Event-by-event fluctuations of the average transverse momentum of produced particles near midrapidity have been measured by the PHENIX Collaboration in √sNN = 200 GeV Au + Au, and p + p collisions at the Relativistic Heavy Ion Collider. The fluctuations are observed to be in excess of the expectation for statistically independent particle emission for all centralities. The excess fluctuations exhibit a dependence on both the centrality of the collision and on the pT range over which the average is calculated. Both the centrality and pT dependence can be well reproduced by a simulation of random particle production with the addition of contributions from hard-scattering processes.