Stratified sampling example

What it shows

Stratified sampling divides the population into groups that do not overlap, the strata, and then samples each one separately. Here 120 units fall into stratum A (20 units), stratum B (40) and stratum C (60), the 1 : 2 : 3 ratio of the three-town example in Wikipedia’s stratified sampling entry (see Sources).

The sample of 12 is allocated in proportion to stratum size (proportionate allocation), so the strata get 2, 4 and 6 units, a sampling fraction of 1 in 10 in each. Within each stratum the units are drawn by simple random sampling.

How to read it

1. 1

   Each shaded band is one stratum, labeled with its number of units and the number drawn from it.

2. 2

   Units are numbered within their own stratum, because each stratum is sampled from its own list.

3. 3

   Filled circles are the units drawn at random within each stratum.

The numbers behind it

• Population N = 120: stratum A, 20 units; stratum B, 40; stratum C, 60 (1 : 2 : 3).
• Proportionate allocation, n_h = n × N_h / N with n = 12: 12 × 20 / 120 = 2, 12 × 40 / 120 = 4, 12 × 60 / 120 = 6.
• Selected: stratum A, 17 and 20; stratum B, 11, 18, 23 and 34; stratum C, 3, 6, 31, 35, 48 and 50.
• Each stratum’s draw comes from a seeded random number generator (mulberry32; seeds 20261019, 20261220 and 20261021 for strata A, B and C), so it can be repeated.

Ways to use it in teaching

• Set it beside the quota sampling diagram: both keep the groups in proportion, but only this one draws at random within each group.

• Have students compute the allocation for a sample of 30 from the same strata (5, 10 and 15) and then for strata of their own.

• Discuss when a stratum would deserve more than its proportionate share, such as a thinly populated region a proportionate sample would barely reach, and what that does to the estimate.

For when each method suits a study, and how to justify the choice in a methodology chapter, see our guide to sampling methods.

Sources

• Penn State Eberly College of Science. (n.d.). 6.1 How to use stratified sampling. In STAT 506: Sampling theory and methods. https://online.stat.psu.edu/stat506/Lesson06
• Stratified sampling. (n.d.). In Wikipedia. Retrieved October 19, 2026, from https://en.wikipedia.org/wiki/Stratified_sampling