I have a dataset that describes groups of 2-D linear features. Each group is a collection of angles (orientations) and lengths describing segments or linear features. The data is axial - meaning that 90 degrees and 270 degrees are the same for the purpose of the analysis.

I want to calculate a sort of mean that would reflect not only directions but also length, so that longer segments will have more weight. I can use regular circular statistics but I can't see any way to incorporate the length since the calculation of the mean involves sines and cosines (the length is in meters and can be several thousands of meters per segment).

Here is an example of my data:

orientation length

0.0000 787.5000

0.1041 567.7509

6.2346 183.5858

9.4623 307.9399

25.8636 1527.5020

39.8056 790.7878

45.0000 429.5674

56.6532 1592.2180

86.6252 535.1076

92.6115 1530.8080

97.9916 498.1029

99.0622 979.3255

104.036 695.7741

Any ideas?

p.s. I also need the standard deviation.

Thank you,

Neta