meandirektion

Meandirektion, or mean direction, is a core concept in circular statistics describing the average orientation of a set of directions or angles. It is used when data are directional and lie on a circle, such as wind directions, migratory bearings, or geological orientations. The mean direction represents the orientation of the resultant vector obtained when each observed direction is represented as a unit vector on the circle.

To compute the mean direction for a set of N angles theta_i (typically in radians), one can sum the cosine and sine components: x = sum cos(theta_i) and y = sum sin(theta_i). The mean direction mu is the angle of the resultant vector, given by mu = atan2(y, x). The length of the resultant vector is R = sqrt(x^2 + y^2), and characteristic measures follow: the mean resultant length r = R/N, and the circular variance V = 1 − r. The circular standard deviation can be defined as s = sqrt(2V). These quantities help quantify concentration and dispersion around the mean direction.

Notes and limitations: the mean direction is well defined for unimodal circular data but can be misleading if data are bimodal or multimodal, or if many values cluster around opposite directions. In such cases alternative summaries (such as circular medians or multimodal analyses) may be appropriate. Related concepts include the von Mises distribution, circular variance, and tests for uniformity like the Rayleigh or Kuiper tests.

Applications span meteorology, biology, geology, and engineering, wherever directional data require a meaningful average orientation.