Representing Relationships Between Two Quantitative Variables
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AP Statistics › Representing Relationships Between Two Quantitative Variables
A meteorology student recorded data for 20 days in one city. For each day, the student recorded the high temperature (in °F) and the amount of electricity used that day (in kWh) for air conditioning in the student’s home. Each point in the scatterplot represents one day. Which statement best describes the relationship between temperature and electricity use?
There is a strong positive linear association: hotter days tend to use more electricity for air conditioning.
There is no association because electricity use varies across all temperatures.
There is a strong negative linear association: hotter days tend to use less electricity for air conditioning.
Higher temperature causes higher electricity use for air conditioning on every day.
There is a strong association but it is clearly non-linear and U-shaped.
Explanation
This question tests understanding of the relationship between temperature and electricity use for air conditioning. The correct answer is B because as temperature increases (moving right), electricity use increases (moving up), showing a positive association. The points cluster tightly around an upward-sloping pattern, indicating a strong linear relationship. This makes practical sense - hotter days require more air conditioning. Choice A incorrectly reverses the relationship, claiming hotter days use less electricity. When interpreting real-world scatterplots, consider whether the relationship makes logical sense based on your understanding of the variables.