U3 FRQ Practice
Master AP Statistics Unit 3 free-response questions: sampling designs, experiments, randomization, and generalizability. Learn how to earn every point with precise, in-context answers.
What you'll do in this lesson
A voice-first session with the Crimsora tutor on U3 FRQ Practice, then targeted practice and FRQs — with the tutor adapting to where you get stuck.
What this lesson covers
Unit 3 free-response questions reward students who can describe data-collection designs clearly and justify their choices. The AP exam rarely just asks for a definition — it hands you a real scenario and asks you to design a study, critique someone else's plan, or explain why a conclusion can or cannot be generalized. This lesson shows you how to attack those prompts efficiently.
You already know the building blocks from earlier lessons: sampling methods, bias, experimental design, and inference. Here we focus on the writing skill itself — turning your knowledge into complete, in-context responses that graders can score point-by-point. The single biggest driver of Unit 3 FRQ scores is specificity: naming the design, describing the mechanics of randomization, and always connecting your answer to the context of the problem.
You already know the building blocks from earlier lessons: sampling methods, bias, experimental design, and inference. Here we focus on the writing skill itself — turning your knowledge into complete, in-context responses that graders can score point-by-point. The single biggest driver of Unit 3 FRQ scores is specificity: naming the design, describing the mechanics of randomization, and always connecting your answer to the context of the problem.
What Unit 3 FRQs Actually Ask
Unit 3 free-response prompts fall into a few recognizable families. Recognizing the family tells you what the graders want before you write a word.
The exam almost always embeds these in a paragraph of context — a school, a farm, a clinic, a store. A response that says "take a random sample" without describing how earns little credit. A response that says "number each of the 500 students to , use a random number generator to select distinct numbers, and survey those students" earns full credit.
A common misconception is that longer answers score higher. They do not. Graders look for specific required elements. Padding wastes time and can even contradict a correct statement, costing you the point.
| Prompt type | What they ask | What earns points |
|---|---|---|
| Design a sample | Select participants from a population | Name the method, describe randomization mechanics, avoid bias |
| Design an experiment | Assign treatments to units | Random assignment, treatment groups, response variable, comparison |
| Critique a study | Find the flaw | Identify the specific bias or confounding, explain its effect on results |
| Scope of inference | Can you generalize? Can you claim cause? | Tie conclusions to random sampling and random assignment |
A common misconception is that longer answers score higher. They do not. Graders look for specific required elements. Padding wastes time and can even contradict a correct statement, costing you the point.
Describing Randomization So It Scores
Most lost points on Unit 3 FRQs come from vague randomization. Whenever a prompt says "describe how," you must give a reproducible procedure — enough detail that another person could carry it out identically.
For a simple random sample, state three things: how you label the units, what randomizing device you use, and how you handle repeats. For example: "Assign each of the employees a unique number from to . Use a random number generator to produce numbers from to , ignoring repeats, until different employees are selected."
For stratified sampling, first define the strata explicitly ("separate employees into two groups: full-time and part-time"), then describe an SRS within each stratum. For a randomized experiment, describe how you randomly assign units to treatments, not how you select them.
A frequent error is confusing selection with assignment. Sampling is about who gets studied; assignment is about who gets which treatment. If a scenario involves treatments, the key phrase graders want is "randomly assign." If it involves a survey or observational study, they want "randomly select." Using the correct verb signals you understand the distinction between drawing conclusions about a population and drawing conclusions about cause and effect.
For a simple random sample, state three things: how you label the units, what randomizing device you use, and how you handle repeats. For example: "Assign each of the employees a unique number from to . Use a random number generator to produce numbers from to , ignoring repeats, until different employees are selected."
For stratified sampling, first define the strata explicitly ("separate employees into two groups: full-time and part-time"), then describe an SRS within each stratum. For a randomized experiment, describe how you randomly assign units to treatments, not how you select them.
A frequent error is confusing selection with assignment. Sampling is about who gets studied; assignment is about who gets which treatment. If a scenario involves treatments, the key phrase graders want is "randomly assign." If it involves a survey or observational study, they want "randomly select." Using the correct verb signals you understand the distinction between drawing conclusions about a population and drawing conclusions about cause and effect.
Blocking, Stratifying, and Justifying Choices
Higher-scoring FRQs often ask you not just to design but to explain why one design beats another. This is where blocking and stratifying appear.
Stratifying (in sampling) and blocking (in experiments) do the same conceptual job: group units that are similar on a variable expected to affect the response, so that comparisons are more precise. To earn the justification point, name the grouping variable and explain the benefit in context.
A strong justification reads: "Because older and younger plants may respond differently to the fertilizer, block by age group. Within each block, randomly assign half the plants to each fertilizer. This ensures the treatment comparison is not distorted by age differences."
Notice the structure: identify the nuisance variable, group by it, randomize within groups, and state the payoff. Graders reward this chain of reasoning. A vague statement like "blocking makes it more accurate" does not name a variable or a mechanism, so it typically earns no credit.
Stratifying (in sampling) and blocking (in experiments) do the same conceptual job: group units that are similar on a variable expected to affect the response, so that comparisons are more precise. To earn the justification point, name the grouping variable and explain the benefit in context.
| Concept | Setting | Purpose |
|---|---|---|
| Stratified sample | Survey/observational | Ensure representation, reduce variability in estimates |
| Blocking | Experiment | Control a known source of variation before assigning treatments |
| Completely randomized | Experiment | Simplest; randomization alone balances variables on average |
Notice the structure: identify the nuisance variable, group by it, randomize within groups, and state the payoff. Graders reward this chain of reasoning. A vague statement like "blocking makes it more accurate" does not name a variable or a mechanism, so it typically earns no credit.
Scope of Inference: The Two-Question Rule
The final part of many Unit 3 FRQs asks what conclusions are justified. Answer it with two independent questions.
First: Was there random selection from a population? If yes, results generalize to that population. If no, they apply only to the units studied.
Second: Was there random assignment of treatments? If yes, a cause-and-effect conclusion is possible. If no, you can only describe association.
This table is one of the most tested ideas in the entire course. The most common mistake is claiming causation from an observational study because a difference "looks" large. Without random assignment, a confounding variable could explain the difference, so you may only report an association. The second most common mistake is over-generalizing a convenience sample. Always anchor your final sentence to the specific population and design described in the prompt.
First: Was there random selection from a population? If yes, results generalize to that population. If no, they apply only to the units studied.
Second: Was there random assignment of treatments? If yes, a cause-and-effect conclusion is possible. If no, you can only describe association.
| Random assignment | No random assignment | |
|---|---|---|
| Random selection | Cause-and-effect, generalizes to population | Association only, generalizes to population |
| No random selection | Cause-and-effect, only for these units | Association only, only for these units |
Key terms
- Simple Random Sample (SRS).
- A sample chosen so that every group of a given size has an equal chance of being selected. Described by labeling units and using a random device without bias.
- Random Assignment.
- Using chance to allocate experimental units to treatment groups, which balances confounding variables on average and permits cause-and-effect conclusions.
- Stratified Random Sampling.
- Dividing a population into similar groups (strata) and taking an SRS within each stratum to improve representation and precision.
- Blocking.
- Grouping experimental units by a variable expected to affect the response, then randomizing treatments within each block to control that variation.
- Confounding.
- When a variable is associated with both the explanatory variable and the response, making it impossible to attribute effects to the treatment alone.
- Scope of Inference.
- The extent to which results can generalize to a population (requires random sampling) and support causal claims (requires random assignment).
- Response Variable.
- The outcome measured in a study to compare treatments or characterize a population.
Worked example
A researcher wants to test whether a new study-app improves quiz scores for the 120 students in an algebra course. Half the students have a math tutor outside school and half do not. Design an experiment to investigate the app's effect, and explain whether the results can be generalized to all algebra students in the district.
Start by identifying that treatments are involved, so this is an experiment requiring random assignment, and that tutoring is a variable likely to affect quiz scores, so blocking is appropriate.
Step 1 — Define blocks. Separate the students into two blocks: the with an outside tutor and the without.
Step 2 — Randomly assign within each block. In the tutor block, label students to , use a random number generator to select distinct numbers; those students use the study-app and the remaining do not. Repeat the same process in the no-tutor block.
Step 3 — Apply treatments and measure the response. Have the assigned groups use the app for the unit while the others study as usual, then compare mean quiz scores between app and no-app groups within and across blocks.
Step 4 — Scope of inference. Because treatments were randomly assigned, a cause-and-effect conclusion about the app's effect on these students is justified. However, the students were not randomly selected from all district algebra students — they are one course — so the results cannot be generalized beyond this group. The final sentence should state both facts explicitly to earn the inference point.
Step 1 — Define blocks. Separate the students into two blocks: the with an outside tutor and the without.
Step 2 — Randomly assign within each block. In the tutor block, label students to , use a random number generator to select distinct numbers; those students use the study-app and the remaining do not. Repeat the same process in the no-tutor block.
Step 3 — Apply treatments and measure the response. Have the assigned groups use the app for the unit while the others study as usual, then compare mean quiz scores between app and no-app groups within and across blocks.
Step 4 — Scope of inference. Because treatments were randomly assigned, a cause-and-effect conclusion about the app's effect on these students is justified. However, the students were not randomly selected from all district algebra students — they are one course — so the results cannot be generalized beyond this group. The final sentence should state both facts explicitly to earn the inference point.
Practice questions
A store manager wants to survey customer satisfaction. She hands a form to every tenth customer who leaves the store on a Saturday. Which is the best description of this sampling method and its main limitation?
- Stratified sample; it may overrepresent one stratum
- Systematic sample; results may not generalize because only Saturday customers were surveyed
- Simple random sample; it has no limitations
- Convenience sample; every customer had an equal chance of selection
Answer: Systematic sample; results may not generalize because only Saturday customers were surveyed
Selecting every tenth customer is a systematic sample. The limitation is coverage: sampling only on Saturday excludes weekday customers, who may differ, so the results generalize only to Saturday shoppers. It is not an SRS because not every group of customers is equally likely, and it is not a convenience sample because a systematic rule is used.
An agricultural scientist compares two fertilizers on tomato yield using 40 plants in a greenhouse. Describe how to carry out random assignment for a completely randomized design, and explain what type of conclusion the design supports.
Answer: Label the plants 1 to 40, use a random number generator to select 20 distinct numbers to receive fertilizer A, and assign the remaining 20 to fertilizer B; because treatments are randomly assigned, a cause-and-effect conclusion about the fertilizers' effect on yield for these plants is justified.
Full credit requires reproducible randomization mechanics: labeling, a random device, and how many go to each treatment. Because assignment is random, confounding variables are balanced on average, permitting a causal conclusion. Since the plants were not randomly selected from a larger population, the conclusion should not be generalized beyond the plants studied.
A study finds that people who drink green tea have lower blood pressure than those who do not, based on a survey of volunteers. A student concludes that green tea lowers blood pressure. Explain why this conclusion is not justified and what conclusion is appropriate.
Answer: The study is observational with no random assignment, so a confounding variable such as overall diet or exercise could explain the difference; only an association between green tea and lower blood pressure can be claimed, not causation.
Cause-and-effect requires random assignment of treatments, which did not occur — participants chose whether to drink green tea. A lurking variable like healthier lifestyle among tea drinkers could cause both behaviors. The correct conclusion is that green tea consumption is associated with lower blood pressure in this sample, without implying causation.
FAQ
- How do I know whether an FRQ wants random selection or random assignment?
- Look at what is being studied. If the scenario surveys or observes people to learn about a population, describe random selection. If it applies treatments to units and compares outcomes, describe random assignment. Some experiments involve both, but the treatment comparison always needs random assignment.
- How much detail do I need when describing a sampling procedure?
- Enough that someone else could reproduce it exactly. State how you label the units, which randomizing device you use (such as a random number generator or slips in a hat), and how you handle repeats. Vague phrases like 'choose randomly' without mechanics usually lose the point.
- When should I block or stratify in my answer?
- Block or stratify when the prompt mentions a variable expected to affect the response, such as age, gender, or prior experience. Name that variable, group by it, randomize within groups, and explain that this reduces variability so the comparison is more precise. If no such variable stands out, a completely randomized design or SRS is fine.
- What is the safest way to write a scope-of-inference conclusion?
- Use two sentences. First, address causation: if treatments were randomly assigned, you may claim cause and effect; otherwise report only association. Second, address generalization: if units were randomly selected from a population, extend results to that population; otherwise limit conclusions to the units studied. Always name the specific population and context.
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