  We present a statistical analysis of the properties of a large sample of
dynamically hot old stellar systems, from globular clusters to giant
ellipticals, which was performed in order to investigate the origin of
ultra-compact dwarf galaxies. The data were mostly drawn from Forbes et al.
(2008). We recalculated some of the effective radii, computed mean surface
brightnesses and mass-to-light-ratios, estimated ages and metallicities. We
completed the sample with globular clusters of M31. We used a multivariate
statistical technique (K-Means clustering), together with a new algorithm (Gap
Statistics) for finding the optimum number of homogeneous sub-groups in the
sample, using a total of six parameters (absolute magnitude, effective radius,
virial mass-to-light ratio, stellar mass-to-light ratio and metallicity). We
found six groups. FK1 and FK5 are composed of high- and low-mass elliptical
galaxies respectively. FK3 and FK6 are composed of high-metallicity and
low-metallicity objects, respectively, and both include globular clusters and
ultra-compact dwarf galaxies. Two very small groups, FK2 and FK4, are composed
of Local Group dwarf spheroidals. Our groups differ in their mean masses and
virial mass-to-light ratios. The relations between these two parameters are
also different for the various groups. The probability density distributions of
metallicity for the four groups of galaxies is similar to that of the globular
clusters and UCDs. The brightest low-metallicity globular clusters and
ultra-compact dwarf galaxies tend to follow the mass-metallicity relation like
elliptical galaxies. The objects of FK3 are more metal-rich per unit effective
luminosity density than high-mass ellipticals.
