Elementary Descriptive Statistics

Engineering data are always variable. Given precise enough measurement, even supposedly constant process conditions produce differing responses. Therefore, it is not individual data values that demand an engineer’s attention as much as the pattern or distribution of those responses. The task of summarizing data is to describe their important distributional characteristics. This chapter discusses simple methods that are helpful in this task.

The chapter begins with some elementary graphical and tabular methods of data summarization. The notion of quantiles of a distribution is then introduced and used to make other useful graphical displays. Next, standard numerical summary measures of location and spread for quantitative data are discussed. Finally comes a brief look at some elementary methods for summarizing qualitative and count data.

Elementary Graphical and Tabular Treatment of Quantitative Data

Almost always, the place to begin in data analysis is to make appropriate graphical and/or tabular displays. Indeed, where only a few samples are involved, a good picture or table can often tell most of the story about the data. This section discusses the usefulness of dot diagrams, stem-and-leaf plots, frequency tables, histograms, scatterplots, and run charts.

Dot Diagrams and Stem-and-Leaf Plots

When an engineering study produces a small or moderate amount of univariate quantitative data, a dot diagram, easily made with pencil and paper, is often quite revealing. A dot diagram shows each observation as a dot placed at a position corresponding to its numerical value along a number line.

Figure 3.1                Dot diagrams of runouts