🧱 See It
A population is every single member of the group being studied. A sample is a smaller subset used to make inferences about the whole population, since surveying everyone is often impossible or impractical. For the sample's results to reliably reflect the whole population, the sample must be representative — random, and large enough.
✏️ Draw It
Every grey tile is a member of the population. The green "S" tiles, spread evenly through the group, are the sample actually surveyed.
🔢 Write It
A biased sample — not randomly chosen, or systematically excluding some part of the population — leads to unreliable conclusions about the population, even if every calculation performed on the sample itself is completely correct.
💡 Worked Examples
Example 1 — A school wants to know students' favorite subject, so it surveys only the math club.
- Math club members are far more likely to favor math than the average student.
- This is a biased sample — it systematically over-represents one group.
- A better approach: randomly select students from every grade and every class, not just one club.
Example 2 — A poll about a school issue only surveys students in the cafeteria at lunchtime.
- This misses students with a different lunch period, students who eat elsewhere, and students who are away that day.
- Whoever is missing might feel differently about the issue than whoever showed up — another biased sample.