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 {dzero} collaborations have measured the top quarks 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 $173.18 pm 0.56 thinspace ({rm stat}) pm 0.75 thinspace ({rm syst})$ GeV or $173.18 pm 0.94$ GeV, which has a precision of $pm 0.54%$, making this the most precise determination of the top quark mass.
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