  In this paper, the recently introduced M&m sequences and associated
mean-median map are studied. These sequences are built by adding new points to
a set of real numbers by balancing the mean of the new set with the median of
the original. This process, although seemingly simple, gives rise to
complicated dynamics. The main result is that two conjectures put forward by
Chamberland and Martelli are shown to be true for a subset of possible starting
conditions.
