  We have selected an all--sky sample of 893 galaxies from the IRAS FSC--2,
defined by a total (ADDSCAN) 12um flux limit of 0.22~Jy. Completeness is
verified to 0.30~Jy, below which we have quantified the incompleteness down to
0.22~Jy for our statistical analysis. \P The Seyfert subsample is the largest
unbiased sample of (118) Seyfert galaxies ever assembled and is complete not
only to 0.30~Jy at 12um, but also with respect to a bolometric flux limit of
$\sim2.0\times10^{-10}$~(cgs). The average $V/V_{max}$ for the full sample,
corrected for incompleteness at low fluxes, is $0.51\pm0.04$, while that for
Seyferts is $0.46\pm0.10$, suggesting that several Seyferts are yet to be
identified in our sample. The AGN luminosity functions (LFs) are more complete
than those of the optically selected CfA Seyfert galaxies for all luminosities
and AGN types. \P The 60um LF for a complete 60um--flux--limited (at 8.3~Jy)
subsample of 235 galaxies is in satisfactory agreement with those derived from
the bright galaxy sample (BGS) and the deep high--galactic latitude sample,
both selected at 60um. Over the high lum. range where our sample and the BGS
overlap, however, our space densities are systematically lower by a factor of
$\sim 1.5$, whereas at low lum. our space densities are higher by about the
same amount. Comparable results are obtained when comparing the far--IR LF of
our entire sample with the one derived from the BGS. This is not unexpected,
because of the bias towards high-luminosity spirals caused by selection at
60um.
