ABSTRACT
Because its value is obtained when a sequence of well-defined numerical operations is executed, a property is to a curve as a one-word abstract is to a sentence. Examples are E , whose interpretation in terms of curve geometry is discussed in the next chapter, and the property that in this chapter is represented by the six capital letters M-E-D-I-A-N, and “a mode,” a point over which a density assumes a relative maximum value. (The possibility that a density has multiple modes is discussed at length in Chapter 6.)
It will be shown that E can be interpreted as the area between two curves. Thus, because area is involved, the abstracting process that defines E is a statistical counterpart of the mathematical concept, integration. Unlike E's connection to an area, in the many situations where it exists unambiguously, the MEDIAN curve property is defined as a value assumed by the inverse of a distribution’s cdf.
