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AP Statistics 5.1 Graphical Representations Between Two Quantitative Variables Questions

Construct, describe, and compare scatterplots using form, direction, strength, unusual features, and contextual evidence for claims.

Syllabus
Effective Fall 2026
Course
AP Statistics

Exam points

  • plot paired quantitative observations with explanatory x and response y axes, labels, and preserved pairs
  • describe a quantitative association in context using its form, direction, and strength
  • identify clusters, outliers, and influential points that depart from or alter the overall pattern
  • compare scatterplots or subgroups to explain changes in strength, direction, form, or apparent trend
  • use scatterplot evidence to support or reject a contextual claim about two quantitative variables

Covered syllabus points

5.1.A—Construct scatterplots depicting the relationship between two quantitative variables5.1.B—Describe the characteristics of a scatterplot5.1.C—Justify a claim using scatterplots depicting the relationship between two quantitative variables

Question 1

[Maximum number: 4]

Natural gas is used in some households to heat the home, to heat the water, and to cook. A utility company sent the following bar chart to a household to show the amount of natural gas, measured in therms (a unit of heat energy), that the household used last year. The chart shows the number of therms and the average monthly temperature, in degrees Fahrenheit, for each month of the year.

Month and Average Monthly Temperature

Figure for Question 1 — AP Statistics

Question (a)

(a)

Construct a graph showing therm use versus average monthly temperature.

Figure for Question (a) — AP Statistics

Question (b)

(b)

Describe what the scatterplot reveals that the bar chart does not.

Question 2

A biologist gathered data on the length, in millimeters (mm), and the mass, in grams (g), for 11 bullfrogs. The data are shown in Plot 1.

Figure for Question 2 — AP Statistics

From the data, the biologist calculated the least-squares regression line for predicting mass from length. The least-squares regression line is shown in Plot 2.

Official question visual

Official question visual

Based on the scatterplot, describe the relationship between mass and length, in context.

Question 3

[Maximum number: 4]

Attendance at games for a certain baseball team is being investigated by the team owner. The following boxplots summarize the attendance, measured as average number of attendees per game, for 47 years of the team's existence. The boxplots include the 30 years of games played in the old stadium and the 17 years played in the new stadium.

Figure for Question 3 — AP Statistics

Question (a)

(a)

Compare the trends in average attendance over time between the old and new stadium.

Question (b)

(b)

Consider the following scatterplots.

Graph I

Graph I

Question (i)

(i)

Graph I shows the average attendance versus number of games won for each year. Describe the relationship between the variables.

Question (ii)

(ii)

Graph II shows the same information as Graph I, but also indicates the old and new stadiums. Does Graph II suggest that the rate at which attendance changes as number of games won increases is different in the new stadium compared to the old stadium? Explain your reasoning.

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