31.3 Numbers of orderings and sortings

Often there are surprisingly many possible orderings. The basic Titanic dataset has 4 variables. The Survived variable should doubtless always be the final variable, but the other three variables, Class, Age, and Sex could be ordered in 3!=6 ways. The categories of the three binary variables could each be ordered in 2 ways, making 8 in all. The four categories of Class have a natural order, but could be reversed giving another two possibilities. Altogether that makes 96 orderings of variables and categories that might be considered.

The letters of the word ‘sorting’ can be ordered themselves in 7! = 5040 ways, but only one other makes a common word, ‘storing’. A random ordering would have little chance of making sense, although some subsets of the letters, for instance “strong”, “ingots”, “string” or “grist”, would. Sortings and orderings in graphics have a better chance of conveying information, especially when guided by context and statistics. As always with graphics there is unlikely to be an ‘optimal’ solution, and so the task is more to find a set of informative sortings and orderings.