Bivariate data

Bivariate data is a set of ordered pairs, one pair per observational unit, so the two values inside a pair were recorded on the same individual. That pairing is the entire content of the data set. Two columns of equal length are not bivariate data unless row $i$ of one column describes the same unit as row $i$ of the other. When both variables are quantitative the pairs go on a scatterplot; when both are categorical they go in a two-way table.

Five people record hours slept, $x$, and errors on a proofreading task, $y$: $(4, 12)$, $(5, 10)$, $(6, 9)$, $(7, 6)$, $(8, 3)$. The correlation is $r = -0.9839$ and the least-squares line is $\hat{y} = 21.2 - 2.2x$ (y-hat). More sleep, fewer errors.

"I have a sleep column and an error column, so I have bivariate data." Not until the rows line up. Sort the error column ascending in a spreadsheet while the sleep column stays where it is, and you now hold $(4, 3)$, $(5, 6)$, $(6, 9)$, $(7, 10)$, $(8, 12)$. Same ten numbers. Each column still has the mean and standard deviation it had before, so nothing in either one alone looks wrong. And $r = +0.9839$: the finding reversed by one careless sort.

Two lists from two different groups are not bivariate either. Twenty men's heights and twenty-five women's heights are one variable measured on two samples, which is univariate data compared across groups. Pairs also have to be complete: a unit missing one of its two values contributes to neither the scatterplot nor $r$. And pairing is not causation, only the arithmetic that lets you ask about association at all.

The Fall 2026 course framework defines a bivariate quantitative data set as ordered pairs from two quantitative variables collected from the same individuals, in topic 5.1, Graphical Representations Between Two Quantitative Variables. Two categorical variables get their own treatment in topic 2.1.