A reliable method
A simple random sample gives every possible sample of the stated size an equal chance of selection. Stratified sampling takes a sample within each defined subgroup. Cluster sampling selects intact groups and measures members of the chosen groups.
The common trap
Convenient or voluntary samples may omit people systematically. Increasing their size reduces some random variability but does not repair the selection mechanism.
Make the connection
Specify the sampling frame and nonresponse process. Generalization is strongest when a probability sample represents the population you actually want to describe.
Compare strata with clusters
To sample 24 students across four grades, randomly choose six from every grade: the grades are strata. To select two classrooms and question every student in them: the rooms are clusters. The key difference is whether every group is sampled within or only selected groups are fully measured.
Random invitation is only the first stage
Suppose 240 residents are randomly invited and only 24 respond. The invitation procedure may be sound while the response process is biased. A smaller follow-up sample of nonrespondents can help investigate the problem. Simply sending the same invitation to more people does not establish that response is unrelated to the outcome.
Transfer check
Design a sample of 60 students from three campuses. Explain how you would form a complete sampling frame, make selections within campuses, record nonresponse, and avoid replacing missing people with convenient volunteers. A proportionate allocation could give larger campuses more selections; equal allocations answer a different precision concern.
A district divides 240 students by grade, then randomly selects 4 students from every grade. What sampling design is used?
- Grade defines strata before selection.
- Random selection occurs within every stratum.
- This is stratified random sampling, not selecting intact clusters.
Compare the other answer choices
Confuse sampling within every stratum with selecting whole groups.
Ignore that selection, rather than participation, was randomized.
Treat measurements of a sample as measurements of everyone.
Explain your thinking.
Optional written extension. Self-assessed only; it does not change your automatic practice result. These are teaching criteria, not official awarded marks.
For the four-grade sampling design, each grade has 60 students and four are randomly selected per grade: (a) Give an implementable selection procedure. (b) Explain why this is stratified rather than cluster sampling. (c) If one selected student per grade does not respond, explain a remaining risk and a suitable follow-up.
This draft stays on this page only. Use paper if you want to keep your working.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
AP Statistics 2026–27 course framework