Kinematic distributions from an inclusive sample of 1.41 x 10^6 charged-current nu_mu interactions on iron, obtained using the MINOS Near Detector exposed to a wide-band beam with peak flux at 3 GeV, are compared to a conventional treatment of neutrino scattering within a Fermi gas nucleus. Results are used to guide the selection of a subsample enriched in quasielastic nu_mu Fe interactions, containing an estimated 123,000 quasielastic events of incident energies 1 = 2.79 GeV. Four additional subsamples representing topological and kinematic sideband regions to quasielastic scattering are also selected for the purpose of evaluating backgrounds. Comparisons using subsample distributions in four-momentum transfer Q^2 show the Monte Carlo model to be inadequate at low Q^2. Its shortcomings are remedied via inclusion of a Q^2-dependent suppression function for baryon resonance production, developed from the data. A chi-square fit of the resulting Monte Carlo simulation to the shape of the Q^2 distribution for the quasielastic-enriched sample is carried out with the axial-vector mass M_A of the dipole axial-vector form factor of the neutron as a free parameter. The effective M_A which best describes the data is 1.23 +0.13/-0.09 (fit) +0.12/-0.15 (syst.) GeV.