In this work, the effect of the stochastic nature of porous medium on porosity, effective diffusion and mass dispersion was investigated. To this end, a methodology to build idealized media composed by solid particles with random size has been introduced. Gaussian and uniform probability distribution functions were employed to design the size and orientation of rectangular cylinders and cubes. Predictions of effective parameters were performed by using numerical procedures based on the volume averaging method. From the porosity and effective diffusion analysis, it was found that a minimum number of particles minimizes fluctuations of predictions. Thus, a minimum sampling size to measure properties was inferred. The minimum number of particles depends on the probability distribution functions and the dimensionality of particles used (cylinders or cubes). The methodology to build porous media also allows the creation of anisotropic media, and its effect is marked over the longitudinal and transverse components of effective diffusivity tensor. But this is not the case for the mass dispersion tensor, where the flow direction is the main cause for anisotropy. In fact, the flow taking place at pore-scale increases noticeable the randomness of predictions of mass dispersion, specifically when the number of particles or the particle Peclet number are increased. This effect is more significant on the transverse mass dispersion.