We determine types of double magma associated with Ward quasigroups, double Ward quasigroups, their duals and the groups they generate. Ward quasigroup double magma and unipotent, right modular, left-unital double magma are proved to be improper. Necessary and sucient conditions are found on a pair of right modular, left unital magma (and right-left unital magma) for them to form a double magma. We give further insight into the intimate connection between the property of mediality and the interchange law by proving that a quasigroup is medial if and only if any pair of its parastrophic binary operations satisfy the interchange law.