  In experiments with superconducting quantum circuits, characterizing the
photon statistics of propagating microwave fields is a fundamental task. We
quantify the $n^{2}\,{+}\,n$ photon number variance of thermal microwave
photons emitted from a black-body radiator for mean photon numbers
$0.05\,{\lesssim}\,n\,{\lesssim}\,1.5$. We probe the fields using either
correlation measurements or a transmon qubit coupled to a microwave resonator.
Our experiments provide a precise quantitative characterization of weak
microwave states and information on the noise emitted by a Josephson parametric
amplifier.
