We obtain a new determination of the metallicity distribution function (MDF) of stars within $sim5$-$10$ kpc of the Sun, based on recently improved co-adds of $ugriz$ photometry for Stripe 82 from the Sloan Digital Sky Survey. Our new estimate uses the methodology developed previously by An et al. to study in situ halo stars, but is based on a factor of two larger sample than available before, with much-improved photometric errors and zero-points. The newly obtained MDF can be divided into multiple populations of halo stars, with peak metallicities at [Fe/H] $approx -1.4$ and $-1.9$, which we associate with the inner-halo and outer-halo populations of the Milky Way, respectively. We find that the kinematics of these stars (based on proper-motion measurements at high Galactic latitude) supports the proposed dichotomy of the halo, as stars with retrograde motions in the rest frame of the Galaxy are generally more metal-poor than stars with prograde motions, consistent with previous claims. In addition, we generate mock catalogs of stars from a simulated Milk Way halo system, and demonstrate for the first time that the chemically- and kinematically-distinct properties of the inner- and outer-halo populations are qualitatively in agreement with our observations. The decomposition of the observed MDF and our comparison with the mock catalog results suggest that the outer-halo population contributes on the order of $sim35%$-$55%$ of halo stars in the local volume.
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