There are four major questions in statistics. These can be listed under the headings of description, probability, inference, and homogeneity. An appreciation of the relationships between these four areas is essential for successful data analysis. This column outlines these relationships and provides a guide for data analyses.

The description question

Given a collection of numbers, what arithmetic functions will summarize the information contained in those numbers in some meaningful way?

To be effective, a descriptive statistic has to make sense—it has to distill some essential characteristic of the data into a value that is both appropriate and understandable. In every case, this distillation takes on the form of some arithmetic operation:

Data + Arithmetic = Statistic

As soon as we have said this, it becomes apparent that the justification for computing any given statistic must come from the nature of the data themselves. The meaning of any statistic depends upon the context for the data, while the appropriateness of any statistic depends on the use we intend to make of that statistic.

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