Besides the mean, the median is the most widely used single-valued descriptor of data sets. It is well-known that the orness level of the median operator is 1/2. In this paper we provide approximations of the median operator under a given level of orness. We find the exact optimal weighting vector for the 1-norm approximation problem in all conceivable cases and for 2-norm approximation up to nine aggregates. The analytical results show that if the orness level is not 1/2, then not only the middle, but the extreme values also matter.