  We measure the width of the MgII $\lambda2799$ line in quasar spectra from
the SDSS, 2QZ and 2SLAQ surveys and, by invoking an unnormalised virial mass
estimator, relate the scatter in line width to the scatter in mass in the
underlying black hole population. We find conclusive evidence for a trend such
that there is less scatter in line width, and hence black hole mass, in more
luminous objects.
  However, the most luminous objects in our sample show such a low degree of
scatter in line width that, when combined with measures for the intrinsic
scatter in the radius-luminosity relation for the broad-line region in active
galaxies, an inconsistency arises in the virial technique for estimating black
hole masses. This analysis implies that, at least for the most luminous
quasars, either there is little-to-no intrinsic scatter in the
radius-luminosity relation or the MgII broad emission line region is not
totally dominated by virial velocities.
  Finally we exploit the measured scatter in line widths to constrain models
for the velocity field of the broad-line region. We show that the lack of
scatter in broad line-widths for luminous quasars is inconsistent with a pure
planar/disk-like geometry for the broad-line region... (abridged)
