A procedure is described that can be used to reconstruct the quantum state of a molecular ensemble from time-averaged position probability density functions determined by time- resolved electron diffraction (TRED). The procedure makes use of established techniques for evaluating the density matrix and the phase space joint probability density; i.e., the Wigner function. A novel expression for describing electron diffraction intensities in terms of the Wigner function is presented. An approximate variant of the method, neglecting the off-diagonal elements of the density matrix, was tested by analyzing gas electron diffraction data for N2 in a Boltzmann distribution, and TRED data obtained from the 193 nm photodissociation of CS2 to carbon monosulfide, CS, at 20, 40, and 120 ns after irradiation. Although the diagonal density matrix elements do not define completely the quantum state of a system, nonetheless, the approximate Wigner functions derived from them display the expected features of a Gaussian-like function in the case of N2; and, in the case of CS, they are in agreement with other investigations, indicating collision-less vibrational energy transfer mechanisms for nascent CS during the first 20 ns, and collision-induced electronic S(1DJ) to vibrational CS(X1(Sigma) g+) energy transfer.