  We have analyzed the atmospheric neutrino data to study the octant of
$\theta_{23}$ and the precision of the oscillation parameters for a large Iron
CALorimeter (ICAL) detector. The ICAL being a tracking detector has the ability
to measure the energy and the direction of the muon with high resolution. From
bending of the track in magnetic field it can also distinguish its charge. We
have generated events by Nuance and then considered only the muons (directly
measurable quantities) produced in charge current interactions in our analysis.
This encounters the main problem of wide resolutions of energy and baseline.
The energy-angle correlated two dimensional resolution functions are used to
migrate the energy and the zenith angle of the neutrino to those of the muon. A
new type of binning has been introduced to get better reflection of the
oscillation pattern in chi-square analysis. Then the marginalization of the
$\chi^2$ over all parameters has been carried out for neutrinos and
anti-neutrinos separately. We find that the measurement of $\theta_{13}$ is
possible at a significant precision with atmospheric neutrinos. The precisions
of $\Delta m_{32}^2$ and $\sin^2\theta_{23}$ are found $\sim$ 8% and 38%,
respectively, at 90% CL. The discrimination of the octant as well as the
deviation from maximal mixing of atmospheric neutrinos are also possible for
some combinations of ($\theta_{23}, ~\theta_{13}$). We also discuss the impact
of the events at near horizon on the precision studies.
