Scatterplot in AP Statistics

In AP Statistics, a scatterplot is a graph that shows the relationship between two quantitative variables measured on the same individuals. The explanatory variable goes on the x-axis, the response variable goes on the y-axis, and each individual is plotted as one dot.

What is Scatterplot?

A scatterplot is the go-to graph whenever you have two quantitative variables measured on the same individuals. Think wolf length and wolf weight, or engine size and fuel efficiency. Each individual becomes one dot. Its x-coordinate is the value of the explanatory variable and its y-coordinate is the value of the response variable.

The point of a scatterplot is to let you see the relationship before you calculate anything. On the AP exam, describing a scatterplot means hitting four features in context. Direction is positive or negative. Form is linear or curved. Strength is how tightly the dots follow the pattern. Unusual features include outliers and clusters. Think of a scatterplot as the "look before you leap" step. Correlation and regression are only trustworthy after the picture tells you the pattern is roughly linear.

Why Scatterplot matters in AP® Statistics

Scatterplots live in topic 5.1, Graphical Representations Between Two Quantitative Variables, and they are the entry point to everything else in two-variable quantitative data. Every later tool assumes you've already looked at the scatterplot. That includes correlation, least-squares regression lines, residuals, and spotting influential points. The big exam idea is that a graph comes before a number. A correlation of r = 0 doesn't mean "no relationship" if the scatterplot shows a strong curve, and a regression line is meaningless on curved data. Scatterplots are also where you practice the AP habit of describing in context. You say "heavier wolves tend to be longer," not just "positive."

How Scatterplot connects across the course

Correlation (Unit 5)

Correlation (r) is a scatterplot's linear pattern squeezed into one number between -1 and 1. It only measures linear strength and direction, so always check the scatterplot first. A perfect U-shaped curve can have r near 0.

Linear Regression (Unit 5)

A least-squares regression line is drawn right on top of a scatterplot. It's the line that best summarizes the dots. If the scatterplot isn't roughly linear, the line is the wrong model no matter how nicely it fits on paper.

Outlier (Unit 5)

In one-variable data, an outlier is just far from the center. In a scatterplot, a point can be an outlier because it falls far from the overall pattern, even if its x and y values look normal on their own. These points can pull correlation and the regression line in big ways.

Response Variable (Unit 5)

Which variable goes on which axis isn't random. The response variable (the outcome you're trying to predict or explain) goes on the y-axis. Getting this right is what makes the regression line predict the thing you actually care about.

Is Scatterplot on the AP® Statistics exam?

Scatterplots show up constantly, often as the opening setup for FRQ Question 1. Released FRQs have used scatterplots of wolf length versus weight (2017 Q1), number of customers in line versus checkout time (2018 Q1), and bullfrog length versus mass (2022 Q1). In questions like these, you're expected to:

• Describe the relationship with direction, form, strength, and unusual features, in context using the variable names.
• Choose axes correctly. Multiple-choice stems ask things like which variable belongs on the x-axis for engine size and fuel efficiency. The explanatory variable (engine size) goes on x.
• Spot non-linear form. Questions ask which features suggest a curved relationship, such as a clear bend or a pattern that levels off.
• Handle unusual points and clusters. If you see distinct clusters (like height vs. weight splitting into groups), the next step is to look for a lurking categorical variable that separates the groups. If two points sit far from a tight linear pattern, identify them as outliers and think about how they affect r and the line.

The easiest points to lose are context points. "Strong, positive, linear" with no variable names usually won't earn full credit.

Scatterplot vs Correlation

A scatterplot is a picture of any relationship between two quantitative variables, whether it's linear, curved, clustered, or messy. Correlation (r) is a number that only measures the strength and direction of a linear relationship. The scatterplot can reveal curves and outliers that r completely hides, which is why you look at the graph before you trust the number.

Key things to remember about Scatterplot

• A scatterplot displays two quantitative variables measured on the same individuals, with one dot per individual.

• Put the explanatory variable on the x-axis and the response variable on the y-axis.

• To describe a scatterplot, state its direction, form, strength, and any unusual features like outliers or clusters, always using the context of the variables.

• Always look at the scatterplot before computing correlation or fitting a regression line, because both assume the relationship is roughly linear.

• Distinct clusters in a scatterplot often signal a hidden categorical variable that splits the individuals into groups.

• A point can be an outlier in a scatterplot by falling far from the overall pattern, even if its x and y values are ordinary on their own.

Frequently asked questions about Scatterplot

What is a scatterplot in AP Statistics?

A scatterplot is a graph of two quantitative variables measured on the same individuals, with each individual shown as a dot. The explanatory variable goes on the x-axis and the response variable goes on the y-axis, so you can see the direction, form, and strength of the relationship.

Does a correlation near 0 mean the scatterplot shows no relationship?

No. A correlation near 0 only means there's no linear relationship. The scatterplot could still show a strong curved pattern, like a U shape, which is exactly why you check the graph first.

How is a scatterplot different from correlation?

A scatterplot is a graph that can show any kind of pattern, including curves, clusters, and outliers. Correlation is a single number from -1 to 1 that summarizes only the linear part of that pattern.

Which variable goes on the x-axis of a scatterplot?

The explanatory variable goes on the x-axis and the response variable goes on the y-axis. For engine size and fuel efficiency, engine size is explanatory (x) and miles per gallon is the response (y).

How do I describe a scatterplot on the AP Stats FRQ?

Name the direction (positive/negative), form (linear/curved), strength (strong/moderate/weak), and any unusual features, all in context. For example, for the 2017 wolf FRQ you'd describe how wolf weight changes as wolf length increases, using those variable names.