Scatter Plots & Association

A scatter plot shows two measurements for each person or thing in a data set — one on the $x$ -axis, one on the $y$ -axis. Each point is one member of the data set: one student, one car, one game. Looking at the whole cloud of points tells you whether the two measurements move together.

That overall pattern is called association. Your job on these problems is to name one of three patterns — positive, negative, or no association — and to spot outliers, the points that ignore the pattern.

The three associations

Positive association: the points rise from left to right. As $x$ increases, $y$ tends to increase. Hours worked and money earned rise together.

Negative association: the points fall from left to right. As $x$ increases, $y$ tends to decrease. A car's age and its resale value fall together — older cars tend to be worth less.

No association: the points are scattered with no clear rise or fall. Knowing $x$ tells you nothing about $y$ , like the number of letters in a student's name and their quiz score.

The scatter plot below shows a positive association — the cloud of points climbs from the lower left toward the upper right.

Read it with one sweep

Sweep your eyes across the plot from left to right and ask one question: are the points climbing, dropping, or wandering? The pattern does not need to be a perfect line — the key phrase is tends to. A loose upward drift is still a positive association, even if a few points sit off the trend.

Outliers

An outlier is a point that sits far away from the pattern the rest of the points follow. In a rising cloud of points, a point in the upper left — a small $x$ paired with a large $y$ — breaks the pattern, so it is an outlier. One outlier does not change the name of the association; it is the exception to it.

Worked examples

Example 1: naming a positive association

A scatter plot has points at $(1, 2)$ , $(3, 3)$ , $(4, 5)$ , $(6, 6)$ , and $(8, 9)$ . Describe the association.

Sweep from left to right — the

y

-values go

2,\; 3,\; 5,\; 6,\; 9

The points rise from left to right

Rising from left to right means positive association

Answer: Positive association

Example 2: naming a negative association

A scatter plot compares hours of TV watched to quiz scores, with points at $(1, 9)$ , $(2, 8)$ , $(4, 6)$ , $(6, 4)$ , and $(8, 2)$ . Describe the association.

Sweep from left to right — the

y

-values go

9,\; 8,\; 6,\; 4,\; 2

The points fall from left to right

Falling from left to right means negative association

In context: more TV time predicts a lower quiz score

Answer: Negative association

Example 3: spotting an outlier

A scatter plot has points at $(1, 1)$ , $(2, 3)$ , $(4, 4)$ , $(6, 6)$ , $(7, 8)$ , and $(1, 8)$ . Which point is an outlier?

Find the pattern most points follow — they rise steadily from lower left to upper right

Check each point against that pattern

(1, 8)

pairs a small

x

with a large

y

, far above the rising pattern

A point far from the pattern is an outlier

Answer: $(1, 8)$ is the outlier

Try one yourself

Common questions

Does a positive association mean one variable causes the other?

No. Association only says the two measurements move together in the data. Ice cream sales and swimming accidents rise together because both happen in summer — neither causes the other. To claim cause, you need much more than a scatter plot.

The points rise, but they are not in a straight line. Is that still positive association?

Yes. Association describes the overall tendency, not a perfect line. If the cloud of points drifts upward from left to right, the association is positive even when individual points bounce around.

How far off does a point have to be to count as an outlier?

There is no exact cutoff at this level — an outlier is a point clearly separated from the pattern the rest of the points follow. If you cover it with your thumb and the pattern looks cleaner, it is an outlier.

Is no association the same as bad data?

No. It is a real, correct answer. It means the two variables do not move together — like shoe size and test scores. The data is fine; the variables are just unrelated.

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