  The sample median is often used in statistical analyses of physical or
astronomical data wherein a central value must be found from samples polluted
by elements which do not belong to the population of interest or when the
underlying probability law is such that the sample mean is useless for the
stated purpose. Although it does not generally possesses the nice linearity
properties of the mean, the median has advantages of its own, some of which are
explored in this paper which elucidates analogies and differences between these
two central value descriptors. Some elementary results are shown, most of which
are certainly not new but not widely known either. It is observed that the
moment and the quantile approaches to the description of a probability
distribution are difficult to relate, but that when the quantile description is
used, the sample median can be characterized very much in the same way as the
sample mean; this opens the possibility of using it for estimation purposes
beyond what is usually done. In order to relate the two approaches, a
derivation is given of the asymptotic joint distribution of the mean and the
median for a general continuous probability law.
