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
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 2
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 3
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 4
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 5
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 6
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 7
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 8
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.
Question 9
A city planner needs to survey residents about a new policy but has a very limited travel budget and no complete list of all residents. The city is organized into blocks that are each considered to be a miniature representation of the city's overall demographic diversity. Which sampling method is most appropriate?
Cluster sampling, because it reduces data collection costs by surveying every resident in a few randomly selected blocks.
Stratified sampling, because it reduces data collection costs by surveying every resident in a few randomly selected blocks.
Cluster sampling, because it increases statistical precision by surveying every resident in a few randomly selected blocks.
Systematic sampling, because it reduces data collection costs by surveying every resident in a few randomly selected blocks.
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Answer: (A)
Cluster sampling is appropriate here because the blocks are heterogeneous (mini-populations) and the method reduces costs by concentrating data collection in specific geographic areas.
Question 10
A quality control manager must inspect widgets on a moving assembly line that produces 10,000 units daily. The widgets pass a checkpoint one by one. Which sampling method is most appropriate for ensuring coverage across the entire production run while being easy to implement?
Systematic sampling, because it is logistically simple to select every kth widget from the moving line.
Simple random sampling, because it ensures each widget has an equal probability of selection from the 10,000 daily units.
Stratified sampling, because it is logistically simple to select every kth widget from the moving line.
Systematic sampling, because it provides the most precise estimate of widget quality across all 10,000 units produced daily.
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Answer: (A)
Systematic sampling is ideal for assembly lines because it is easy to implement (select every kth item) and ensures the sample is spread evenly across the entire production time.
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 2342 multiple-choice questions and 27 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 (10 questions)
- FRQ 2 – Multi-Focus on Practices 3 and 4 (8 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