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Daily Math Minute

Collecting Data

Sampling Methods

Comparing simple random, stratified, and cluster sampling.

Intermediate15 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Choosing How to Select a Sample

A company with 800 employees, split evenly across 4 departments of 200 each, wants to survey job satisfaction using a sample of 80. Before reading on: would it matter, for the survey's usefulness, whether all 80 came from the same department or were spread across all four?

Definition — Simple Random, Stratified, and Cluster Sampling

A simple random sample (SRS) gives every possible group of the intended size an equal chance of being chosen. Stratified sampling divides the population into groups (strata) first, then randomly samples separately within each — guaranteeing every group is represented. Cluster sampling divides the population into naturally occurring groups (clusters) and randomly selects entire clusters — often more practical, but only as reliable as how representative each cluster happens to be.

Worked Example — Comparing Three Sampling Methods on the Same Population

For the 800-employee company (4 departments of 200): an SRS numbers all 800 employees and randomly selects 80 — every employee, and every possible group of 80, equally likely. A stratified sample instead randomly selects 20 employees from each of the 4 departments (20×4 = 80) — guaranteeing representation from Sales, Engineering, Support, and Admin alike, useful if satisfaction plausibly differs by department. Suppose instead the 800 employees are organized into 20 existing teams of 40 people each; a cluster sample randomly selects 2 whole teams (2×40 = 80) — far less work to administer, but relying on those 2 teams being reasonably representative of the whole company.

Tip

Stratified sampling is worth the extra setup specifically when the strata are expected to genuinely differ on the variable being measured — if all four departments were expected to feel about the same, a plain SRS would work just as well with less effort.

Common Mistakes

  • Assuming a cluster sample is just a smaller, more convenient version of an SRS.

    A cluster sample only includes people from the selected clusters, entirely skipping everyone else — an SRS could include any combination of individuals from across the whole population, which a cluster sample structurally cannot.

Key Takeaways

  • SRS, stratified, and cluster sampling all rely on randomization, but structure it differently for different practical reasons.
  • Stratified sampling guarantees representation from every group; cluster sampling only samples from a few selected groups.
  • Choosing between these methods often depends on whether the population's subgroups are expected to differ on what's being measured.

Summary

The next lesson turns from how a sample is selected to how a study is designed — and what that design allows you to conclude.

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