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We have investigated the relationship between the X-ray variability amplitude and black hole mass for a sample of 46 radio-quiet active galactic nuclei observed byASCA. 33 of the objects in our sample exhibited significant variability over a time-scale of∼40 ks. We determined the normalized excess variance in the 2–10 keV light curves of these objects and found a significant anticorrelation between excess variance and black hole mass. Unlike most previous studies, we have quantified the variability using nearly the same time-scale for all objects. Moreover, we provide a prescription for estimating the uncertainties in variance which accounts both for measurement uncertainties and for the stochastic nature of the variability. We also present an analytical method to predict the excess variance from a model power spectrum accounting for binning, sampling and windowing effects. Using this, we modelled the variance–mass relation assuming all objects have a universal twice-broken power spectrum, with the position of the breaks being dependent on mass. This accounts for the general form of the variance–mass relationship but is formally a poor fit and there is considerable scatter. We investigated this scatter as a function of the X-ray photon index, luminosity and Eddington ratio. After accounting for the primary dependence of excess variance on mass, we find no significant correlation with either luminosity or X-ray spectral slope. We do find ananticorrelationbetween excess variance and the Eddington ratio, although this relation might be an artefact owing to the uncertainties in the mass measurements. It remains to be established that enhanced X-ray variability is a property of objects with steep X-ray slopes or large Eddington ratios. Narrow-line Seyfert 1 galaxies, in particular, are consistent with being more variable than their broad-line counterparts solely because they tend to have smaller masses. [ABSTRACT FROM AUTHOR]