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AP Statistics Practice Quiz: Introducing Statistics: Are My Results Unexpected?

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

When analyzing categorical data, what does the term 'variation' primarily refer to?

All Questions (7)

When analyzing categorical data, what does the term 'variation' primarily refer to?

A) The range of different categories observed.

B) The difference between the results of two separate studies.

C) The discrepancy between the counts observed in the data and the counts that were expected.

D) The natural fluctuation in data over time.

Correct Answer: C

The provided content specifies that statistical questions arise from the 'variation between observed and expected counts in categorical data'. This variation is the difference between what was actually counted and what was theoretically expected.

A researcher expects a fair six-sided die to land on each number 10 times in 60 rolls. However, the number '4' appears 15 times. According to the provided content, what is the fundamental question the researcher should ask about this result?

A) Is the die loaded, or is this difference from the expected 10 occurrences simply due to random chance?

B) What is the probability of rolling a '4' exactly 15 times?

C) Should the experiment be repeated with a different die?

D) Were the 60 rolls sufficient to make a conclusion?

Correct Answer: A

The content states that the key question suggested by variation between observed (15) and expected (10) counts is whether that variation is random or not. Option A directly addresses this by questioning if the outcome is due to chance or a non-random factor (a loaded die).

The core principle of analyzing observed versus expected counts is to understand that any difference found between them can be attributed to one of two possibilities. What are these two possibilities?

A) A correct hypothesis or an incorrect hypothesis.

B) A large sample size or a small sample size.

C) Random variation or a non-random effect.

D) Experimenter error or measurement error.

Correct Answer: C

The provided content explicitly states that 'Variation between observed and expected counts may be random or not.' This highlights the two fundamental possibilities for explaining the difference: it is either due to chance (random) or it is due to a systematic, underlying reason (not random).

If statisticians conclude that the variation between observed and expected counts is 'random', what does this imply about the expected counts?

A) The expected counts were calculated incorrectly.

B) The observed results are consistent with the model that produced the expected counts, and the difference is due to chance.

C) The data is flawed and cannot be used for inference.

D) A non-random factor is definitely influencing the results.

Correct Answer: B

Concluding that variation is random means that the observed differences are not surprising and could have happened by chance alone. This suggests that the underlying model used to generate the expected counts is plausible, and the data does not provide strong evidence against it.

A marketing team expects that 25% of website visitors will click on a new ad. In a sample of 200 visitors, 60 people (30%) click the ad. What question does this variation between the observed (30%) and expected (25%) rates suggest?

A) How can we increase the click rate to 50%?

B) Is the 5% difference a result of random fluctuation, or does it suggest the ad is genuinely more effective than expected?

C) Was the sample of 200 visitors representative of all visitors?

D) What is the exact monetary value of this 5% increase?

Correct Answer: B

The core task is to identify the question suggested by the variation. The difference between the observed 30% and expected 25% leads directly to the question of whether this variation is a meaningful (non-random) indicator of the ad's effectiveness or just a random occurrence.

Which of the following scenarios is NOT an example of investigating variation between observed and expected counts in categorical data?

A) Comparing the number of wins for a sports team at home versus away to see if it matches an expected 50/50 split.

B) Checking if the number of students choosing each of four lunch options aligns with the school's prediction.

C) Measuring the average height of students in a class to see how it compares to the national average height.

D) Observing the frequency of different colored cars in a parking lot to see if it matches the manufacturer's production numbers.

Correct Answer: C

The analysis of observed versus expected counts applies to categorical data (categories like 'home/away', 'lunch options', 'car color'). Measuring average height involves quantitative, not categorical, data, and thus falls outside the scope of this specific type of analysis.

A city planner observes that 40% of commuters use the bus, while a city model predicted that 35% would use the bus. The discovery of a variation between these counts is the first step in determining if...

A) the city model is completely useless.

B) the bus system is profitable.

C) the observed difference is meaningful or if it could have occurred by chance.

D) all commuters were surveyed accurately.

Correct Answer: C

According to the provided content, identifying a variation between observed and expected counts leads to the question of whether that variation is random or not. Option C perfectly captures this next step: deciding if the difference is a real, non-random effect or just a random fluctuation.