3.12 So What do We do with All this Stuff?
How are the various descriptive measures developed in this chapter to be used in analyzing a data set? To answer this question, we need only remember that the characteristics of interest of a data set are shape, central location (“center” for short), and dispersion (“spread” for short). In this regard:
If a distribution is symmetric (or nearly so) with no outliers, then
provide us with legitimate descriptions of center and spread, respectively. (This is so because the values of
are sensitive to both inordinately large or small extreme values of a variable X
. And if the distribution lacks symmetry, no single number can adequately describe spread since the two sides of a highly skewed distribution have different spreads.)
If a distribution is skewed and/or exhibits outliers, then
are inadequate for describing center and spread respectively. In this instance, a boxplot
should be used in order to obtain a summary of both center and spread. To construct a boxplot, we need as inputs the five number summary
along with ...