Question

a school principal wants to know what theme students prefer for the spring dance there are 150 students in 6th grade 200 in 7th and 187 in 8th. select all the representative samples that can help the principal draw conclusions about themes the students prefer

Answer 1

First compute the population: 150 + 200 + 187 = 537 students.

Representative sampling methods (good — select all that apply)

- Simple random sample of students from the full 537 (every student has equal chance).
- Stratified random sample by grade with proportional allocation (choose students from each grade in proportion to its size). Example: for a sample of 100 choose ≈28 sixth, ≈37 seventh, ≈35 eighth (because 150/537 ≈ 0.280, 200/537 ≈ 0.373, 187/537 ≈ 0.348).
- Systematic random sample (e.g., list all 537, pick a random start and every k-th student) — produces a representative sample if the list has no periodic pattern.
- Cluster sampling where whole classes (homerooms) are randomly chosen from across grades (preferably several classes from each grade so the clusters capture grade differences).

Non‑representative methods (avoid)

- Convenience sample (e.g., first 50 students in the cafeteria).
- Voluntary response sample (e.g., an open online poll or suggestion box).
- Sampling only one grade or only a few friends — these will bias the results.

If you want a single recommendation: use a stratified random sample proportional to grade sizes — it ensures each grade is represented and gives the most precise estimate for the school as a whole.