Reading scatter plots on ACT Science: describing the correlation (positive, negative, or none) and its strength, and using a line of best fit to estimate values and spot outliers.

What this topic is asking

A scatter plot shows many individual data points rather than a single smooth line, and ACT Science uses it to test whether you can describe a correlation (its direction and strength), use a line of best fit to make estimates, and spot outliers. It also sets up a reasoning point the ACT values: that a correlation does not prove causation.

Describing a correlation

A correlation has two parts: direction and strength.

Direction:

• Positive correlation: as x increases, y tends to increase; the cloud rises from lower left to upper right.
• Negative correlation: as x increases, y tends to decrease; the cloud falls from upper left to lower right.
• No correlation: the points show no clear direction; they form a shapeless cloud.

Strength:

• Strong correlation: the points cluster tightly around a line.
• Weak correlation: the points are loosely scattered, with a direction you can still see but with a lot of spread.

So a full description is a pairing, such as "strong positive" or "weak negative." Direction sets the sign; tightness of the cluster sets the strength.

Using a line of best fit

A line of best fit (trend line) is the single straight line that passes as close as possible to the middle of the scattered points. Once it is drawn, you read it exactly like a line graph:

• To estimate a y-value, go up from the x-value to the line, then across to the y-axis.
• To compare with a real data point, see whether that point sits above or below the line.

The line lets you interpolate within the data and, with more caution, extrapolate beyond it, the same logic as in interpolation and extrapolation.

Spotting outliers

An outlier is a point that lies far from the trend the rest of the data follow, for example a single point well above the best-fit line when every other point hugs it. The ACT may ask you to identify the outlier or to reason about its effect: a single outlier can pull a best-fit line toward it and can signal a measurement error or an unusual case. Identifying the point that does not fit the pattern is a common, quick question.

Correlation versus causation

The reasoning point the ACT cares about is that a correlation between two variables does not prove one causes the other. Two quantities can move together because one causes the other, because a third factor drives both, or by coincidence. A strong positive correlation between ice cream sales and drowning rates does not mean ice cream causes drowning; warm weather raises both. On the ACT, be cautious about any answer that leaps from "these are correlated" to "this causes that," especially in Evaluation questions, developed in evaluating models and inferences.

Try this

Q1. A scatter plot's points fall from upper left to lower right but are loosely spread. Describe the correlation in two words. [2 points]

• Cue. Weak negative: falling direction (negative), loosely scattered (weak).

Q2. A scatter plot shows a strong positive correlation between two variables. Why can you not conclude that one variable causes the other? [2 points]

• Cue. Correlation does not prove causation; a third factor could drive both, or the link could be coincidental, so causation needs more than a correlation.