What is Bivariate Data?
Data that involves two variables collected from the same subject or situation, allowing us to explore whether a relationship exists between them.
In everyday life, we often wonder whether two things are connected — does studying more lead to higher grades? Does temperature affect ice cream sales? Does height relate to shoe size? These are all bivariate questions.
When we collect two measurements from each individual or event, we have bivariate data. For example:
- Each student's hours of study AND their exam score
- Each day's temperature AND number of cold drinks sold
- Each person's height AND their arm span
Think of bivariate data like a pair of shoes — they always come together! You record both values at the same time, for the same person or event. One shoe without the other doesn't tell the whole story.
The two variables are usually labelled:
- x — the independent variable (the one we think might be causing or influencing)
- y — the dependent variable (the one we expect to change as a result)
Bivariate statistics is about finding, describing, and measuring relationships between two numerical variables. It does not automatically prove that one variable causes the other to change — that requires further investigation.
Scatter Graphs (Scatter Diagrams)
A scatter graph (also called a scatter diagram or scatter plot) is a type of graph where each data point is plotted as a coordinate pair on a set of axes, used to visually display the relationship between two variables.
Scatter graphs are the primary tool for visualising bivariate data. Here's how to construct one:
- Choose your axes — the independent variable () goes on the horizontal axis, the dependent variable () on the vertical axis.
- Scale your axes — choose a scale that fits all your data comfortably with no wasted space.
- Plot each pair — for each data pair , place a single point at that coordinate.
- Label everything — give both axes a title with units, and give the graph a title.
- Do NOT join the dots — scatter graphs never have lines connecting individual points.
Example: A student records the number of hours studied () and exam score () for 7 classmates:
| Hours studied () | Exam score () |
|---|---|
| 1 | 45 |
| 2 | 52 |
| 3 | 58 |
| 4 | 65 |
| 5 | 70 |
| 6 | 78 |
| 7 | 85 |
Each row becomes one plotted point. For instance, the pair (3, 58) is plotted 3 units along the -axis and 58 units up the -axis.
A very common mistake is to join the plotted points with lines like a line graph. Do not do this. Each point stands alone — we are not tracking one thing changing over time.
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