Introduction: Why Sampling Matters in AP Statistics
Sampling is one of the first big concepts you’ll encounter in AP Statistics — and one that carries through the entire exam. Nearly every inference test relies on the idea of a random sample, so knowing the differences between sampling methods is crucial.
The College Board loves to ask about biased vs unbiased sampling, and students often lose points for mixing up cluster vs stratified sampling.
This guide will cover:
- The major sampling methods tested on AP Stats.
- Real-world examples for each.
- Common traps to avoid.
- Practice strategies with RevisionDojo resources.
Step 1: Why We Sample
Populations are often too large to measure completely. Instead, we:
- Take a sample.
- Use it to make inferences about the population.
Key requirement: The sample must be representative, or results will be biased.
Step 2: The Four Major Sampling Methods
1. Simple Random Sample (SRS)
- Definition: Every individual has an equal chance of being chosen.
- Example: Picking 50 students using a random number generator.
- Strength: Minimizes bias, easy to justify.
- Weakness: May miss subgroup representation.
2. Stratified Random Sample
- Definition: Population divided into strata (groups), then random samples taken from each.
- Example: Divide students by grade (freshman, sophomore, junior, senior), then randomly select 25 from each.
- Strength: Ensures subgroup representation.
- Weakness: Requires knowing subgroup info ahead of time.
3. Cluster Sample
- Definition: Population divided into clusters, then entire clusters are randomly selected.
- Example: Randomly select 5 classrooms, survey every student in those rooms.
- Strength: Easier and cheaper.
- Weakness: Risk of non-representative clusters.
4. Systematic Sample
- Definition: Select every k-th individual after a random start.
- Example: Survey every 10th person who enters the cafeteria.
- Strength: Quick and convenient.
- Weakness: Risk of periodic patterns biasing results.
Step 3: Biased Sampling Methods (To Avoid)
- Convenience Sampling: Asking only nearby people.
- Voluntary Response Sampling: Only those with strong opinions respond.
👉 These always produce bias and should be avoided on the AP exam.
Step 4: Common Exam Questions
MCQ Example
A school surveys every student in 10 randomly chosen classes. Which method is this?
- A) SRS
- B) Stratified
- C) Cluster
- D) Systematic
Answer: C (Cluster).
FRQ Example
Design a sampling method to survey students about cafeteria food.
Strong Response:
- Divide students into groups by grade (strata).
- Randomly select 30 from each grade.
- Justify representativeness.
👉 RevisionDojo provides sample FRQs with scoring rubrics for these designs.
Step 5: How to Tell Stratified vs Cluster
This distinction confuses many students:
- Stratified: Sample some individuals from every group.
- Cluster: Sample all individuals from some groups.
👉 Mnemonic from RevisionDojo:
- Stratified = Subgroups represented.
- Cluster = Clumps chosen.
Step 6: Simulation of Sampling
Using technology, you can simulate sampling:
- TI-84: Use
randInt(1,n,k)for SRS. - Random Number Tables: Assign digits to individuals.
- RevisionDojo Labs: Practice simulations of cluster and stratified samples.
Step 7: Real-World Examples
- SRS: Randomly choosing 1,000 voters from a national registry.
- Stratified: Pollsters ensuring representation by age, gender, region.
- Cluster: Randomly choosing zip codes, surveying everyone in them.
- Systematic: Checking every 20th car at a toll booth.
Step 8: Common Mistakes on the AP Exam
- Mixing up stratified vs cluster.
- Forgetting to specify how randomness is generated.
- Describing vague procedures (“pick randomly” without detail).
- Choosing biased methods (convenience or voluntary response).
👉 RevisionDojo’s Error Tracker highlights these mistakes.
Step 9: How Sampling Connects to Inference
Remember:
- All confidence intervals and hypothesis tests assume random sampling.
- Bad sampling → Biased results → Inference invalid.
This makes sampling foundational for the entire AP Stats course.
RevisionDojo Resources for Sampling Mastery
- Sampling Method Flashcards: Stratified vs cluster vs systematic.
- Design Your Own Survey Tool: Create and test survey plans.
- FRQ Practice Bank: Full solutions with rubrics.
- Error Checklists: Avoid common misinterpretations.
👉 Check out RevisionDojo’s Sampling & Surveys Hub here.
Frequently Asked Questions (FAQs)
Q: Which sampling method is best for the AP exam?
A: SRS is safest — but stratified is often better for subgroup representation.
Q: What’s the difference between biased and unbiased sampling?
A: Unbiased samples reflect the population fairly. Biased methods (voluntary response, convenience) do not.
Q: How do I earn full credit on a sampling FRQ?
A: Be specific about procedure — how randomness is generated and why it’s representative.
Q: Can I just write “randomly pick” on an exam?
A: No — you must explain how (random digits, number generator, etc.).
Q: Do I need to calculate probabilities for sampling problems?
A: Rarely — most questions test your ability to describe methods.
Final Thoughts
Sampling methods are one of the most fundamental topics on the AP Statistics exam. They determine whether results are valid and whether inferences are trustworthy.
Remember:
- SRS = Equal chance.
- Stratified = Subgroups represented.
- Cluster = Clumps chosen.
- Systematic = Every k-th individual.
With practice using RevisionDojo’s survey design tools, FRQs, and flashcards, you’ll never confuse these methods on test day.
