Sample some from every group, or everyone from some groups?
You will be able to: Distinguish stratified and cluster sampling and justify a design for a context.
Sample some from every group, or everyone from some groups?
A school has several grade levels and many homerooms. Sampling within every grade answers a different logistical problem from choosing a few whole homerooms.
A useful starting point: How do you select a reproducible random sample? →
Words and symbols before equations
- Stratum
- A non-overlapping group formed around a relevant shared characteristic.
- Stratified sample
- Randomly sample individuals within every stratum.
- Cluster
- A group used as a unit of selection, ideally reflecting the population’s variety.
- Cluster sample
- Randomly select groups and include all their members.
What this picture assumes
24 labeled units in four groups of six; every method selects 12 units without replacement. The seeded pseudo-random demonstration illustrates selection patterns, not a real survey. Positions have no measurement units; group characteristics must justify the design.
Read the picture in three steps
- Read the axes and labels first. Identify what each symbol and line represents. Read the units and fixed conditions before comparing quantities.
- 12 of 24 selected: 1, 4, 5, 7, 8, 11, 13, 16, 18, 19, 21, 22. Groups contain 3, 3, 3, 3 selected units.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the mathematics
If grade affects homework time, sample students randomly within each grade. Every grade contributes, and comparisons within more homogeneous groups may improve precision.
If travel between homerooms is costly, randomly choose homerooms and survey every student in them. Ideally clusters resemble small mixed versions of the school. Similar people within each cluster can make estimates more variable than an SRS of the same number of people.
The lab’s 24 tokens form four groups of six. Stratified mode selects some tokens in all groups; cluster mode selects every token in chosen groups. The layout illustrates the selection pattern only. A real design needs relevant characteristics and an appropriate analysis, including weights if sampling fractions differ.
| Feature | Stratified | Cluster |
|---|---|---|
| Group participation | Every stratum | Selected clusters |
| Individuals selected | Some in each stratum | All in chosen clusters |
| Design motivation | Representation and precision | Practical collection costs |
A worked example, step by step
From four grades of 100 students each, select 10 students per grade. Compare with randomly selecting two mixed-grade clubs and surveying every member.
- The first design forms grade strata.
- Within each grade, use an SRS of 10; combine 40 students.
- The second uses clubs as clusters, assuming they form a non-overlapping frame covering the target population.
- Surveying all members of selected clusters differs from sampling individuals inside every stratum; overlapping clubs would need a different frame.
Stratified and cluster designs both use groups, but what is selected and whether every group contributes are different.
Does stratified sampling choose just one stratum?
Compare with an explanation
No. It randomly samples within every stratum and combines those selections.
Predict. Change one thing. Explain.
Switch stratified and cluster modes. Rotate the optional 3D model to inspect all four groups, then verify the same selected IDs in the 2D map. Explain why group characteristics matter beyond the picture.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
12 of 24 selected: 1, 4, 5, 7, 8, 11, 13, 16, 18, 19, 21, 22. Groups contain 3, 3, 3, 3 selected units.
| Group | Selected IDs / treatment A |
|---|---|
| 1 | 1, 4, 5 |
| 2 | 7, 8, 11 |
| 3 | 13, 16, 18 |
| 4 | 19, 21, 22 |
24 labeled units in four groups of six; every method selects 12 units without replacement. The seeded pseudo-random demonstration illustrates selection patterns, not a real survey. Positions have no measurement units; group characteristics must justify the design.
Explain what you noticed: Answer the investigation prompt above. State one observation and explain it using the data values, graph scales, summary statistics or study-design conditions. Identify what the representation cannot tell you.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA district needs all grade levels represented. Propose a stratified plan and contrast it with a cluster plan using schools.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: Partition eligible students into non-overlapping grade strata.
- 1 point: Randomly select students within every grade and combine them.
- 1 point: Alternatively, randomly choose schools and include all eligible students in each selected school.
- 1 point: Grade strata target representation; school clusters may reduce collection costs but depend on between- and within-school variation.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Which design samples within every group?
Stratified sampling.
RECALL 2Which design selects whole groups?
Cluster sampling.
RECALL 3Does the 3D position change selection probabilities?
No; it only helps inspect group membership and selection.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Sample some from every group, or everyone from some groups?
- Stratified: some from every group.
- Cluster: all from selected groups.
- Groups must fit the question and form a valid frame.
Remember: Stratified and cluster designs both use groups, but what is selected and whether every group contributes are different.
Conditions: 24 labeled units in four groups of six; every method selects 12 units without replacement. The seeded pseudo-random demonstration illustrates selection patterns, not a real survey. Positions have no measurement units; group characteristics must justify the design.
Refresh Kid · AP Statistics Unit 1 · Objectives 1.11.A, 1.11.B · Review edition
Framework, scope and review status
Mapped to College Board, AP Statistics CED, Topic 1.11, objectives 1.11.A, 1.11.B. Framework effective Fall 2026, checked September 17, 2026. Unit 1 includes one-variable data and data collection; it is part of the revised five-unit course.
Examples and datasets are synthetic, independently authored teaching material. Quartile calculations state a median-of-halves convention. Outlier screens identify values to investigate, not data to discard. Random selection and random assignment have different inferential roles. These lessons introduce design and descriptive reasoning; formal inference comes in later units.
The Organic Chemistry Tutor companion title and destination were checked; the full video was not reviewed. Khan Academy’s destination was checked, but its lesson content was not fully readable by the research tool. OpenStax provides optional reference reading. No provider scripts, questions or graphics were copied. Refresh Kid is not affiliated with these providers.
GitHub’s 3D website collection informed optional spatial inspection. Our original sampling model uses self-hosted Three.js with its MIT license. It shows labeled units in four groups; camera rotation does not change the sampling procedure. Quantitative graphs remain 2D to avoid perspective distortion. Complete labeled diagrams, selected IDs and explanations remain available without 3D.
Independent teacher review and observation of students remain pending. Technical checks do not certify statistical accuracy, accessibility or learning effectiveness. This is a review edition.
Released AP Statistics questions and scoring guides are optional. Older exams use the earlier framework, so check alignment before selecting parts. All practice on this page is original, not official AP material.
Learn → Explore → Practice → Review is informed by the IES learning guide. This implementation has not yet been evaluated with learners.
Want to work through this with a tutor?
Bring your question about Sample some from every group, or everyone from some groups? Your explanation and answers remain free to access.