  A calibration is made for the correlation between the X-ray Variability
Amplitude (XVA) and Black Hole (BH) mass. The correlation for 21
reverberation-mapped Active Galactic Nuclei (AGN) appears very tight, with an
intrinsic dispersion of 0.20 dex. The intrinsic dispersion of 0.27 dex can be
obtained if BH masses are estimated from the stellar velocity dispersions. We
further test the uncertainties of mass estimates from XVAs for objects which
have been observed multiple times with good enough data quality. The results
show that the XVAs derived from multiple observations change by a factor of 3.
This means that BH mass uncertainty from a single observation is slightly worse
than either reverberation-mapping or stellar velocity dispersion measurements;
however BH mass estimates with X-ray data only can be more accurate if the mean
XVA value from more observations is used. Applying this relation, the BH mass
of RE J1034+396 is found to be $4^{+3}_{-2} \times 10^6$ $M_{\odot}$. The high
end of the mass range follows the relationship between the 2$f_0$ frequencies
of high-frequency QPO and the BH masses derived from the Galactic X-ray
binaries. We also calculate the high-frequency constant $C= 2.37 M_\odot$
Hz$^{-1}$ from 21 reverberation-mapped AGN. As suggested by Gierli\'nski et
al., $M_{\rm BH}=C/C_{\rm M}$, where $C_{\rm M}$ is the high-frequency
variability derived from XVA. Given the similar shape of power-law dominated
X-ray spectra in ULXs and AGN, this can be applied to BH mass estimates of
ULXs. We discuss the observed QPO frequencies and BH mass estimates in the
Ultra-Luminous X-ray source M82 X-1 and NGC 5408 X-1 and favor ULXs as
intermediate mass BH systems (abridged).
