In this concluding part of the series of three papers dedicated to the Swift BAT hard X-ray survey (BXS), we focus on the X-ray spectral analysis and statistical properties of the source sample. Using a dedicated method to extract time-averaged spectra of BAT sources, we show that Galactic sources have, generally, softer spectra than extragalactic objects and that Seyfert 2 galaxies are harder than Seyfert 1s. The averaged spectrum of all Seyfert galaxies is consistent with a power-law with a photon index of 2.00 ± 0.07. The cumulative flux-number relation for the extragalactic sources in the 14-170 keV band is best described by a power-law with a slope α = 1.55 ± 0.20 and a normalization of 9.6 ± 1.9 × 10?3 AGNs deg?2 (or 396 ± 80 AGNs all-sky) above a flux level of 2 × 10?11 ergs cm?2 s?1 (~0.85 mcrab). The integration of the cumulative flux per unit area indicates that BAT resolves 1%-2% of the X-ray background emission in the 14-170 keV band. A subsample of 24 extragalactic sources above the 4.5 σ detection limit is used to study the statistical properties of AGNs. This sample is composed of local Seyfert galaxies (z = 0.026, median value) and ~10% blazars. We find that 55% of the Seyfert galaxies are absorbed by column densities of NH 1022 H atoms cm?2 but that none is genuinely bona fide Compton thick. This study shows the capabilities of BAT to probe the hard X-ray sky to the millicrab level.
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