What it shows
A population of 120 units, numbered 1 to 120, with 8 selected at random. Every unit had the same chance of selection, and so did every possible set of 8; the second condition is what defines a simple random sample.
The numbering stands for the sampling frame, the complete list of the population that this method requires.
How to read it
Open circles are the population; filled circles are the sample.
The selected units follow no pattern. Some rows contain two and some none.
The systematic sample in the same set, by contrast, has fixed spacing.
The numbers behind it
- Population N = 120, numbered 1 to 120 in rows of 15. Sample n = 8, drawn without replacement.
- Selected units: 16, 35, 38, 47, 59, 75, 89, 97.
- The draw comes from a seeded random number generator (mulberry32, seed 20261018), so it can be repeated exactly.
Ways to use it in teaching
Have students draw their own sample of eight with a random number table or a spreadsheet and compare results across the room.
Ask what would be needed to take a sample like this from a real population; the answer is a sampling frame.
Introduce the set with this figure, as the baseline for the other five methods.
For when each method suits a study, and how to justify the choice in a methodology chapter, see our guide to sampling methods.
Sources
- Cochran, W. G. (1977). Sampling techniques (3rd ed.). Wiley.
