In a prior post, I showed a chart of Pisa test scores that can be used to investigate differences between any pair of countries. At least one reader found it confusing, containing too much data. I then realize that if the objective of the chart is re-stated as "How the UK fared relative to other OECD countries", which was the intent of the original Guardian chart, the chart could be presented in the following simplified fashion:
Simplification can be achieved in many ways, one of which is simplifying the objective. In fact, I'd not be opposed to showing just the left side of the chart, which addresses an even more general question, which is how the countries fared in a general sense.
While the lines in the Guardian chart display correlations of math, reading and science scores within specific countries, essentially a parallel coordinates plot, the same correlation can be visualized in a scatterplot matrix (see this post).
Each scatter plot here relates the scores of two subject areas as indicated by the axis labels. The simplest observation is the high degree of positive correlation on all three panels: in other words, countries in general do well in all three subjects, or poorly in all three subjects.
This pattern confirms why it isn't very productive to focus readers' attention on this set of correlations when dealing with this data set.
You'll notice the use of colored dots on the scatter plots. Imagine that I have put the countries into groups based on overall scores (rather than just reading scores) as in my earlier analysis. The dots of the same color represent countries that are deemed to have performed similarly. The black cross indicates the "average country".
Focusing on the colors for the moment, you can confirm yet again that a country doing well in one subject is highly predictive of it doing well in the other subjects.
As I pointed out at the start of the prior post, using a little statistical technique allows us to understand the data better, and plotting summaries of the data allows us to draw more interesting conclusions than putting all the data, unperturbed, onto a canvass.