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Compare simple random sampling, stratified, cluster, and systematic sampling methods.
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A census (measuring every individual in the population) is often impractical. Instead, we take a sample and use statistics to make inferences about the population.
The key requirement: the sample must be representative of the population.
Every possible sample of size has an equal chance of being selected.
How to select an SRS:
An SRS ensures that every individual has an equal probability of being selected, and every pair, triple, etc. of individuals is equally likely.
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When to use: When the population has distinct subgroups and you want to ensure each subgroup is represented proportionally.
Example: Stratify by grade level (9, 10, 11, 12) and sample from each.
When to use: When the population is spread out geographically and it's costly to reach individuals.
Example: Randomly select 5 schools from a district and survey all students at those schools.
Example: Survey every 10th customer entering a store.
| Method | Pros | Cons |
|---|---|---|
| SRS | Unbiased, simple | May not represent subgroups |
| Stratified | Ensures subgroup representation | Requires knowledge of strata |
| Cluster | Practical for large/spread populations | Higher variability |
| Systematic | Easy to implement | Risk of hidden patterns |
AP Tip: Know the difference between strata and clusters. Strata are homogeneous groups (sample FROM each); clusters are heterogeneous groups (sample entire clusters).