An experimental study has been performed on the dynamics of a large turbulent buoyant helium plume. Two-dimensional velocity fields were measured using particle image velocimetry (PIV) while helium mass fraction was determined by planar laser-induced fluorescence (PLIF). PIV and PLIF were performed simultaneously in order to obtain velocity and mass fraction data over a plane that encompassed the plume core, the near-field mixing zones and the surrounding air. The Rayleigh-Taylor instability at the base of the plume leads to the vortex that grows to dominate the flow. This process repeats in a cyclical manner. The temporally and spatially resolved data show a strong negative correlation between density and vertical velocity, as well as a strong 90 degrees phase lag between peaks in the vertical and horizontal velocities throughout the flow field owing to large coherent structures associated with puffing of the turbulent plume. The joint velocity and mass fraction data are used to calculate Favre-averaged statistics in addition to Reynolds-(time) averaged statistics. Unexpectedly, the difference between both the Favre-averaged and Reynolds-averaged velocities and second-order turbulent statistics is less than the uncertainty in the data throughout the flow field. A simple analysis was performed to determine the expected differences between Favre and Reynolds statistics for flows with periodic fluctuations in which the density and velocity fields are perfectly correlated, but have the phase relations as suggested by the data. The analytical results agree with the data, showing that the Favre and Reynolds statistics will be the same to lead order. The combination of observation and simple analysis suggests that for buoyancy-dominated flows in which it can be expected that density and velocity are strongly correlated, phase relations will result in only second-order differences between Favre-and Reynolds-averaged data in spite of strong fluctuations in both density and velocity.