8 Event Length (number of planes) 0 20 40 60 80 100 Events 0 50 100 150 200 Far Detector Data Oscillated MC CC Background a  (GeV) reco E 0 10 20 30 40 Purity ,  Efficiency 0 0.2 0.4 0.6 0.8 1 Near detector MC Efficiency Far detector MC Efficiency Near detector MC Purity Far detector MC Purity Track Extension (number of planes) −10 0 10 20 Events 0 10 20 30 40 50 Far Detector Data Oscillated MC CC Background b  (GeV) reco E 0 10 20 30 40 Purity ,  Efficiency 0 0.2 0.4 0.6 0.8 1 Near detector MC Efficiency Far detector MC Efficiency Near detector MC Purity Far detector MC Purity FIG. 5: Selection efficiency and sample purity for Monte Carlo (MC) events selected as neutral-current candidates in the near and far-detectors, as a function of reconstructed event energy. Detector selection, fiducial volume and neutral- current/charged-current separation requirements have been applied. The shapes of both efficiency and purity distribu- tions are observed to be very similar for each of the two MI- NOS detectors. FIG. 4: Far-detector data versus predictions from the Monte Carlo (MC) simulation including ν$_{µ}$ → ν$_{τ}$ oscillations, for distributions of the classification variables (a) event length and (b) track extension . The data quality requirements of Sec. III are applied. The shaded bands show the systematic errors on the MC predictions. The arrows indicate events selected as neutral-current-like. FIG. 6: Distributions of selection efficiency (lower curves) and sample purity (upper curves) versus reconstructed event en- ergy, for Monte Carlo (MC) events selected as charged-current candidate events in the near-detector and in the far-detector. V. FAR-DETECTOR PREDICTION lected charged-current sample which contains very little neutral-current background. For both samples, the data points are seen to fall within or near the 1 standard de- viation range of the systematic uncertainty of the Monte Carlo simulation. The predictions of the energy spectra of the neutral- current and charged-current samples at the far-detector are based on the observed near-detector data and make use of the expected relationship between the neutrino fluxes at the two sites. The process of making the pre- dictions is called “extrapolation” and may be viewed as making corrections to the simulation of interactions in the far-detector based on the energy spectrum measured in the near-detector. This analysis uses an extrapolation technique called the “far over near” (F/N) method [4, 30]. This method makes the prediction of the far-detector spectrum by tak- ing the product of two quantities. The first quantity is the ratio of the expected number of events from the Monte Carlo simulation for each energy bin in the far- detector and near-detector spectra. The expected num- ber of events for each energy bin in the far-detector spec- tra depends on the composition of event types entering the samples and the corresponding oscillation probabili- ties for that energy. The second quantity is the number