Describe trends and associations in scatter plots

A scatter plot represents paired numerical measurements and reveals how one quantity tends to vary with another, including positive, negative, or no association and patterns that are approximately linear or nonlinear. Descriptions attend to overall direction, clustering, gaps, and outliers while distinguishing a relationship in the data from proof that one variable causes changes in the other; fitting equations or calculating correlation coefficients is beyond this scope.

Detailed Explanation: Describe trends and associations in scatter plots

A scatter plot shows pairs of measurements as points. To describe it, look for:

Direction:
- Positive association: As $x$ increases, $y$ tends to increase.
- Negative association: As $x$ increases, $y$ tends to decrease.
- No association: The points do not show a clear direction.
Shape: Decide whether the pattern is approximately linear (like a straight-line trend) or nonlinear (curved or changing direction).
Clustering and gaps: Notice where many points are grouped and whether there are empty spaces.
Outliers: Look for points that are far from the main pattern.
Causation: An association shows that two quantities are related in the data. It does not prove that one quantity causes the other to change.

Worked example

A teacher records how many hours students studied and their quiz scores.

Hours studied, $x$	Quiz score, $y$
4	62
5	65
5	68
6	70
6	72
7	75
7	78
8	80
8	82
9	84
10	86
6	95

Each row becomes one point on a scatter plot. For example, the first row becomes $(4,62)$ .

Step 1: Describe the direction.
Most points rise as you move from left to right. Students who studied more hours generally had higher quiz scores. This is a positive association.

Step 2: Describe the shape.
The main group of points follows a pattern that is roughly straight, so the association is approximately linear.

Step 3: Look for clustering and gaps.
Most points are grouped between about $4$ and $10$ hours of studying and between scores of $62$ and $86$ . There is no large gap in this main group.

Step 4: Look for an outlier.
The point $(6,95)$ is much higher than the other scores for about $6$ hours of studying. It is an outlier because it is separated from the main pattern.

Step 5: Write a description.
A good description is:

The scatter plot shows a positive, approximately linear association between hours studied and quiz score. The points generally rise from left to right and are fairly close to a straight-line pattern. There is one high outlier at about $(6,95)$ . This association does not prove that studying more hours causes higher quiz scores.

Learn by doing: Describe trends and associations in scatter plots

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Graphing - Scatter Plot (Linear) - Graph to Association Direction

Earned ?