  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 $\chi^2$ 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. The
binning of data is made in two-dimensional grids of $\log_{10} E - L^{0.4}$
plane to get a better reflection of the oscillation pattern in the $\chi^2$
analysis. Then the $\chi^2$ 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 $\theta_{13}$ for marginalization is
found to be very crucial in determining the sensitivity of hierarchy for a
given $\theta_{13}$. Finally, we show that one can discriminate atmospheric
neutrino mass hierarchy at $>$90% C.L. if the lower limit of $\theta_{13} \ge
5^\circ$.
