, not Circular lists?

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