  In Phys. Lett. B 753, 629-638 (2016) [arXiv:1507.08188] the BESIII
collaboration published a cross section measurement of the process $e^+e^-\to
\pi^+ \pi^-$ in the energy range between 600 and 900 MeV. In this erratum we
report a corrected evaluation of the statistical errors in terms of a fully
propagated covariance matrix. The correction also yields a reduced statistical
uncertainty for the hadronic vacuum polarization contribution to the anomalous
magnetic moment of the muon, which now reads as $a_\mu^{\pi\pi\mathrm{,
LO}}(600 - 900\,\mathrm{MeV}) = (368.2 \pm 1.5_{\rm stat} \pm 3.3_{\rm
syst})\times 10^{-10}$. The central values of the cross section measurement and
of $a_\mu^{\pi\pi\mathrm{, LO}}$, as well as the systematic uncertainties
remain unchanged.
