  Using a set of 73 numerically simulated galaxy clusters, we have
characterised the statistical and physical biases for three velocity dispersion
and mass estimators, namely biweight, gapper and standard deviation, in the
small number of galaxies regime ($N_{gal} \leq 75$), both for the determination
of the velocity dispersion and the dynamical mass of the clusters via the
$\sigma-M$ relation. These results are used to define a new set of unbiased
estimators, that are able to correct for those statistical biases. By applying
these new estimators to a subset of simulated observations, we show that they
can retrieve bias-corrected values for both the mean velocity dispersion and
the mean mass.
