  We have performed a systematic study of Gamma-Ray Bursts (GRBs), which have
various values in the peak energy of the ${\nu}F_{\nu}$ spectrum of the prompt
emission, $E_{{\rm peak}}$, observed by \textsl{Swift}/BAT and
\textsl{Fermi}/GBM, investigating their prompt and X-ray afterglow emissions.
We cataloged the long-lasting GRBs observed by the \textsl{Swift} between 2004
December and 2014 February in 3 categories according to the classification by
\citet{2008ApJ...679..570S}: X-Ray Flashes (XRFs), X-Ray Rich GRBs (XRRs), and
Classical GRBs (C-GRBs). We then derived $E^{{\rm obs}}_{{\rm peak}}$, as well
as $E^{{\rm src}}_{{\rm peak}}$ if viable, of the \textsl{Swift} spectra of
their prompt emission. We also analyzed their X-Ray afterglows and found the
trend that the GRB events with a lower $E_{{\rm peak}}^{{\rm src}}$, i.e.
softer GRBs, are fainter in the 0.3--10 keV X-ray luminosity and decay more
slowly than harder GRBs. The intrinsic event rates of the XRFs, XRRs, and
C-GRBs were calculated, using the \textsl{Swift}/BAT trigger algorithm. That of
either of the XRRs and XRFs is larger than that of the C-GRBs. If we assume
that the observational diversity of $E_{{\rm peak}}$ is explained with the
off-axis model \citep{2002ApJ...571L..31Y,2004ApJ...607L..103Y}, these results
yield the jet half-opening angle of $\Delta\theta\sim 0.3^\circ$, and the
variance of the observing angles $\theta_{{\rm obs}} \lesssim0.6^{\circ}$. This
implies that the tiny variance of the observing angles of $\lesssim0.6^{\circ}$
would be responsible for the $E_{{\rm peak}}$ diversity observed by
\textsl{Swift}/BAT, which is unrealistic. Therefore, we conclude that the
$E_{{\rm peak}}$ diversity is not explained with the off-axis model, but is
likely to originate from some intrinsic properties of the jets.
