Classical solutions to the problem of different measurements of a single phenomenon are generally treated by the theory of measurement and the theory of errors. The underlying idea is that the thing being measured should be represented by a single value. Flaws in the classical theory have led the author and his colleagues to propose a more coherent framework. Rather than mapping into single real numbers, he proposes that a measure of a parameter should be a whole set of numbers tied to a unit called a value span, identified by its central element and half-width. This approach clarifies the role of statistics in measurement as follows: (a) statistics is used in the calibration of instruments to determine instrumental uncertainty; (b) statistics is used in the description of parameters defined in such a way that their fine structure may be treated as a statistical distribution. The point of the article is to propose a new, coherent description of the process actually carried out.