  Many data in the High Energy Physics are, in fact, sample means. It is shown
that when this exact meaning of the data is taken into account and the most
weakly bound states are removed from the hadron resonance gas, the whole
spectra of pions, kaons and protons measured at midrapidity in Pb-Pb collisions
at $\sqrt{s_{NN}} = 2.76$ TeV can be fitted simultaneously. The invariant
distributions are predicted with the help of the single-freeze-out model in the
chemical equilibrium framework. The method is applied to the measurements in
centrality bins of Pb-Pb collisions and gives acceptable fits for all but
peripheral bins. The comparison with the results obtained in the framework of
the original single-freeze-out model is also presented. Some more general,
possible implications of this approach are pointed out.
