🧱 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

S
S
S
S

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.

The bias is in WHO was asked, not in any calculation. Perfect arithmetic on a bad sample still gives a bad answer.

💡 Worked Examples

Example 1 — A school wants to know students' favorite subject, so it surveys only the math club.

  1. Math club members are far more likely to favor math than the average student.
  2. This is a biased sample — it systematically over-represents one group.
  3. 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.

  1. This misses students with a different lunch period, students who eat elsewhere, and students who are away that day.
  2. Whoever is missing might feel differently about the issue than whoever showed up — another biased sample.

🧠 Quick Reference

Population = everyone being studied. Sample = a smaller, ideally RANDOM and REPRESENTATIVE subset. A biased sample — not randomly chosen, or systematically excluding some group — gives unreliable conclusions about the whole population, no matter how carefully the sample itself was analyzed.
👪 For Parents & Tutors

BC Curriculum (Level 4 / Grade 9, Data): "Statistics: population versus sample analysis; examining bias, ethics, and reliability in data and representation."

Watch for: assuming any sample is automatically fine as long as the math (mean, median, percentages, etc.) is calculated correctly. The reliability question is entirely about WHO was included, before any calculation ever happens. Make "who got left out, and does that matter for this question?" a standing habit whenever a survey or sample is described.

Comes up again: connects to Interpolation and Extrapolation — both are about how much to trust a conclusion beyond what was directly observed.