This approach is also used to extend concepts like the median into higher dimensions and non-euclidian spaces. What is the "median" or "mean" of a set of point

This approach is also used to extend concepts like the median into higher dimensions and non-euclidian spaces. What is the "median" or "mean" of a set of points located on the surface of a sphere, or a torus, or some more complicated manifold (which may only be defined implicitly by a distance function)? If you try to start from the one-dimensional definition it's not really clear. You can define such concepts, however, by minimizing the corresponding norms. If you minimize the sum of L1 norms then you get something like a median. If you minimize the sum of L2 norms then you get something like a mean. Once you have something like a mean you can also define something like a variance. Wikipedia has a short article about the concept [1]. It really deserves more treatment, as it's a central (no pun in intended) idea in topological data analysis [2]. [1] https://en.wikipedia.org/wiki/Fr%C3%A9chet_mean https://en.wikipedia.org/wiki/Fr%C3%A9chet_mean [2] https://en.wikipedia.org/wiki/Topological_data_analysis https://en.wikipedia.org/wiki/Topological_data_analysis