Distance to a MultivariateStatistics median

Question

I have a population of objects (each of which is described by a sequence of real numbers), and I'd like to find the "distance" between a single test object and the median of the population.

I believe that I can use the MultivariateStatistics package to characterize my population, and then either SpatialMedian[] or SimplexMedian[] to find the "center." My goal is to find the distance between a test object and this median. I gather that a simple Euclidean distance would be incorrect, because I need to account for the ellipsoid's size and orientation (I believe, but I'm not certain, that this is the Mahalanobis distance). I don't see a function in the MultivariateStatistics package that lets me find such distances.

Is it possible to compute a distance from a test object to the median of the population, and if so, how?