Over the last number of decades much progress has been made in the investigation of the hyperconvex hull, the investigations of Dress and Isbell being most widely known. The aim of this research is to provide sufficient background on the q-hyperconvex hull in T0-quasimetric spaces, to ensure that the reader may enjoy the theory later on, whereby the results obtained earlier are used in measuring the skewness of a T0-quasimetric space. It starts off with a general introduction into T0-quasimetric spaces and the concepts of convexity and q-hyperconvexity, whereby we later discuss a summary of results for q-hyperconvex hulls in T0-quasimetric spaces which has been investigated in the past. We conclude by commencing an investigation in the measurement of skewness of asymmetric distances in T0-quasimetric spaces. We compare our method of measuring skewness with that of Plastria's. Here several results obtained from the q-hyperconvex hull and tight extensions are generalised, and some original results for the measuring of skewness in T0-quasimetric spaces are presented. ukryj opis