Section author: Danielle J. Navarro and David R. Foxcroft

Descriptive statistics

Any time that you get a new data set to look at one of the first tasks that you have to do is find ways of summarising the data in a compact, easily understood fashion. This is what descriptive statistics (as opposed to inferential statistics) is all about. In fact, to many people the term “statistics” is synonymous with descriptive statistics. It is this topic that we’ll consider in this chapter, but before going into any details, let’s take a moment to get a sense of why we need descriptive statistics. To do this, let’s open the aflsmall_margins data set and see what variables are stored in the file (Fig. 19).

Variables stored in ``aflsmall margins``

Fig. 19 Screenshot of jamovi showing the variables in the aflsmall_margins data set

In fact, there is just one variable here, afl.margins. We’ll focus a bit on this variable in this chapter, so I’d better tell you what it is. Unlike most of the data sets in this book, this is actually real data, relating to the Australian Football League (AFL).[1] The afl.margins variable contains the winning margin (number of points) for all 176 home and away games played during the 2010 season.

This output doesn’t make it easy to get a sense of what the data are actually saying. Just “looking at the data” isn’t a terribly effective way of understanding data. In order to get some idea about what the data are actually saying we need to calculate some descriptive statistics (this chapter) and draw some nice pictures (chapter Drawing graphs). Since the descriptive statistics are the easier of the two topics I’ll start with those, but nevertheless I’ll show you a histogram of the afl.margins variable since it should help you get a sense of what the data we’re trying to describe actually look like, see Fig. 20. We’ll talk a lot more about how to draw histograms. For now, it’s enough to look at the histogram and note that it provides a fairly interpretable representation of the afl.margins variable.

Histogram of AFL 2010 winning margin data

Fig. 20 Histogram of the AFL 2010 winning margin data (the afl.margins variable). As you might expect, the larger the winning margin the less frequently you tend to see it.

[1]Note for non-Australians: the AFL is an Australian rules football competition. You don’t need to know anything about Australian rules in order to follow this section.