AP Statistics Unit 1 practice questions
Try 10 multiple-choice questions from Unit 1 here. Pick an answer to see why it's right or wrong, then take the timed test above for a full AP-style set.
Question 1
Source:Fiveable derived practice dataset. Values are synthetic and designed for AP Statistics exam practice.
A school compared a new review method with its standard method. The 120 participating students were first grouped by prior achievement level. Within each achievement group, students were randomly assigned to one of the two review methods. All students then took the same assessment.
Prior achievement Standard method n Standard mean New method n New mean Lower 30 72.4 30 77.1 Higher 30 84.8 30 86.2 The response variable is assessment score, measured in points.
Which of the following best justifies the researchers' decision to group students by prior achievement level before randomly assigning the review methods?
To reduce variation in assessment scores attributed to prior achievement, making it easier to detect treatment differences.
To eliminate all potential confounding variables, ensuring that prior achievement cannot influence the final assessment scores.
To guarantee that the standard and new review method groups have identical distributions of prior achievement levels.
To establish a direct cause-and-effect relationship between a student's prior achievement level and their final assessment score.
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Answer: (A)
The primary purpose of a randomized block design is to reduce unexplained variability in the response variable. By grouping students by prior achievement, the researchers account for the variance in scores caused by baseline knowledge, which makes any difference caused by the review methods easier to identify.
Question 2
A school administration wants to estimate the average GPA of students and suspects that GPA varies significantly by grade level. Which piece of information best justifies using a stratified random sample rather than a simple random sample in this context?
Strong association between grade level and GPA reduces variation within strata
Weak association between grade level and GPA reduces variation within strata
Strong association between grade level and GPA increases variation within strata
Weak association between grade level and GPA increases variation within strata
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Answer: (A)
Recognizing that stratifying by a variable strongly associated with the response creates homogeneous groups. This reduces variability within each stratum, leading to more precise estimates than a simple random sample.
Question 3
A biologist divides a large forest into grid plots to estimate the total tree population. Which condition must be met for a cluster sample of these plots to be an appropriate method?
Each grid plot mirrors the diversity of the entire forest population
Each grid plot contains trees that are identical to one another
Each grid plot represents a unique homogeneous subgroup of the forest
Each grid plot excludes trees with the smallest trunk diameters
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Answer: (A)
Identifying that cluster sampling relies on clusters being representative 'mini-populations.' If each cluster (grid plot) is heterogeneous and reflects the diversity of the whole, the method provides an unbiased estimate.
Question 4
A factory quality control manager selects every 100th item from an assembly line. Which feature of the production process would make this systematic sampling method inappropriate?
A periodic defect pattern that coincides with the selection interval
An insufficient sample size that fails to represent the overall production process
A defect pattern that occurs randomly throughout production without any regular interval
A quality control process that changes the selection interval based on production speed
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Answer: (A)
Identifying that systematic sampling is vulnerable to periodicity. If defects occur in a cycle that matches the sampling interval (e.g., every 100th item), the sample will be biased (either all defective or all non-defective).
Question 5
A researcher intends to conduct a simple random sample of all residents in a large metropolis. Which requirement represents the most significant practical barrier to using this method?
Obtaining a complete list of every individual in the population is impossible
Obtaining a complete list of every individual in the population is time-consuming
Obtaining a complete list of every individual in the population is expensive
Obtaining a complete list of every individual in the population is subject to constant change
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Answer: (A)
Identifying that a simple random sample (SRS) requires a sampling frame containing every member of the population. In a large city, creating such a list is often logistically impossible, making SRS inappropriate.
Question 6
To decide between stratified and cluster sampling, a statistician examines how a variable is distributed among groups. Which distribution supports using stratified sampling?
Groups are internally homogeneous but different from one another
Groups are internally heterogeneous and similar to one another
Groups are internally homogeneous and similar to one another
Groups are internally heterogeneous but different from one another
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Answer: (A)
Recognizing that stratified sampling is most efficient when strata are homogeneous within (low variance) but differ significantly from each other (high variance between). This allows the sample to capture all variations precisely.
Question 7
An analyst conducts an exit poll by selecting every 10th voter leaving a polling station. Why is systematic sampling preferred over simple random sampling in this specific physical setting?
It is easier to execute because subjects appear in a sequential stream
It reduces bias because subjects appear in a sequential stream
It is easier to execute because the sampling interval is predetermined
It is easier to execute because it requires less training for data collectors
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Answer: (A)
Identifying that systematic sampling is logistically superior when the population presents itself sequentially (a stream). Simple random sampling would require stopping everyone to list them before selecting, which is impractical.
Question 8
A principal wants to know the exact number of students with allergies in a school of 100 students. Which factor best justifies using a census rather than a sample in this situation?
The population is small enough to measure every individual cost-effectively
The population is large enough to measure every individual cost-effectively
The population is small enough to measure selected individuals accurately
The population is large enough to measure selected individuals accurately
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Answer: (A)
Recognizing that a census (measuring the entire population) is appropriate when the population is small. In this case, checking 100 students eliminates sampling error entirely without incurring prohibitive costs.
Question 9
A television network asks viewers to text a code to vote on a debate performance. Which piece of information identifies the primary reason this method is inappropriate for estimating public opinion?
Participants are self-selected, creating potential for voluntary response bias
Participants are self-selected, creating potential for nonresponse bias
Participants are self-selected, creating potential for sampling error
Participants are self-selected, creating potential for measurement bias
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Answer: (A)
Identifying that the method relies on individuals choosing to participate (self-selection). This leads to voluntary response bias, where those with strong opinions are overrepresented, making the sample unrepresentative.
Question 10
A researcher wants to estimate the average yield of a crop across a large farm with three distinct soil types. The crop yield is known to vary significantly depending on the soil type. Which sampling method is most appropriate for minimizing the variability of the estimate?
Stratified random sampling, because it reduces variability by ensuring proportional representation of each soil type.
Cluster random sampling, because it reduces variability by ensuring proportional representation of each soil type.
Stratified random sampling, because it eliminates bias by ensuring proportional representation of each soil type.
Simple random sampling, because it reduces variability by ensuring proportional representation of each soil type.
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Answer: (A)
Stratified sampling is most appropriate when the population contains distinct groups (strata) that are homogeneous internally but different from each other. By sampling from each soil type, the researcher reduces the variability of the estimator compared to a simple random sample.
What's on the AP Statistics Unit 1 practice test
The standard version takes about 88 minutes and follows the timing and directions of the AP exam, sized to one unit:
- 20 Multiple Choice Questions (43 minutes)
- 1 FRQ – FRQ 1 – Multi-Focus on Practices 1 and 2 (23 minutes)
- 1 FRQ – FRQ 2 – Multi-Focus on Practices 3 and 4 (23 minutes)
Questions are drawn from 4051 multiple-choice questions and 24 FRQs written for Unit 1, Exploring One–Variable Data and Collecting Data.
Practice AP Statistics Unit 1 FRQs
Answer the unit's free-response questions one at a time and get a score on every part.
- FRQ 1 – Multi-Focus on Practices 1 and 2 (8 questions)
- FRQ 2 – Multi-Focus on Practices 3 and 4 (7 questions)
- FRQ 4 – Multi-Focus on Practices 2, 3, and 4 (9 questions)
Review Unit 1 before you start
- 1.1 Introducing Statistics: What Can We Learn from Data?
- 1.2 Variables
- 1.3 Tabular Representation and Summary Statistics for One Categorical Variable
- 1.4 Graphical Representations for One Categorical Variable
- 1.5 Graphical Representations for One Quantitative Variable
- 1.6 Descriptions for One Quantitative Variable Distributions
- 1.7 Summary Statistics for One Quantitative Variable
- 1.8 Graphical Representations of Summary Statistics
- 1.9 Comparisons of the Distributions for One Quantitative Variable
- 1.10 The Investigative Question Revisited and Data Collection
- 1.11 Random Sampling
- 1.12 Potential Problems with Sampling
- 1.13 Experimental Design
- Unit 1 Overview: Exploring One-Variable Data and Collecting Data