Abstract:  Biplots are among the most powerful—and perhaps most misunderstood—tools for visualizing multivariate data. In this minicourse, we will unpack what a biplot really is by starting from its mathematical foundations and building up to the familiar joint display of observations and variables derived from a low-dimensional approximation (most often via singular value decomposition). We will also examine why this approximation can be both the source of a biplot’s insight and the reason it can be misleading. We will cover the classic PCA biplot using both standardized and non-standardized data. Participants will learn how to read a biplot responsibly: interpreting groups and gradients among observations, understanding variable contributions and correlations, recognizing when apparent patterns are projection artifacts, and diagnosing common misreading (e.g., over-interpreting angles or ignoring explained variance). The session will also provide practical guidance on construction and reporting: choosing the scaling that matches the question, handling mixed units, and dealing with outliers. The goal is to leave you with a clear mental model of biplots, a checklist for interpretation, and the confidence to use them as an exploratory tool in real analyses —while knowing what the plot can and cannot tell you.