The production of $W^\pm Z$ events in proton--proton collisions at a centre-of-mass energy of 13 TeV is measured with the ATLAS detector at the LHC. The collected data correspond to an integrated luminosity of 3.2 fb${}^{-1}$ . The $W^\pm Z$ candidates are reconstructed using leptonic decays of the gauge bosons into electrons or muons. The measured inclusive cross section in the detector fiducial region for leptonic decay modes is $\sigma(W^\pm Z\to\ell^\prime\nu\ell\ell \text{fid.}) = 63.2\pm 3.2$(stat.)$\pm 2.6$(sys.)$\pm 1.5$(lumi.) fb. In comparison, the next-to-leading-order Standard Model prediction is 53.4-2.8+3.6 fb. The extrapolation of the measurement from the fiducial to the total phase space yields $\sigma(W^\pm Z\text{tot.})=50.6\pm 2.6$(stat.)$\pm 2.0$(sys.)$\pm 0.9$(th.)$\pm 1.2$(lumi.) pb, in agreement with a recent next-to-next-to-leading-order calculation of 48.2-1.0+1.1 pb. The cross section as a function of jet multiplicity is also measured, together with the charge-dependent $W^+Z$ and $W^-Z$ cross sections and their ratio. Users should note that explicit matching of lepton flavour between individual SM neutrinos and charged leptons is used in this analysis routine, to match the MC-based correction to the fiducial region applied in the paper. The data are therefore only valid under the assumption of the Standard Model and cannot be used for BSM reinterpretation.
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