Simple random, systematic, and stratified sampling are random methods, while convenience and quota sampling are non-random methods. They differ mainly in how individuals are selected and how well the sample represents the population.
This is part of SL 4.1: Introduction to Statistics in IB Mathematics: Applications and Interpretation.
| Sampling method | How the sample is selected | Main strength or limitation |
|---|---|---|
| Simple random sampling | Every member of the population has an equal chance of selection, usually using random numbers. | Reduces selection bias, but requires a complete sampling frame. |
| Convenience sampling | Select people who are easiest to access, such as students in one nearby class. | Fast and inexpensive, but often strongly biased and unrepresentative. |
| Systematic sampling | Choose a random starting point, then select every th member, where . | Simple to perform, but periodic patterns in the list may create bias. |
| Quota sampling | Divide the population into categories and fill a fixed quota from each, without random selection within categories. | Represents chosen categories, but interviewer choice can introduce bias. |
| Stratified sampling | Divide the population into strata, then randomly sample from each stratum, usually in proportion to its population size. | Produces representation across important groups, but requires accurate population information. |
For example, a school has 600 students, of whom 360 are female. For a proportional stratified sample of 50 students, the number selected from this stratum is
Those 30 students must then be selected randomly from the female students.
A common misconception is that quota and stratified sampling are identical. Both divide the population into groups, but stratified sampling uses random selection within every stratum, whereas quota sampling does not.
Exam Technique
When asked to identify or justify a method, state both the selection procedure and its effect on bias or representativeness. For stratified sampling, show the proportional calculation; for systematic sampling, mention both the random starting point and every th member.
