We present an analysis of X-ray variability in a flux-limited sample of qua
si-stellar objects (QSOs). Selected from our deep ROSAT survey, these QSOs
span a wide range in redshift (0.1 < z < 3.2) and are typically very faint,
so we have developed a method to constrain the amplitude of variability in
ensembles of low signal-to-noise ratio light curves. We find evidence for
trends in this variability amplitude with both redshift and luminosity. The
mean variability amplitude declines sharply with luminosity, as seen in lo
cal active galactic nuclei (AGN), but with some suggestion of an upturn for
the most powerful sources. We find tentative evidence that this is caused
by redshift evolution, since the high-redshift QSOs (z > 0.5) do not show t
he anticorrelation with luminosity seen in local AGN. We speculate on the i
mplications of these results for physical models of AGN and their evolution
. Finally, we find evidence for X-ray variability in an object classified a
s a narrow-emission-line galaxy, suggesting the presence of an AGN.