  We measured the average Compton profile of 461 clusters detected jointly by
the South Pole Telescope (SPT) and Planck. The number of clusters included in
this analysis is about one order of magnitude larger than in previous analyses.
We propose an innovative method developed in Fourier space to combine optimally
the Planck and SPT-SZ data, allowing us to perform a clean deconvolution of the
point spread and transfer functions while simultaneously rescaling by the
characteristic radial scale $R_{\rm 500}$ with respect to the critical density.
The method additionally corrects for the selection bias of SPT clusters in the
SPT-SZ data. We undertake a generalised Navarro-Frenk-White (gNFW) fit to the
profile with only one parameter fixed, allowing us to constrain the other four
parameters with excellent precision. The best-fitting profile is in good
agreement with the universal pressure profile based on REXCESS in the inner
region and with the Planck intermediate paper V profile based on Planck and the
XMM-Newton archive in the outer region. We investigate trends with redshift and
mass, finding no indication of redshift evolution but detecting a significant
difference in the pressure profile of the low- versus high-mass subsamples, in
the sense that the low mass subsample has a profile that is more centrally
peaked than that of the high mass subsample. [abridged]
