  We reconsider correlations among the spectral peak energy ($E_p$), 1-second
peak luminosity ($L_p$) and isotropic energy (\Eiso), using the database
constructed by \citet{yonetoku10} which consists of 109 Gamma-Ray Bursts (GRBs)
whose redshifts are known and $E_p$, $L_p$ and \Eiso are well determined. We
divide the events into two groups by their data quality. One (gold data set)
consists of GRBs with peak energies determined by the Band model with four free
parameters. On the other hand, GRBs in the other group (bronze data set) have
relatively poor energy spectra so that their peak energies were determined by
the Band model with fixed spectral index (i.e. three free parameters) or by the
Cut-off power law (CPL) model with three free parameters. Using only the gold
data set we found the intrinsic dispersion in $\log L_p$ ($=\sigma_{\rm int}$)
is 0.13 and 0.22 for \tsutsui correlation ($T_L \equiv E_{\rm iso}/L_p$) and
\yonetoku correlation, respectively. We also find that GRBs in the bronze data
set have systematically larger $E_p$ than expected by the correlations
constructed with the gold data set. This means that the intrinsic dispersion of
correlations among $E_p$, $L_p$, and \Eiso of GRBs depends on the quality of
data set. At present, using \tsutsui correlation with gold data set, we would
be able to determine the luminosity distance with $\sim 16%$ error, which might
be useful to determine the nature of the dark energy at high redshift $z > 3$.
