Collecting data and sampling · Grade 10
In Grade 10 you learn: stratified sampling.
To learn about a whole population, you usually collect data from only a sample. A good sample is big enough and represents the population fairly. A biased sample gives misleading results, however carefully you analyse it.
Key facts
- Population: everyone or everything you want to find out about. Sample: the part you actually collect data from.
- Simple random sample: every member has an equal chance of being chosen.
- Systematic sample: pick a random start, then take every kth member of a list. k = population ÷ sample size.
- Stratified sample: sample each group in proportion. Number from a group = (group size)/population × sample size.
- Convenience (opportunity) samples are quick but often biased.
- Capture–recapture: N ≈ number marked × size of second catch ÷ number marked in the second catch.
- Bigger random samples give more reliable results.
Worked examples
Example 1
A gym has 600 members. Describe how to take a systematic sample of 30.
Answer: Pick a random start from 1 to 20, then every 20th member
Example 2
A school has 250 pupils in Year A, 200 in Year B and 150 in Year C. A stratified sample of 60 is taken. How many come from each year?
Answer: 25, 20 and 15