We introduce a set of statistical shape parameters that quantify the concept of the "average shape" of flexible molecules in isotropic and in nematic media. These shape parameters are obtained as conformational averages of geometrical tensors constructed from the relative positions and orientations of the sub-molecular units. The deformability of the average molecular shape is quantified in terms of the variation of the respective shape parameters under the action of an ordering field. The quantification of shape and deformability is applied to the description of dimers consisting of two rod-like mesogenic units connected by an alkyl spacer.