One-Variable vs Bivariate Data
Learn how bivariate data differs from one-variable data for NSW Year 12 Mathematics Standard 1 (NESA outcome MST-12-S1-06). One-variable data records a single measurement for each person or object; bivariate data records two measurements for each one, kept together as a pair.
You will decide which type of data a situation calls for and why, read a bivariate table and see what each dot on a scatter plot stands for — the first step in finding out whether two quantities, such as height and arm span, are related.
Theory
One-variable data records a single measurement for each individual; bivariate data records two measurements for each individual, kept together as a pair. This Year 12 Standard 1 (NSW) guide shows how to tell them apart, name the two variables, read a bivariate table and understand what each dot on a scatter plot shows.
One-variable (univariate) data records one measurement for each individual, such as just the mass of every parcel. It is shown in a dot plot, column graph or histogram.
Bivariate data records two measurements for each individual, kept together as a pair, such as the height and the shoe size of every student. It is shown in a two-row table or a scatter plot.
Each pair belongs to one individual, so on a scatter plot one dot stands for one individual and shows two values. To find out whether two quantities are related, you must collect bivariate data.
There is no formula here — the test is a count. Ask how many things are measured for each individual:
Bivariate data is written as pairs, one pair for each individual:
How to decide if data is one-variable or bivariate
- Identify the individuals — the people, objects or days the data is about.
- Count the measurements recorded for each individual: one or two.
- Name the variable(s), with units, and state the type of data.
- Read a two-row table by finding the given value in the first row and reading the value directly below it.
Count the measurements for each individual.
| \(\text{(i) time only}\) | \(\Rightarrow\) | \(1\ \text{measurement}\) |
| \(\text{(ii) age and blood pressure}\) | \(\Rightarrow\) | \(2\ \text{measurements}\) |
| \(\text{(iii) number of pets only}\) | \(\Rightarrow\) | \(1\ \text{measurement}\) |
(i) one-variable, (ii) bivariate, (iii) one-variable.
List what is recorded for each unit, then count.
| \(\text{Variable 1}\) | \(=\) | \(\text{number of bedrooms}\) |
| \(\text{Variable 2}\) | \(=\) | \(\text{weekly rent (\$)}\) |
| \(2\ \text{per unit}\) | \(\Rightarrow\) | \(\text{bivariate}\) |
Number of bedrooms and weekly rent: bivariate data.
| Temperature (\(^\circ\)C) | 18 | 22 | 26 | 30 | 34 |
|---|---|---|---|---|---|
| Swimmers | 45 | 70 | 95 | 120 | 160 |
Find \(26\) in the temperature row, then read straight down.
| \(\text{temperature}\) | \(=\) | \(26^\circ\text{C}\) |
| \(\text{swimmers below it}\) | \(=\) | \(95\) |
95 swimmers came that day.
Each dot has an across value and an up value.
| \(\text{(i) across and up}\) | \(\Rightarrow\) | \(2\) |
| \(\text{(ii) variables}\) | \(=\) | \(\text{age and value}\) |
| \(\text{(iii) two per car}\) | \(\Rightarrow\) | \(\text{bivariate}\) |
(i) \(2\). (ii) Age and value. (iii) Bivariate.
Common pitfalls
Frequently asked questions
What is the difference between univariate and bivariate data?
Univariate (one-variable) data records one measurement for each individual, such as just the height of each student. Bivariate data records two measurements for each individual, kept together as a pair, such as height and arm span.
What is an example of bivariate data?
The age and the value of each used car, the temperature and the number of swimmers each day, or the study hours and the test mark of each student. Each individual gives a pair of values.
How do you know if data is bivariate?
Count how many things are measured for each person, object or day. One measurement means one-variable data; two measurements recorded together as a pair means bivariate data.
Is data bivariate if you measure lots of people?
No. Measuring 200 people is still one-variable data if you only record one thing about each of them. It only becomes bivariate when two things are recorded for each person.
What graph is used for bivariate data?
A scatter plot. Each dot stands for one individual and is placed using its two values, one across and one up. One-variable data uses a dot plot, column graph or histogram instead.