Introduction

Some fundamental concepts of descriptive statistics, like frequencies, relative frequencies, and histograms, have been introduced informally. Here we want to illustrate and expand those concepts in a slightly more systematic way. Our treatment will be rather brief since, within the framework descriptive statistics is essentially a tool for building some intuition paving.

We introduce basic statistical concepts in Section 4.1, drawing the line between descriptive and inferential statistics, and illustrating the difference between sample and population, as well as between qualitative and quantitative variables. Descriptive statistics provides us with several tools for organizing and displaying data, some of which are outlined in Section 4.2. While displaying data graphically is useful to get some feeling for their distribution, we typically need a few numbers summarizing their essential features; quite natural summary measures such as mean and variance are dealt with in Section 4.3. Then, in Section 4.4 we consider measures of relative standing such as percentiles, which are a less obvious but quite important tool used to analyze data. We should mention that basic descriptive statistics does not require overly sophisticated concepts, and it is rather easy to understand. However, sometimes concepts are a bit ambiguous, and a few subtleties can be better appreciated when armed with a little more formal background. Percentiles are a good case in point, as there is no standard definition and software packages may compute them in different ways; yet, they are a good way to get some intuitive feeling for probabilistic concepts, like quantiles, that are relevant in many applications in logistics and finance. Finally, in Section 4.5 we move from data in a single dimension to data in multiple dimensions. We limit the discussion to two dimensions, but the discussion here is a good way to understand the need for the data reduction methods discussed.