[en] We have studied the mass hierarchy with atmospheric neutrinos considering the muon energy and zenith angle of the event at the magnetized iron calorimeter detector. For χ² analysis we have migrated the number of events from neutrino energy and zenith angle bins to muon energy and zenith angle bins using the two-dimensional energy-angle correlated resolution functions. Then the χ² is marginalized considering all possible systematic uncertainties of the atmospheric neutrino flux and cross section. The effects of the ranges of oscillation parameters on the marginalization are also studied. The lower limit of the range of θ₁₃ for marginalization is found to be very crucial in determining the sensitivity of hierarchy for a given θ₁₃. Finally, we show that one can discriminate atmospheric neutrino mass hierarchy at >90% C.L. if the lower limit of θ₁₃≥5 deg.