Scatterplots and Association
A scatterplot shows paired data as points: each point is one observation, with one measurement on the x-axis and the other on the y-axis. Plot hours studied against test scores for a whole class and you get a cloud of points — and the shape of that cloud tells a story.
The pattern in the cloud is called the association. Reading it takes two quick judgments: which direction do the points trend (up, down, or no trend), and how tightly do they follow that trend (strong or weak)? That is the entire skill.
The three directions
Positive association: the points trend upward from left to right. As increases, increases too. Height and shoe size, hours studied and test score, temperature and lemonade sales — bigger one, bigger the other.
Negative association: the points trend downward from left to right. As increases, decreases. Days since a phone charge and battery percent, or price of an item and units sold.
No association: the points are scattered with no visible trend. Knowing tells you nothing useful about — like shoe size and test score. There is no line worth drawing.
The scatterplot below shows a positive association: the cloud of points drifts upward from left to right, so larger -values tend to come with larger -values.
Strong vs. weak
Direction is only half the description. If the points hug an invisible line tightly, the association is strong; if they follow the trend loosely with lots of spread, it is weak. A full answer names both: strong positive, weak negative, and so on.
Strength matters because it controls how much you should trust predictions. A strong association means a trend line will predict well; a weak one means predictions come with a lot of miss.
Outliers
An outlier is a single point far away from the overall pattern — the student who barely studied but aced the test. One or two outliers do not change the direction of the association, but they can make a strong pattern look weaker, and they are worth mentioning when you describe a plot.
When you see an outlier, describe the association of the main cloud first, then note the outlier separately: for example, a strong positive association with one outlier.
Worked examples
Example 1: an upward trend
A scatterplot compares minutes spent practicing free throws () with free throws made (). The points rise from the lower left to the upper right, packed close to a line. Describe the association.
Answer: Strong positive association
Example 2: a downward trend
A scatterplot compares a car's age in years () with its resale value (). The points fall from left to right, but with a fair amount of spread. Describe the association.
Answer: Weak negative association
Example 3: no pattern
A scatterplot compares students' birth month () with their quiz scores (). The points are spread evenly with no visible trend. Describe the association.
Answer: No association
Try one yourself
Common questions
How do I tell strong from weak?
Imagine the single straight line that fits the cloud best. If most points sit close to that line, the association is strong. If the points spread far above and below it, the association is weak. It is a judgment call, not a calculation — the correlation coefficient handles the exact number later.
Does positive association mean the y-values are positive?
No. Positive describes the direction of the trend, not the sign of the numbers. Data with all negative -values can still show a positive association if rises as rises.
Can a scatterplot show a pattern that isn't a line?
Yes. Points can follow a curve — a ball's height over time arcs up and comes back down. This lesson focuses on linear association, so a clear curve is usually described as nonlinear rather than positive or negative.
Does a strong association mean one variable causes the other?
No. Association only says the variables move together. Ice cream sales and drowning both rise in summer, but neither causes the other — hot weather drives both. Correlation vs. causation is its own lesson.
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