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:

1. If a distribution is symmetric (or nearly so) with no outliers, then and s provide us with legitimate descriptions of center and spread, respectively. (This is so because the values of and s 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.)

2. If a distribution is skewed and/or exhibits outliers, then and s 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 ...

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