How do you select a reproducible random sample?
You will be able to: Describe simple random and systematic sampling with a complete selection procedure.
How do you select a reproducible random sample?
A club has 24 members and wants feedback from 6. “Ask whoever is nearby” is easy, but it may miss students with different schedules.
A useful starting point: How far can a conclusion go? →
Words and symbols before equations
- Sampling frame
- The list or mechanism from which units can be selected.
- Simple random sample SRS
- Every subset of the specified size has the same chance.
- Without replacement
- A selected unit cannot be selected again.
- Systematic sample
- Choose a random start, then every kth unit.
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
For an SRS without replacement, number all 24 members uniquely, use an unbiased random number generator to select six distinct IDs, and contact those members. Skip repeated or out-of-range IDs if generating one at a time.
With replacement, selected units return to the pool and repeats are allowed; the number of draws may exceed the number of unique people. Specify which procedure you mean.
For a systematic sample of 6 from 24, randomly select a start from 1–4, then take every fourth ID. Equal individual selection probabilities do not make this an SRS: most six-person subsets are impossible. Periodicity in the list can align with the interval and produce unrepresentative realized samples.
A worked example, step by step
Describe a systematic sample of 5 from an ordered list of 20 using a random start of 3.
- The interval is 20/5=4.
- The start must have been randomly chosen from 1,2,3,4.
- Starting at 3, select IDs 3,7,11,15,19.
- Check whether a repeating list pattern matches interval 4; an SRS may be preferable if it does.
Equal chance for each person is not enough to establish an SRS; every fixed-size subset must be equally possible.
For 12 people, selecting every third after a start from 1–3 gives how many?
Compare with an explanation
Four people, with possible IDs determined by the random start.
Predict. Change one thing. Explain.
Choose SRS or systematic sampling, then change the demonstration seed. Compare selected IDs. The seed creates a repeatable classroom simulation, not a real survey recruitment tool.
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 questionWrite an SRS procedure to choose 4 of 18 students and explain how it differs from taking every fourth name.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: Label all 18 eligible students 1–18.
- 1 point: Use a random generator to draw four distinct IDs, ignoring repeats and invalid values.
- 1 point: Stop after four distinct IDs and contact those students; plan follow-up for nonresponse.
- 1 point: A fixed-interval method permits only certain subsets and requires a random start; it is not generally an SRS.
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 1What must a sampling frame include?
All intended eligible units, without inappropriate omissions or duplicates.
RECALL 2Are repeated IDs kept without replacement?
No.
RECALL 3Why specify a random start in systematic sampling?
It makes selection chance-based rather than fixing the same initial pattern.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
How do you select a reproducible random sample?
- SRS: equal probability for every size-n subset.
- Systematic: random start plus fixed interval.
- Describe labels, random mechanism, replacement and stopping rule.
Remember: Equal chance for each person is not enough to establish an SRS; every fixed-size subset must be equally possible.
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.
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