  Estimating the temperature and metal abundance of the intracluster and the
intragroup media is crucial to determine their global metal content and to
determine fundamental cosmological parameters. When a spatially resolved
temperature or abundance profile cannot be recovered from observations (e.g.,
for distant objects), or deprojection is difficult (e.g., due to a significant
non-spherical shape), only global average temperature and abundance are
derived. After introducing a general technique to build hydrostatic gaseous
distributions of prescribed density profile in potential wells of any shape, we
compute the global mass weighted and emission weighted temperature and
abundance for a large set of barotropic equilibria and an observationally
motivated abundance gradient. We also compute the spectroscopic-like
temperature that is recovered from a single temperature fit of observed
spectra. The derived emission weighted abundance and temperatures are higher by
50% to 100% than the corresponding mass weighted quantities, with overestimates
that increase with the gas mean temperature. Spectroscopic temperatures are
intermediate between mass and luminosity weighted temperatures. Dark matter
flattening does not lead to significant differences in the values of the
average temperatures or abundances with respect to the corresponding spherical
case (except for extreme cases).
