The Main Injector Neutrino Oscillation Search (MINOS) observes the disappearance of muon neutrinos as they propagate in the long baseline Neutrinos at the Main Injector (NuMI) beam. MINOS consists of two detectors. The near detector samples the initial composition of the beam. The far detector, 735 km away, looks for an energy-dependent deficit in the neutrino spectrum. This energy-dependent deficit is interpreted as quantum mechanical oscillations between neutrino flavors. A measurement is made of the effective two-neutrino mixing parameters Δm ² ≈ Δm²₂₃ and sin²2&thetas; ≈ sin²2&thetas;₂₃. The primary MINOS analysis uses charged current events in the fiducial volume of the far detector. This analysis uses the roughly equal-sized sample of events that fails the fiducial cut, consisting of interactions outside the fiducial region of the detector and in the surrounding rock. These events provide an independent and complementary measurement, albeit weaker due to incomplete reconstruction of the events. This analysis reports on an exposure of 7.25×10²⁰ protons-on-target. Due to poor energy resolution, the measurement of sin²2&thetas; is much weaker than established results, but the measurement of sin ²2&thetas; > 0.56 at 90% confidence is consistent with the accepted value. The measurement of Δm² is much stronger. Assuming sin²2&thetas; = 1, Δm² = (2.20 ± 0.18[stat] ± 0.14[syst]) × 10⁻³ eV ² .