Descriptive Statistics for Symbolic Data

Abstract

The intention of this chapter is to extend the concept of frequency distribution, and the standard definitions of descriptive statistics for real-valued data, such as the empirical mean the empirical standard deviation and the median, to the general framework of symbolic variables. We denote by E={1,…, n} the set of units that are described by p symbolic variables Y₁,…, Y_p. The domain of each variable Y _j for j = 1,…, p, is denoted by Y _j and S = × ^p_j=1 y _j denotes the whole domain space. We will examine different types of symbolic variables, namely:

• cases where each symbolic variable Y _j is multi-valu ed or interval-valued;

• including the case wher e logical rules may exist among the values taken by Y₁,…, Y _p