Year 8 - Statistics - Free practice
Year 8 Statistics Worksheets & Practice Tests
Population vs sample, data collection methods, bias.
Quick answer
What is the difference between a population and a sample in statistics?
A population is the entire group being studied; a sample is a smaller group selected from it. When a population is too large to survey everyone, researchers collect data from a sample instead. For example, asking 50 students from a school of 800 about their lunch preferences is sampling the population of 800 students.
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Worked examples
Year 8 statistics: worked examples
Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.
Example 1 · Identifying population, sample and sampling method
A school of 800 students wants to find out the most popular sport among its students. The school captain surveys every 10th student on the school roll. State (a) the population, (b) the sample, and (c) the sampling method used.
Show worked solution
Key idea: The population is the entire group being studied. The sample is the smaller group actually surveyed. The sampling method describes how the sample was chosen.
- The study is about students at this school, so the population is all 800 students at the school.
- Only the students selected from the roll are surveyed, so the sample is the students chosen (every 10th student on the roll).
- Students are selected at a fixed interval (every 10th), so the sampling method is systematic sampling.
Answer: (a) All 800 students at the school. (b) Every 10th student on the school roll. (c) Systematic sampling.
Example 2 · Identifying bias in data collection
A shopping centre manager wants to find out how often local residents visit the shopping centre each month. She surveys 60 people who are inside the shopping centre on a Tuesday morning. Identify one source of bias in this method and explain how it could affect the results.
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Key idea: A sample is biased when it does not fairly represent the population, which can make results misleading.
- The population is all local residents, but the sample is drawn only from people already inside the shopping centre on a Tuesday morning.
- People found in the shopping centre are more likely to visit frequently than the average resident, so frequent visitors are over-represented.
- Tuesday morning shoppers may also not represent people who work full-time and can only visit on weekends.
- Because of this bias, the results will likely overestimate how often local residents visit the shopping centre.
Answer: The sample is biased because it only includes people who are already at the shopping centre. These people are more likely to be frequent visitors, so the results will overestimate how often local residents visit.
Example 3 · Evaluating a statistical claim in the media
A news article states: "9 out of 10 dentists recommend ShineBright toothpaste." The survey contacted 10 dentists by email and received responses from 10 of them. All 10 were dentists employed by the company that makes ShineBright. Identify two problems with this statistical claim.
Show worked solution
Key idea: When evaluating a statistical claim, consider whether the sample is representative of the population, whether the sample size is large enough, and whether there are any conflicts of interest that could introduce bias.
- The sample size is only 10 dentists. This is far too small to represent the views of all dentists, so the claim cannot be reliably generalised.
- All 10 dentists are employed by the company that makes ShineBright. This is a conflict of interest: they may feel pressure to recommend their employer's product, introducing strong bias into the results.
- Together, these problems mean the claim "9 out of 10 dentists recommend ShineBright" is not a reliable or fair representation of dentists' opinions in general.
Answer: (1) The sample of 10 dentists is far too small to represent all dentists. (2) All dentists surveyed work for the company that makes ShineBright, creating a conflict of interest and strong bias in favour of the product.
Common mistakes
Where students usually lose marks
Confusing population and sample
"The population is the 60 people who were surveyed."
The population is the entire group you want to find out about, not the group you actually measured. The sample is the smaller group you collect data from. Ask yourself: who does the study want to learn about? That is the population.
Thinking a larger sample always means no bias
"We surveyed 500 people, so the results must be accurate and unbiased."
A large sample can still be biased if it is collected in a way that excludes or over-represents part of the population. Size and bias are separate issues. Always check how the sample was selected, not just how many people were included.
Mixing up census and sample
"A census is when you survey a large sample of the population."
A census collects data from every single member of the population, with no one left out. A sample only collects data from a selected part of the population. A survey of 10,000 people out of a population of 1,000,000 is still a sample, not a census.
Confusing random and systematic sampling
"Picking every 5th person on the list is random sampling because anyone could be chosen."
Random sampling means every member of the population has an equal chance of being selected independently, for example by drawing names from a hat or using a random number generator. Systematic sampling uses a fixed rule such as selecting every 5th person. They are different methods.
Try one yourself
Your turn
A survey asks every 10th person on an electoral roll of 5000 voters about their transport habits. What is the size of the sample?
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About this worksheet
Why we built it
Year 8 statistics shifts from "calculate the mean" to "why was this data collected this way". These worksheets give your student practice spotting bias, choosing the right sampling method, and interpreting reported statistics from real-world contexts.
What's covered
Sub-skills your student will practise
- ✓Population vs sample
- ✓Random, systematic and stratified sampling
- ✓Census vs sample - when to use each
- ✓Identifying bias in data collection
- ✓Interpreting statistical claims in the media
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Frequently asked
Questions parents ask about statistics
What's the difference between a population and a sample?
A population is the whole group you want information about - every Year 8 student in Australia, say. A sample is a smaller subset of that population, chosen because surveying everyone is impractical.
What's a random sample?
A sample where every member of the population has an equal chance of being chosen. Random samples are less biased than non-random samples like a 'sample of the first 10 people through the door'.
What's biased data?
Data collected in a way that systematically favours certain outcomes. Surveying only swimming-club members about how often Australian kids swim is biased, because swimmers are over-represented.
Why is sampling a Year 8 topic?
Real statistical work always involves samples - censuses are rare and expensive. Year 8 introduces sample design and bias detection so students can critique data they see in the media.
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