Direct numerical simulation is utilized to generate statistics in particle-laden homogeneous plane strain turbulent flows. Assuming the two-phase flow to be dilute (one-way coupling), a variety of cases are considered to investigate the effects of the particle time constant. The carrier phase is incompressible and is treated in the Eulerian frame whereas the particles are tracked individually in a Lagrangian frame. For small particle Reynolds numbers, an analytical expression for the particle mean velocity gradient is found, which is different from the fluid one, and the dispersed phase is shown to be homogeneous. This is not the case for particles with large Reynolds numbers and no statistics involving the particle fluctuating velocity is presented for large particles. The results of the simulations are utilized to investigate the particle velocity autocorrelation, the turbulence kinetic energy, the Reynolds stresses, and the dispersion function.