The study presents IRAS LRS data for 350 galaxies with pointlike IRAS sources having either S(12) or S(25) not less than 1.5 Jy. Techniques are presented which form the mean of an ensemble of LRS spectra, ll of which are only of low signal-to-noise ratio, by quantitative evaluation of the significance of the individual spectra for each object rather than mere acceptance of the 'average spectrum' present in the complete LRS data base. Average LRS spectra for groups of galaxies with distinct optical nuclear properties are formed. Average LRS spectra for several categories of objects are presented and interpreted. H II region galaxies show the polycyclic aromatic hydrocarbon spectrum of bands in emissions; type 2 Seyferts present a broad emission feature parking near 16 microns; LINERs and galaxies without optical emission lines have LRS spectra that decline with wavelength, whereas type 1 Seyferts and WR galaxies have red spectra suggestive of nonthermal emission processes.