Medial representations of shapes are useful due to their use of an object-centered coordinate system that directly captures intuitive notions of shape such as thickness, bending, and elongation. However, it is well known that an object's medial axis transform (MAT) is unstable with respect to small perturbations of its boundary. This instability results in additional, unwanted branches in the skeletons, which must be pruned in order to recover the portions of the skeletons arising purely from the uncorrupted shape information. Almost all approaches to skeleton pruning compute a significance measure for each branch according to some heuristic criteria, and then prune the least significant branches first. Current approaches to branch significance computation can be classified as either local, solely using information from a neighborhood surrounding each branch, or global, using information about the shape as a whole. In this paper, we propose a third, groupwise approach to branch significance computation. We develop a groupwise skeletonization framework that yields a fuzzy significance measure for each branch, derived from information provided by the group of shapes. We call this framework the Groupwise Medial Axis Transform (G-MAT). We propose and evaluate four groupwise methods for computing branch significance and report superior performance compared to a recent, leading method. We measure the performance of each pruning algorithm using denoising, classification, and within-class skeleton similarity measures. This research has several applications, including object retrieval and shape analysis.