Kinematic distributions from an inclusive sample of 1.41×106 charged-current νμ 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 νμFe interactions, containing an estimated 123,000 quasielastic events of incident energies 1<Eν<8GeV, with 〈Eν〉=2.79GeV. 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 Q2 show the Monte Carlo model to be inadequate at low Q2. Its shortcomings are remedied via inclusion of a Q2-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 Q2 distribution for the quasielastic-enriched sample is carried out with the axial-vector mass MA of the dipole axial-vector form factor of the neutron as a free parameter. The effective MA which best describes the data is 1.23-0.09+0.13(fit)-0.15+0.12(syst)GeV.