Statistics & Probability

Scatter Plots

Constructing and interpreting a scatter plot to investigate patterns of association.

Intermediate20 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Do Two Quantities Move Together?

Before reading on, predict: do you think students who study more hours for a test tend to score higher, lower, or about the same as students who study less? A list of study hours and a separate list of test scores wouldn't make this obvious — but what if each student's two numbers were plotted together, as a single point?

Definition — Scatter Plot

A graph plotting pairs of related values as points, one axis for each quantity, used to investigate whether a relationship (an association) exists between them.

Plotting each student's study hours against their score, as one point per student, reveals a pattern a plain list never could: if the points generally trend upward from left to right, more studying is associated with higher scores — a positive association. If they trend downward, it's a negative association. If the points look like a random scatter with no visible trend, there's no clear association at all.

Worked Example — Identifying the Direction of an Association

A scatter plot of a car's age (x) versus its resale value (y) shows points trending downward from left to right — older cars generally have lower resale values. This is a negative association.

Worked Example — Identifying an Outlier

In a scatter plot of hours worked versus pay, one point sits far above the general trend of the rest of the data, representing an employee paid much more than their hours alone would suggest. This point is an outlier — a value that doesn't fit the overall pattern.

Graph Visualizer

Trace modePoint mode (click graph to plot)

Show x^2

Color

Expression

Domain & range

x min

x max

y min

y max

Precision (decimal places)2

Evaluate a point

Evaluate at x =

x^2 = 0

Tip

An association shown in a scatter plot describes a pattern, not a guaranteed cause — two quantities trending together doesn't automatically mean one directly causes the other.

Common Mistakes

Assuming an association shown in a scatter plot proves that one quantity directly causes changes in the other.
A scatter plot only reveals whether two quantities tend to move together — confirming an actual cause requires more than just an observed association.
Confusing a positive association (both quantities increasing together) with a negative association (one increasing as the other decreases).
Check the overall direction of the trend in the points: rising left to right is positive, falling left to right is negative.

Key Takeaways

A scatter plot displays paired data as points, revealing whether an association exists between two quantities.
A positive association trends upward, a negative association trends downward, and no clear trend means no association.
An outlier is a point that doesn't fit the overall pattern of the rest of the data.

Summary

Scatter plots reveal patterns of association between two quantities that a plain list of numbers would hide. The final lesson fits an actual line to that pattern, turning a visual trend into a usable predictive model.

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