As I understand a wedge product in two dimensions considers bivectors as natural extesion of vectors and assigns a magnitude (the area of the parellogram encolsed by the vectors) and a direction.
If there is a distribution of points in a plane, is there any meaningful way we can assign a "direction" to the distribution taking a wedge product between all pairs of vectors? For example, if all the points lie in one direction then each pair of their wedge products will be zero and distribution will have a zero "direction". I think such a distribution is a truncated Generalized Pareto Distribution, Beta distribution, or power distribution. In general it wil be good to know if there could be a meaningful association of a "direction" to a distribution, if such a thing could be defined.