Statistics: Sampling
Understand how data is collected using samples, why random sampling reduces bias, and how to evaluate the quality of different data collection methods.
Populations and Samples
In statistics, a population is the entire group you want to study. A sample is a smaller group selected from the population. We use samples because it is often impractical or impossible to collect data from an entire population.
Population
The entire group being studied. Can be people, objects, or events.
Example: All 2,500 students at a high school.
Sample
A selected subset of the population used to make inferences about the whole group.
Example: 100 randomly chosen students from that school.
Population vs Sample
Population (large)
Sample (smaller)
A good sample should represent the population as accurately as possible.
Sampling Methods
Random Sampling
Every member of the population has an equal chance of being selected. Minimises bias and gives the most reliable results.
Example: Using a random number generator to select 50 students from a list of 500.
Systematic Sampling
Select every nth member of the population after a random start.
Example: Selecting every 10th student from an alphabetical class list.
Convenience Sampling
Selecting whoever is easiest to reach. Often biased — not recommended for important research.
Example: Only surveying your friends about their favourite subject.
Self-Selected (Voluntary) Sampling
People choose to participate themselves. Highly biased — those with strong opinions are more likely to respond.
Example: An online poll where people choose to click and vote.
Understanding Bias
Bias occurs when the sample is not representative of the population — certain groups are over- or under-represented. Biased data leads to inaccurate conclusions.
Common Sources of Bias
- ●Sampling bias: sample not chosen randomly
- ●Question bias: leading or unclear questions
- ●Response bias: people not answering truthfully
- ●Non-response bias: certain people choosing not to respond
How to Reduce Bias
- ●Use random sampling
- ●Use a large enough sample
- ●Ask neutral, unbiased questions
- ●Ensure the sample represents all groups in the population
Biased Question Example:
"Don't you agree that homework should be abolished?" — This leads respondents towards a "yes" answer.
Better Version:
"What is your opinion on homework? (Choose: Strongly Support / Support / Neutral / Oppose / Strongly Oppose)"
Key Vocabulary
Population
The complete group that is the subject of a statistical study.
Sample
A subset of the population selected to represent the whole group in a study.
Bias
A systematic error in data collection that causes the sample to not accurately represent the population.
Random Sample
A sample where every member of the population has an equal chance of being selected, minimising bias.
Worked Examples
A researcher wants to know Year 8 students' favourite sport. She surveys all 30 students in her class. Identify the population and sample.
Population: All Year 8 students (at the school or more broadly).
Sample: The 30 students in her class.
Issue: The sample may be biased if this class has an unusual makeup (e.g., all sporty students).
A council wants to survey residents about a new park. They place an ad in the local newspaper asking people to call in. Is this a good method? Why?
This is voluntary/self-selected sampling — it is biased.
Only those who read the paper and feel strongly enough to call will respond. Those who don't read the paper are excluded.
Better method: Randomly select residents from the electoral roll and mail them a survey.
A school has 800 students numbered 1–800. A researcher uses a random number table to select 40 students. What type of sampling is this?
Every student has an equal chance of being selected (1 in 800 chance).
Answer: This is random sampling — it is unbiased and will give reliable results.
Knowledge Check
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Key Concepts Summary
- ●A population is the whole group; a sample is a subset used to represent it.
- ●Random sampling gives every member an equal chance and minimises bias — it is the most reliable method.
- ●Bias is a systematic error that makes a sample unrepresentative of the population.
- ●Convenience and voluntary sampling are prone to bias and should be used cautiously.
- ●Larger samples and neutral questions improve the quality and reliability of statistical data.