  In the earlier work on the development of a model-independent data analysis
method for determining the mass of Weakly Interacting Massive Particles (WIMPs)
by using measured recoil energies from direct Dark Matter detection experiments
directly, it was assumed that the analyzed data sets are background-free, i.e.,
all events are WIMP signals. In this article, as a more realistic study, we
take into account a fraction of possible residue background events, which pass
all discrimination criteria and then mix with other real WIMP-induced events in
our data sets. Our simulations show that, for the determination of the WIMP
mass, the maximal acceptable fraction of residue background events in the
analyzed data sets of O(50) total events is ~20%, for background windows of the
entire experimental possible energy ranges, or in low energy ranges; while, for
background windows in relatively higher energy ranges, this maximal acceptable
fraction of residue background events can not be larger than ~10%. For a WIMP
mass of 100 GeV with 20% background events in the windows of the entire
experimental possible energy ranges, the reconstructed WIMP mass and the
1-sigma statistical uncertainty are ~97 GeV^{+61%}_{-35%} (~94
GeV^{+55%}_{-33%} for background-free data sets).
