I teach an introductory economic geography course. To help my students develop a better understanding of the kinds of countries found in the contemporary world economy and an appreciation of data reduction techniques, I want to construct an assignment that creates a typology of different kinds of countries (e.g, high-income high-value added mfg long life expectancy; high income natural resource exporter mid-high life expectancy; with Germany being an element of the first type, and Yemen an example of the second type). This would use publicly available UNDP data (which if I recall correctly contains socioeconomic data on a bit less than 200 countries; sorry no regional data are available).
Prior to this assignment would be another which asks them (using the same --- largely interval or ratio level --- data) to examine correlations between these same variables.
My hope is that they would first develop an intuition for the kinds of relationships between different variables (e.g., a positive relationship between life expectancy and [various indicators of] wealth; a positive relationship between wealth and export diversity). Then, when using the data reduction technique, the components or factors would make some intuitive sense (e.g., factor / component 1 captures the importance of wealth; factor / component 2 captures the importance of education).
Given that these are second to fourth year students, often with limited exposure to analytical thinking more generally, what single data reduction technique would you suggest as most appropriate for the second assignment? These are population data, so inferential statistics (p-vlaues, etc.) are not really necessary.