Bivariate Data and the Scatter Diagram

Every statistical idea studied so far — mean, dispersion, probability — has described a single variable at a time. Many real business questions instead ask about the relationship between two variables measured on the same set of items: does higher advertising spend go with higher sales, does more experience go with a higher salary. Data where each observation carries a pair of values $(x,y)$ is called bivariate data, and studying how the two move together is the subject of this chapter.

The first, purely visual, tool for exploring a bivariate relationship is the scatter diagram: plot every pair $(x_i,y_i)$ as a point on a graph, with $x$ along the horizontal axis and $y$ along the vertical axis. The overall shape of the resulting cloud of points suggests, at a glance, whether a relationship exists and what kind:

The scatter diagram only gives a visual, qualitative impression — it cannot by itself say exactly how strong the relationship is, or put a precise number on it. That is exactly the gap the correlation coefficient of the next section fills.

This two-variable way of thinking about data, and the scatter diagram as its first visual tool, is a foundational statistical idea used identically across every Indian commerce board's statistics curriculum, wherever the relationship between two business variables is studied.