Aaron at Plan Space from Outer Nine has a valuable insight about how standard statistics textbooks often favor technique over understanding. I think we could extend approach this from “central tendency” to the broader question of “association.” We tend to view various measures of association  (for example, Chi-square χ², Spearman’s rho ρ, Pearson r, R², etc.) as completely different measurements. But the underlying question is the same: do certain types of values of x tend to coincide with certain values of y? That’s the core question behind most descriptive statistics. The way we measure the association depends on the type of data, but the core question is the same. In data visualization, we can think of mosaic plots and scatterplots as similarly related. How can we see associations in the data? We could use a scatterplot, even for nominal data, but a large coincidence would just result in lots of overplotting. That’s why we use a mosaic plot: association becomes a big box. In short, there is great virtue in returning to first principles

A sensible characterization of mode, median, and mean.