AP Statistics · Unit 5 · Topic 5.1

Scatterplots Study Lab

A scatterplot shows the relationship between two quantitative variables measured on the same individuals. The explanatory variable goes on the x-axis and the response variable on the y-axis. Drag points, add your own, and practice the four-part description graders look for: direction, form, strength, and unusual features.

1. Build and describe a scatterplot

Pick a data set, then drag any point. Turn on Click to add points to place new ones. Describe what you see with the four AP words, then check yourself.

Explanatory (x) → Response (y) Describe: direction · form · strength · unusual features
Data sets

Scatterplot

Data pointUnusual pointPattern the computer sees

Describe it yourself

Direction
Form
Strength
Unusual features
Choose one word in each row, then check.
Number of points
Direction
Form
Strength

How the computer decided

The cutoffs here are rough guides, not AP rules. On the exam, any reasonable description earns credit when it matches the graph and is written in context.

2. Key ideas

Variables

Explanatory and response

The explanatory variable (x) may help explain or predict changes in the response variable (y). Put the explanatory variable on the horizontal axis. Example: hours studied (x) and exam score (y).

Direction

Positive, negative, or neither

Positive: as x increases, y tends to increase. Negative: as x increases, y tends to decrease. A curved pattern that goes down and then up has no single direction.

Form

Linear or curved

If the points follow a straight-line pattern, the form is linear. If they bend, the form is nonlinear (curved). A shapeless cloud has no clear form.

Strength

How closely the points follow the form

Strong means the points hug the pattern tightly. Weak means they are widely scattered around it. Strength is about scatter, not steepness: a steep line can be weak, and a flat-ish line can be strong.

Unusual features

Outliers and clusters

An outlier is a point that falls far from the overall pattern. Clusters are separate groups of points with gaps between them. Always mention them, or say there are none.

Association

Association is not causation

A scatterplot shows whether two variables are associated. It cannot show that changing x causes y to change unless the data come from a well-designed experiment.

3. Describing a scatterplot

Each part of the description, what it means, and a model sentence. Always name both variables and the individuals.

FeatureOptionsWhat to look forSample wording
DirectionPositive, negative, noneDo the points rise or fall from left to right?"As hours studied increase, exam scores tend to increase."
FormLinear, curved (nonlinear)Would a straight line or a curve summarize the pattern?"The relationship is roughly linear."
StrengthStrong, moderate, weakHow tightly do points cluster around the pattern?"The points are tightly clustered, so the association is strong."
Unusual featuresOutliers, clusters, nonePoints far from the pattern; separate groups"The student who studied 3 hours and scored 98 is an outlier."
ContextBoth variables + individualsName what x and y measure and who was measured"...between hours studied and exam score for these 14 students."

4. On the FRQ

How to earn the points

  • Use all four parts and context in one or two sentences: "There is a strong, positive, linear association between hours studied and exam score for these students, with no apparent outliers."
  • Identify the explanatory and response variables when asked, and put the explanatory variable on the x-axis when you draw a scatterplot.
  • Label both axes with the variable names and units, and use an even scale.
  • When you mention an outlier, identify it specifically, for example by giving its coordinates.
  • If the data come from an observational study, avoid causal language. Say "is associated with," not "causes" or "leads to."

Common mistakes

  • Describing only direction ("it's positive") and skipping form, strength, and unusual features.
  • Leaving out context. "Strong positive linear" earns little without naming the variables.
  • Confusing strength with slope. A steep pattern with lots of scatter is still weak.
  • Calling a curved pattern "linear" because it trends upward. Check whether a straight line would miss the bend.
  • Saying x causes y because the association is strong.

5. Practice questions

AP-style multiple choice. Pick an answer to see the explanation.

0 / 0 correct

6. Key terms

The vocabulary for topic 5.1. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 5 terminology guide.