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AP Statistics Practice Quiz: Introducing Statistics: Are Variables Related?

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 7 questions to check your progress.

Question 1 of 7

A high school counselor is reviewing student data. Which of the following questions is focused on identifying a possible relationship between two variables?

All Questions (7)

A high school counselor is reviewing student data. Which of the following questions is focused on identifying a possible relationship between two variables?

A) What is the average GPA for the senior class?

B) How many students are enrolled in an art class?

C) Is there an association between the number of absences a student has and their final grade in chemistry?

D) What is the most common score on the final history exam?

Correct Answer: C

This question specifically asks about a potential connection or 'association' between two distinct variables: the number of absences and the final grade. The other options focus on describing a single variable (average GPA, count of students, most common score).

A researcher observes that in a small group of 20 office workers, those who drink tea tend to take fewer sick days. What is the most important initial statistical consideration before concluding that tea drinking is linked to better health?

A) The pattern observed in this small group might be due to random chance and may not exist in the larger population of office workers.

B) The researcher should immediately survey a larger group to prove the connection.

C) The brand of tea consumed is a critical piece of missing information.

D) The observation proves a causal relationship between drinking tea and taking fewer sick days.

Correct Answer: A

A core principle of statistics is recognizing that an apparent pattern or association in a small sample of data could simply be the result of random variation. Before making any broader claims, a statistician must first investigate whether the observed pattern is statistically significant or if it could have easily occurred by chance.

A student flips a coin 10 times and gets 7 heads. They conclude the coin is biased. A statistician would caution that this conclusion is premature because...

A) The student did not record the time of day for each flip.

B) The observed result of 7 heads could plausibly be an apparent pattern caused by random chance in a small number of trials.

C) A result of 5 heads and 5 tails is the only possible outcome for a fair coin.

D) The student should have used a different coin for each flip to ensure independence.

Correct Answer: B

This scenario illustrates the key idea that apparent patterns in data may be random. While 7 heads is more than the expected 5, this level of deviation is not unusual in a small sample of 10 flips. A statistician's first task is to determine if an observed result is outside the realm of what is expected from random variation.

A data scientist is exploring a large dataset from a grocery store. Which of the following represents the best initial question to investigate a relationship between variables?

A) What is the total revenue from the sale of ice cream?

B) Does the outdoor temperature have a relationship with the daily sales of ice cream?

C) How many different flavors of ice cream does the store sell?

D) Which day of the week had the highest overall sales?

Correct Answer: B

This question is designed to identify a possible relationship between two variables: outdoor temperature and ice cream sales. The other options are summary questions about a single variable (total revenue, number of flavors) or a descriptive finding (day with highest sales), not an investigation into an association.

A financial analyst notices that for the last three years, a particular stock's price increased whenever a certain sports team won a championship. When considering if this is a meaningful association, the principle that 'apparent patterns and associations in data may be random' is crucial. Why?

A) Because the sports team's victory directly causes the stock price to increase.

B) Because with only three data points, the observed pattern is very likely a coincidence and does not indicate a real, repeatable relationship.

C) Because the stock market is inherently unpredictable, so no patterns can ever be identified.

D) Because the analyst should look at the team's wins, not just their championships, to find the real pattern.

Correct Answer: B

This question tests the understanding that patterns observed in very small datasets (in this case, n=3) are highly susceptible to being random occurrences. A statistician would not consider this a meaningful association without much more data to show that the pattern is not just a coincidence or the result of random chance.

The fundamental reason for using statistical tests to analyze a relationship between two variables is to...

A) prove that one variable causes the other variable to change.

B) determine if the observed association in the data is likely real or if it could have occurred simply by random chance.

C) create a visually appealing graph of the data for a presentation.

D) calculate the exact value of each variable for every individual in the population.

Correct Answer: B

This question gets at the heart of the second content point. A primary purpose of formal statistical inference is to distinguish between patterns that are statistically significant (unlikely to be random) and those that are not. Statistical tests help us quantify the role that random chance might have played in producing the observed data.

A researcher collects data on hours of sleep and reaction time for 500 students. They find a weak negative association. Before publishing the results, their primary statistical task is to formulate and answer which of the following questions?

A) What mechanism causes less sleep to slow reaction time?

B) Is the weak association observed in this sample strong enough to conclude that it's not just a result of random sampling variability?

C) How can the data be manipulated to show a stronger association?

D) What was the average reaction time for all students in the sample?

Correct Answer: B

Even with a large sample, an observed association could still be the result of random chance ('sampling variability'). The crucial next step is to perform a hypothesis test to determine if the evidence is strong enough to reject the idea that the association is purely random. This directly addresses the concept that apparent associations must be tested to see if they are statistically significant or not.