Population vs Sample
Big Idea: Population = ALL individuals of interest. Sample = a subset (smaller group) from the population.
| Term | Definition | Example |
|---|---|---|
| Population | All units you want to study | All 10,000 students in a school district |
| Sample | Subset from the population | 500 students chosen from the district |
Why sample?: Populations are often huge or impossible to access. A good sample gives reliable results at lower cost.
Random vs Non-random sampling
Random sampling: Each individual in population has an equal chance of selection. Removes selection bias.
Non-random sampling: Individuals are selected deliberately (e.g., easiest to reach). Can introduce bias.
| Method | How it works | Bias risk |
|---|---|---|
| Random (Simple) | Use random number generator or draw names from hat | Low bias |
| Systematic | Select every kth individual (e.g., every 5th) | Can introduce bias if pattern exists |
| Stratified | Divide population into groups, random sample from each | Low bias if groups represent population |
| Cluster | Divide population into clusters, randomly select clusters | Medium bias if clusters differ |
| Convenience | Select easiest/nearest individuals | HIGH BIAS |
| Purposive | Deliberately select specific individuals | HIGH BIAS |
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Simple Random Sampling
Worked example — select a random sample
A school has 800 students. We need a sample of 50 using simple random sampling. Describe the method.
Solution
- Label each student with a number from 001 to 800 (3 digits for consistency).
- Use a random number generator (or table) to generate 50 different numbers between 001 and 800.
- Select the students with those numbers.
Final answer
This ensures every student has equal 1/800 chance of selection, eliminating selection bias.
In exam: You may be asked to: (1) describe the method, (2) explain why it's better than convenience sampling, (3) implement it using random numbers.
Stratified Sampling
When to use: Use stratified sampling when the population has distinct groups (strata) that differ from each other.
Worked example — stratified sampling
A school has: 200 Year 9, 250 Year 10, 180 Year 11. Sample 50 students using stratified sampling by year.
Solution
- Total population = 200 + 250 + 180 = 630
- Calculate proportion per stratum: Year 9: 200/630 = 0.317 Year 10: 250/630 = 0.397 Year 11: 180/630 = 0.286
- Apply proportions to sample size (50): Year 9: 0.317 × 50 ≈ 16 students Year 10: 0.397 × 50 ≈ 20 students Year 11: 0.286 × 50 ≈ 14 students
- Randomly select 16 Year 9, 20 Year 10, 14 Year 11.
Final answer
Sample of 50 now reflects year-group proportions of the population.