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A simple way to calculate the mean of a series of angles (in the interval [0°, 360°)) is to calculate the mean of the cosines and sines of each angle, and obtain the angle by calculating the inverse tangent. Consider the following three angles as an example: 10, 20, and 30 degrees.
The simple method for calculating circular variance requires two passes through the list of values. The first pass determines the circular mean of those values, while the second pass determines the variance. This double-pass method requires access to all values.
There are associated concepts, such as the DRMS (distance root mean square), which is the square root of the average squared distance error, a form of the standard deviation. Another is the R95, which is the radius of the circle where 95% of the values would fall, a 95% confidence interval .
If the mean anomaly is known at any given instant, it can be calculated at any later (or prior) instant by simply adding (or subtracting) n⋅δt where δt represents the small time difference. Mean anomaly does not measure an angle between any physical objects (except at pericenter or apocenter, or for a circular orbit).
The mean of the complex exponential z is then just = () and the circular mean value of the angle x is then taken to be the argument μ. This is the expected or preferred direction of the angular random variables. The circular variance of x is:
Bear all this in mind next time you find yourself in the wild and hopefully you’ll have some success. Or at least enough to stop you from asking anyone if they “come here often”. Show comments
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and the mean angle is: ¯ = (¯). The sample mean for the circular uniform distribution will be concentrated about zero, becoming more concentrated as N increases. The distribution of the sample mean for the uniform distribution is given by: [2]