  We have assembled a large sample of virialized systems, comprising 66 galaxy
clusters, groups and elliptical galaxies with high quality X-ray data. To each
system we have fitted analytical profiles describing the gas density and
temperature variation with radius, corrected for the effects of central gas
cooling. We present an analysis of the scaling properties of these systems and
focus in this paper on the gas distribution and M-T relation. In addition to
clusters and groups, our sample includes two early-type galaxies, carefully
selected to avoid contamination from group or cluster X-ray emission. We
compare the properties of these objects with those of more massive systems and
find evidence for a systematic difference between galaxy-sized haloes and
groups of a similar temperature. We derive a mean logarithmic slope of the M-T
relation within R_200 of 1.84+/-0.06, although there is some evidence of a
gradual steepening in the M-T relation, with decreasing mass. We recover a
similar slope using two additional methods of calculating the mean temperature.
Repeating the analysis with the assumption of isothermality, we find the slope
changes only slightly, to 1.89+/-0.04, but the normalization is increased by
30%. Correspondingly, the mean gas fraction within R_200 changes from
(0.13+/-0.01)h70^-1.5 to (0.11+/-0.01)h70^-1.5, for the isothermal case, with
the smaller fractional change reflecting different behaviour between hot and
cool systems. There is a strong correlation between the gas fraction within
0.3*R_200 and temperature. This reflects the strong (5.8 sigma) trend between
the gas density slope parameter, beta, and temperature, which has been found in
previous work. (abridged)
