In this work, we find that a free axisymmetric jet in air displays self-similarity in the fully developed part of the jet ([Formula: see text] jet exit diameters from the jet exit). We report accurate measurements of first, second, and third order spatially averaged statistical functions of the axial velocity component performed with a laser Doppler anemometer, including the outer (high intensity, [Formula: see text]) regions of the jet. The measurements are compared to predictions derived from a simple jet model, which is described in a separate publication, and we discuss the implications for the further study of self-similarity in a free jet. It appears that all statistical functions included in this study can be scaled with a single geometrical scaling factor—the downstream distance from a common virtual origin, [Formula: see text].