A weighted spatial median is proposed for the multivariate location problem with cluster correlated data. Its limiting distribution is derived under mild conditions and it is shown to be multivariate normal. Asymptotic as well as finite sample efficiencies and breakdown properties are considered, and supplied with illustrative examples. It turns out that there are potentially meaningful gains in estimation efficiency. An affine equivariant weighted spatial median is developed in parallel. This paper provides companion estimates to the weighted affine invariant sign test proposed recently by Larocque, Nevalainen, and Oja (2006).