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.
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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 |
IB-style question — name the sampling technique
A factory lists all 2000 items in production order. An inspector checks every 25th item on the list.
(a) Name this sampling technique. (b) Name the technique if instead the inspector just grabs the 30 items nearest the door.
Step by step
- (a) Choosing every kth item from an ordered list is SYSTEMATIC sampling.
- (b) Taking whatever is easiest to reach is CONVENIENCE sampling (and is likely biased).
Final answer
(a) systematic. (b) convenience (biased).
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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.