Printable Worksheets
Print or save as PDF — or build a custom worksheet from any module's questions.
Data Collection and Sampling
You want to know how students at your school feel about the cafeteria food. Should you ask only your friends?
Learning Intentions
Know
- Population vs sample
- Random sampling
- Bias
- Survey design
Understand
- Why sampling is necessary
- How bias affects results
- When census is preferable
Can Do
- Design an unbiased survey
- Identify sources of bias
- Choose appropriate sampling methods
Population and Sample
The population is the entire group being studied.
A sample is a subset of the population used to make inferences.
A good sample is representative of the population.
A census collects data from every member of the population. This is expensive and time-consuming but gives exact results.
Sampling Methods
Common sampling methods:
- Simple random: Every member has equal chance
- Stratified: Population divided into groups (strata), sampled proportionally
- Systematic: Select every $n$th member
- Convenience: Choose readily available members (often biased!)
Random and stratified sampling generally produce the most representative samples.
Bias in Data Collection
Bias occurs when a sample does not represent the population.
Types of bias:
- Selection bias: Sample not representative (e.g., only asking friends)
- Response bias: Questions worded to influence answers
- Non-response bias: Certain groups less likely to respond
Example: A phone survey during work hours underrepresents working people.
Check Understanding
A school has 600 students: 300 Year 9, 200 Year 10, 100 Year 11. How many from each year should be in a stratified sample of 60?
Sampling Methods
A company has 1000 employees: 600 full-time, 300 part-time, 100 casual. In a stratified sample of 50, how many part-time?
Proportion: $300/1000 = 0.3$
Sample: $0.3 imes 50 = 15$ part-time employees
A survey asks: "Don't you agree that homework is excessive?" Identify the bias.
Response bias — the question is leading, suggesting homework is excessive.
A researcher stands outside a gym and asks people about exercise habits. Identify the bias.
Selection bias — gym-goers are not representative of the general population.
Common Misconceptions
A larger sample is always better. A large biased sample is worse than a small representative one. Quality matters more than quantity.
Random sampling means asking anyone you meet. No — true random sampling gives every member of the population an equal chance of selection.
Online polls are representative. No — they suffer from self-selection bias; only motivated people respond.
Practice — Sampling Practice
Market Research and Polling
Australian election polling uses stratified sampling to ensure representation across states, ages, and genders. The Australian Bureau of Statistics conducts the Census every five years, but conducts sample surveys (like the Labour Force Survey) monthly using carefully designed sampling methods.
📓 Copy Into Your Books
▼Population/Sample
- Population = entire group
- Sample = subset
- Census = everyone
Methods
- Random - equal chance
- Stratified - proportional groups
- Systematic - every nth
- Convenience - often biased
Bias
- Selection - unrepresentative sample
- Response - leading questions
- Non-response - some groups don't respond