Find member of set with minimizing total distance property

Find member of set with minimizing total distance property

I'm looking for efficient solution of following problem: For given set of
points in n-dimensional euclidian space find such member of this set that
minimizes total distance to other points in set.
The obvious naïve approach is quadratic, so I'm looking for something less
than quadratic.
My first thought was that all I need is just to find the center of
bounding sphere and then, find the closest point in set to this point. But
this is actually not true, imagine right triangle - all its vertices are
equidistant from such center, nevertheless, exactly one vertice meets our
requirements.
It would be nice it one will shed some light on this issue.