Currently, on the analysis page, a world average is displayed for many of the nation attributes, this gives players an idea as to whether they are above or below the average, but does not give a sense of scale. Showing the upper and lower quartiles would allow players to determine how much above or below the average they are.
The main problem I can foresee with this is that it would increase the width of the displayed scale most of the time. The first one (and most problematic) that comes to mind is Population as its average of 1186M is far greater than that of a new nation, making the width of the displayed scale already very large, adding the upper quartile to the scale would make it considerably bigger.
I think that showing the quartiles could be toggleable to prevent the issue, or, similar to displaying the average, the quartiles could only be shown for specific attributes. For example, no average is shown for the Taxation attribute, so no quartiles could be shown for Population.