A device and a method for computing a weighted-average-based position of a shear wave in a temporal domain based on a sampling of shear wave displacements along a propagation path of the shear wave. The weighted-average-based position is, for example, by displacement observed at a plurality of times that correspond to sampling, and represents a time of arrival of the shear wave at a location being sampled along the propagation path. Further, times of arrival of the shear wave at respective locations along the propagation path are functionally related to known inter-location distances to derive shear-wave group velocity. The derived shear-wave group velocity serves as an input into algorithms for estimating a shear elasticity of a medium, such as a body tissue, for purposes of a clinical diagnosis and therapy assessment.