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 photon index of 2.00 \pm 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 \alpha = 1.55 \pm 0.20 and a normalization of 9.6 \pm 1.9 \times 10 ^ { -3 } AGN deg ^ { -2 } ( or 396 \pm 80 AGN all-sky ) above a flux level of 2 \times 10 ^ { -11 } erg cm ^ { -2 } s ^ { -1 } ( \sim 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 sub-sample of 24 extragalactic sources above the 4.5 \sigma detection limit is used to study the statistical properties of AGN .
This sample comprises local Seyfert galaxies ( z=0.026 , median value ) and \sim 10 % blazars .
We find that 55 % of the Seyfert galaxies are absorbed by column densities of N _ { H } > 10 ^ { 22 } H-atoms cm ^ { -2 } , but that none is a bona fide Compton-thick .
This study shows the capabilities of BAT to probe the hard X-ray sky to the mCrab level .