  The volume and surface symmetry parts of the nuclear symmetry energy and
other coefficients of the liquid droplet model are determined from the measured
atomic masses by the maximum likelihood estimator. The volume symmetry energy
coefficient extracted from finite nuclei provides a constraint on the nuclear
symmetry energy. This approach also yields the neutron skin of a finite nucleus
through its relationship with the volume and surface symmetry terms and the
Coulomb energy coefficient. The description of nuclear matter from the
isoscalar and isovector components of the density dependent M3Y effective
interaction provide a value of the symmetry energy that is consistent with the
empirical value of the symmetry energy extracted from measured atomic masses
and with other modern theoretical descriptions of nuclear matter.
