  Motivated by the mean value property of harmonic functions, we introduce the
local and global median value properties for continuous functions of two
variables. We show that the Dirichlet problem associated with the local median
value property is either easy or impossible to solve, and we prove that
continuous functions with this property are 1-harmonic in the viscosity sense.
We then close with the following conjecture: a continuous function having the
global median value property and prescribed boundary values coincides with the
function of least gradient having those same boundary values.
