The MINOS experiment is a long-baseline neutrino oscillation experiment which sends a high intensity muon neutrino beam through two functionally identical detectors, a Near detector at the Fermi National Accelerator Laboratory in Illinois, 1km from the beam source, and a Far detector, 734km away, in the Soudan Mine in Minnesota.MINOS may be able to measure the neutrino mixing angle parameter sin 2 2θ 13 for the first time. Detector granularity, however, makes it very hard to distinguish any ν e appearance signal events characteristic of a non-zero value of θ 13 from background neutral current (NC) and short-track ν µ charged current (CC) events. Also, uncertainties in the hadronic shower modeling in the kinematic region characteristic of this analysis are relatively large. A new data-driven background decomposition method designed to address those issues is developed and its results presented. By removing the long muon tracks from ν µ -CC events, the Muon Removed Charge Current (MRCC) method creates independent pseudo-NC samples that can be used to correct the MINOS Monte Carlo to agree with the high-statistics Near detector data and to decompose the latter into components so as to predict the expected Far detector background. The MRCC method also provides an important cross-check in the Far detector to test the background in the signal selected region.MINOS finds a 1.0-1.5 σ ν e -CC excess above background in the Far detector data, depending on method used, for a total exposure of 3.14×10 20 protons-on-target. Interpreting this excess as signal, MINOS can set limits on sin 2 2θ 13 . Using the MRCC method, MINOS sets a limit of sin 2 2θ 13 < 0.265 at the 90% confidence limit for a CP-violating phase δ = 0.3