In the last decade, numerous proposals have been made to deal with imprecision in estimation problems. Those approaches, many of which involve dealing with interval-valued outputs, deal with the subtle difference between uncertainty and imprecision. One of the crucial points − which to our knowledge has never been addressed − is “how to compare an interval-valued method with a precise valued method?” The usual way to compare two estimation methods is to use benchmark data with ground truths and to compute a distance between the estimates of each method and the ground truth. However, most of the mathematical available extensions of distances are either biased in favor of a precise approach or in favor of an imprecise approach. This paper proposes a new tool, the weighted variation of the mid-point distance (WVD), that is more suitable to achieve this kind of comparison, dealing with imprecision with a particular semantic. After reviewing existing distances, we introduce the WVD, first from an intuitive perspective, then from a more mathematical point of view. Its very satisfactory properties are highlighted through an experiment.