A particulate system can be described through the discrete approach at the microscopic level or through the continuum approach at the macroscopic level. It is very significant to develop the method to link the two approaches for the development of models allowing a better understanding of the fundamentals of particulate systems. Several averaging methods have been proposed for this purpose in the past, but they mainly focused on cohesionless particle systems. In this work, a more general averaging method is proposed by extending it for cohesionless particle systems. The application of the method to the particle-fluid flow in a gas fluidized bed is studied. The density, velocity and stress of this flow are examined. A detailed discussion has been conducted to understand the dependence of the averaged variables on sample size.