AP Statistics Quiz: Representing Relationships Between Two Quantitative Variables
19 questions · exam conditions
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Representing Relationships Between Two Quantitative VariablesQuestion 1 of 19

A scatterplot relates the score on a pre-test to the score on a post-test for students in a statistics course. The points are scattered, but generally, students who scored higher on the pre-test also scored higher on the post-test. The relationship, however, is not very tight. The best description would be:

A moderate, positive, linear association.
A strong, negative, linear association.
A weak, positive, non-linear association.
No association between pre-test and post-test scores.
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AP Statistics Quiz

AP Statistics Quiz: Representing Relationships Between Two Quantitative Variables

Practice Representing Relationships Between Two Quantitative Variables in AP Statistics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Representing Relationships Between Two Quantitative Variables, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A scatterplot relates the score on a pre-test to the score on a post-test for students in a statistics course. The points are scattered, but generally, students who scored higher on the pre-test also scored higher on the post-test. The relationship, however, is not very tight. The best description would be:

  1. A moderate, positive, linear association. (correct answer)
  2. A strong, negative, linear association.
  3. A weak, positive, non-linear association.
  4. No association between pre-test and post-test scores.

Explanation: The general trend that higher scores on one test are associated with higher scores on the other indicates a positive direction. The fact that the relationship is 'not very tight' suggests a moderate strength. Unless a curve is evident, a linear form is assumed.

Question 2

A study is conducted to explore the relationship between two variables. For each of 100 participants, their daily screen time (in hours) and their score on a happiness scale (from 1 to 10) are recorded. How is this data best classified?

  1. A set of two univariate datasets, one for screen time and one for happiness score.
  2. A bivariate dataset with one quantitative variable and one categorical variable.
  3. A bivariate quantitative dataset. (correct answer)
  4. An experimental dataset designed to show a causal relationship between the variables.

Explanation: The data consists of two variables measured for each participant. Screen time (in hours) is quantitative. A numerical scale like the happiness score is also treated as quantitative. Therefore, the data are bivariate and quantitative.

Question 3

A scientist plots the concentration of a chemical reactant over time during a reaction. The points on the scatterplot clearly follow a curve that decreases rapidly at first and then flattens out as time progresses. Which of the following is the best description of the form of this association?

  1. Linear, because the relationship can be approximated with a straight line.
  2. Non-linear, because the points clearly follow a curved pattern. (correct answer)
  3. Weak, because the rate of change is not constant throughout the reaction.
  4. Positive, because both time and concentration are positive measurements.

Explanation: The form of an association is its general shape. Since the points are described as following a curve rather than a straight line, the form is non-linear.

Question 4

A scatterplot is created to show the relationship between the number of hours spent exercising per week and the resting heart rate for a group of adults. Which of the following can NOT be determined from viewing the scatterplot alone?

  1. Whether the association between the two variables appears to be linear or curved.
  2. Whether there is a generally positive or generally negative trend in the data.
  3. Whether a change in exercise hours causes a change in resting heart rate. (correct answer)
  4. Whether there are any individuals who deviate significantly from the overall pattern.

Explanation: A scatterplot can show an association or correlation between two variables, but it cannot establish causation. Proving causation requires a well-designed, controlled experiment, not just observational data shown in a scatterplot.

Question 5

A researcher wants to investigate if the number of hours a student studies per week can be used to predict their grade point average (GPA). In this study, what are the explanatory and response variables?

  1. The explanatory variable is the grade point average, and the response variable is the number of hours studied.
  2. The explanatory variable is the number of hours studied, and the response variable is the grade point average. (correct answer)
  3. The explanatory variable is the student, and the response variable is the school they attend.
  4. Both the number of hours studied and the grade point average are response variables in this investigation.

Explanation: The explanatory variable is the one used to explain or predict changes in the response variable. Here, study hours are used to predict GPA, making study hours the explanatory variable and GPA the response variable.

Question 6

A scatterplot of data for the price of a used car versus its age in years shows that as the age of the car increases, its price tends to decrease. How would the direction of this association be described?

  1. A positive association, because both price and age are positive values.
  2. A negative association, because an increase in one variable is related to a decrease in the other. (correct answer)
  3. No association, because the relationship is expected and does not show a statistical pattern.
  4. A curvilinear association, because the price depreciation is not constant over time.

Explanation: A negative association occurs when higher values of one variable tend to be paired with lower values of another variable. As the age (one variable) increases, the price (the other variable) tends to decrease.

Question 7

A biologist creates a scatterplot of the height versus the weight of a sample of adult elephants. The points on the plot appear to follow a pattern that is reasonably straight. How would the form of this relationship be described?

  1. Linear, indicating the points follow a straight-line pattern. (correct answer)
  2. Non-linear, indicating the points follow a curved pattern.
  3. Strong, indicating the points are tightly clustered together.
  4. Positive, indicating that taller elephants tend to be heavier.

Explanation: The 'form' of a relationship in a scatterplot refers to its general shape. If the points follow a pattern that is roughly a straight line, the form is described as linear.

Question 8

An economist plots the gross domestic product (GDP) of a country against its adult literacy rate. The points on the scatterplot are very tightly clustered around a straight line with a positive slope. How would the strength of this association be described?

  1. Weak, because economic data often contains significant variability.
  2. Moderate, because a perfect relationship between these variables is not expected.
  3. Strong, because the points closely follow a clear linear pattern. (correct answer)
  4. Negative, because higher GDP can lead to a decrease in other societal factors.

Explanation: The 'strength' of an association refers to how closely the points in a scatterplot follow a particular form. When points are very tightly clustered around a line, the association is described as strong.

Question 9

A teacher creates a scatterplot of the number of absences for students in a class versus their final exam scores. The plot shows a general downward trend, but the points are widely scattered. Which of the following provides the best description of the association?

  1. A strong, positive, linear association.
  2. A weak, negative, linear association. (correct answer)
  3. A strong, negative, non-linear association.
  4. A moderate, positive, non-linear association.

Explanation: A 'downward trend' indicates a negative direction. 'Widely scattered' points indicate a weak strength. Assuming the general trend is straight, the form is linear. Therefore, the best description is a weak, negative, linear association.

Question 10

A city's environmental protection agency wants to determine if there is a relationship between the amount of rainfall (in inches) and the level of a certain pollutant (in parts per million) in the local river. They plan to use rainfall to help predict pollutant levels. Which variable should be plotted on the horizontal axis of the scatterplot?

  1. The pollutant level, because it is the response variable and is the primary focus of the study.
  2. The amount of rainfall, because it is the explanatory variable being used to make predictions. (correct answer)
  3. Either variable can be plotted on the horizontal axis, as the correlation between them will be the same.
  4. The day of the year on which the measurements were taken, as it is a potential confounding variable.

Explanation: By statistical convention, the explanatory (or predictor) variable is plotted on the horizontal (x) axis, and the response variable is plotted on the vertical (y) axis. Here, rainfall is used to explain or predict pollutant levels.

Question 11

A student creates a scatterplot of their classmates' heights versus their birth months (coded 1 for January, 2 for February, etc.). The points on the scatterplot show no discernible pattern and appear as a random cloud. What conclusion can be drawn about the association?

  1. There is a strong, linear association between height and birth month.
  2. There is a weak, negative association between height and birth month.
  3. There is a distinct non-linear association between height and birth month.
  4. There is no apparent association between height and birth month. (correct answer)

Explanation: A scatterplot where the points form a random cloud with no discernible pattern (no upward or downward trend, no clear curve) indicates that there is no apparent association between the two variables.

Question 12

A scatterplot of property values versus square footage for homes in a large city shows two distinct groups of points. One group consists of smaller, less expensive homes and is clustered in the lower-left area of the plot. The other group consists of larger, more expensive homes clustered in the upper-right area. This type of unusual feature is known as:

  1. An influential point, which drastically changes the regression line if removed.
  2. A high-leverage point, which has an extreme value for the explanatory variable.
  3. Clustering, which indicates that there are distinct subgroups within the data. (correct answer)
  4. A negative association, which shows an inverse relationship between variables.

Explanation: The presence of distinct groups or clouds of points in a scatterplot is referred to as clustering. It often suggests that the data comes from different subgroups that may have different characteristics.

Question 13

A coffee shop owner wants to see if the daily high temperature affects the sales of hot coffee. Over a period of several weeks, she records the daily high temperature and the number of hot coffees sold. Which of the following is the most appropriate setup for a scatterplot?

  1. Explanatory variable: number of hot coffees sold; Response variable: daily high temperature.
  2. Explanatory variable: daily high temperature; Response variable: number of hot coffees sold. (correct answer)
  3. Both variables should be treated as response variables, as they are both outcomes measured daily.
  4. A scatterplot is not appropriate because temperature is a continuous variable while sales are discrete.

Explanation: The owner is investigating how temperature might affect or predict sales. Therefore, daily high temperature is the explanatory variable, and the number of hot coffees sold is the response variable.

Question 14

An automotive engineer examined a scatterplot relating the weight of a car (in pounds) to its fuel efficiency (in miles per gallon). The plot showed a fairly straight pattern sloping downwards, with most points reasonably close to the pattern. One car, a very heavy vehicle, had much lower fuel efficiency than the pattern suggested. Which is the most complete description?

  1. The association is negative and linear, and there appears to be one potential outlier.
  2. The association is moderate to strong, negative, and roughly linear, with one potential outlier. (correct answer)
  3. The association is strong and negative, but its form is non-linear due to the unusual point.
  4. The association is weak and positive because heavy cars are typically more expensive.

Explanation: A complete description of a scatterplot should address direction, form, strength, and any unusual features. The description 'moderate to strong, negative, and roughly linear, with one potential outlier' covers all four of these essential components.

Question 15

What is the primary purpose of constructing a scatterplot in a statistical analysis involving two variables?

  1. To display the distribution of a single quantitative variable, focusing on its shape, center, and spread.
  2. To visually examine the relationship or association between two quantitative variables recorded for the same individuals. (correct answer)
  3. To compare the distributions of a categorical variable across several different populations or groups.
  4. To determine the precise probability of a specific outcome in a chance-based experiment.

Explanation: A scatterplot is a graphical tool specifically designed to show the relationship between two quantitative variables. Each point on the plot represents one individual's values for both variables.

Question 16

When describing a scatterplot of two quantitative variables, what is meant by an "unusual feature" such as an outlier?

  1. A point that has the highest or lowest value for either the explanatory or response variable.
  2. Any point that lies more than two standard deviations from the mean of either variable individually.
  3. A point that deviates from the overall pattern of the relationship shown in the other points. (correct answer)
  4. A point that is located exactly on the horizontal or vertical axis of the scatterplot.

Explanation: In the context of a bivariate relationship, an outlier is a data point that does not fit the general pattern established by the majority of the data points. It stands apart from the overall trend.

Question 17

A scatterplot shows a moderate, positive, non-linear association between two quantitative variables, X and Y. Which of the following statements is most consistent with this description?

  1. The points are tightly clustered around a straight line that goes up from left to right.
  2. The points are somewhat scattered around a gentle curve that goes up from left to right. (correct answer)
  3. The points are widely scattered and show no discernible overall pattern or trend.
  4. The points follow a distinct curve that goes down from left to right.

Explanation: 'Moderate' strength implies the points are somewhat, but not perfectly, close to the pattern. 'Positive' direction means the pattern goes up from left to right. 'Non-linear' form means the pattern is a curve. This statement combines all three characteristics correctly.

Question 18

The athletic department of a university collects data on the heights (in inches) and weights (in pounds) of all its varsity athletes. This dataset is best described as:

  1. A univariate categorical dataset, since athlete sport could be a category.
  2. A bivariate categorical dataset, consisting of two different types of non-numeric labels.
  3. A univariate quantitative dataset, because all athletes are from the same university.
  4. A bivariate quantitative dataset, as two numerical measurements are recorded for each athlete. (correct answer)

Explanation: The data consists of two variables (height and weight) for each individual. Since both height and weight are numerical measurements, this is a bivariate quantitative dataset.

Question 19

A scatterplot of the number of years of education versus annual income for a random sample of adults shows a positive association. What does the phrase "positive association" imply in this context?

  1. Every adult with more education earns a higher income than any adult with less education.
  2. As education level increases, annual income is guaranteed to increase for every individual.
  3. Adults with higher levels of education tend to have higher annual incomes, on average. (correct answer)
  4. An increase in income directly causes an increase in the number of years of education completed.

Explanation: In statistics, an association describes a general trend or tendency in the data, not a deterministic rule that applies to every single individual. A positive association means that, on average, higher values of one variable are paired with higher values of the other.