The top quark is the heaviest known elementary particle, with a mass about 40 times larger than the mass of its isospin partner, the bottom quark. It decays almost 100% of the time to a W boson and a bottom quark. Using top-antitop pairs at the Tevatron proton-antiproton collider, the CDF and D0 Collaborations have measured the top quark's mass in different final states for integrated luminosities of up to 5.8 fb(-1). This paper reports on a combination of these measurements that results in a more precise value of the mass than any individual decay channel can provide. It describes the treatment of the systematic uncertainties and their correlations. The mass value determined is 173.18 +/- 0.56 (stat) +/- 0.75 (syst) GeV or 173.18 +/- 0: 94 GeV, which has a precision of +/- 0.54%, making this the most precise determination of the top-quark mass.
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