Why are (lon, lat) coordinates converted to Cartesian coordinates (x, y, z) before calculating the mean?

This is done for improved precision, although it may be sufficient to calculate the simple mean of geographic coordinates if the points are reasonably close. The following text is taken from the MathWorks manual for the Matlab Mapping Toolbox: "Computing statistics for geospatial data with geographic coordinates as if it were in a Cartesian framework can give statistically inappropriate results. While this assumption can sometimes yield reasonable numerical approximations within small geographic regions, for larger areas it can lead to incorrect conclusions because of distance measures and area assumptions that are inappropriate for spheres and spheroids."

For more details and examples, please see the useful link below and then click on "Mapping Applications" and then "Geographic Statistics". Note: MathWorks products are not used in the GE06 implementation. More.

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