High-energy nuclear collisions create a quark-gluon plasma, whose initial condition and subsequent expansion vary from event to event, impacting the distribution of the eventwise average transverse momentum [P([p_{T}])]. Disentangling the contributions from fluctuations in the nuclear overlap size (geometrical component) and other sources at a fixed size (intrinsic component) remains a challenge. This problem is addressed by measuring the mean, variance, and skewness of P([p_{T}]) …