Convex hulls are hard to analyze even for three points in geodesic metric spaces. Instead, we focus on the question of computing and recognizing weighted means of a finite set of points in the setting of particular Alexandrov spaces with nonpositive curvature where geodesics can be computed efficiently. This talk is based on joint work with A. Goodwin (Cornell University), A. S. Lewis (Cornell University), and G. Lopez-Acedo (University of Seville).