Class 11 · Mathematics and money
Sampling: who did you ask?
Asked the cricket team, 87% want more cricket nets. Does the whole school want them?
What you will learn: Identify sampling bias and judge how sample size affects confidence.
Small test at the end: scroll down to the end of this page for five short questions that check what you have learnt. Tap an answer, then press Check answer. Go to the questions ↓
Jump to: Check yourself · For grown-ups · For teachers
Safety first
Use numbers, not names.
Keep it safe:
- Use numbers instead of names when practising. Real surveys need permission and anonymous answers.
You will need
- Paper and pencil
- A class list with numbers instead of namesFor practising random choice.
- A die or numbered slipsTo pick at random.
Time: About 45 minutes.
The story
Dhruv asks the cricket team whether the school needs more cricket nets, and 13 of the 15 say yes. "Nearly 9 in 10 students want nets!" he announces. Tara smiles. "You asked the cricket team!" Does the whole school really want them?
The idea
The population is everyone you want to know about (for example all 600 students). A sample is the people you actually ask.
A sample should represent the population. Asking only easy-to-reach or interested people causes sampling bias: the cricket team is not like the whole school.
A random sample gives everyone the same chance of being picked, for example drawing names from the full register.
Bigger random samples usually vary less from sample to sample, so you can be more confident. But a bigger biased sample is still biased.
Worked example
Two samples, two answers
- Population: all 600 students.
- Sample A: the cricket team, 15 students. 13 agree: 13 ÷ 15 ≈ 87%.
- Sample B: 60 names drawn at random from the register. 21 agree: 21 ÷ 60 = 35%.
- Sample A over-represents cricket players, so it is biased.
The random sample gives a fairer picture: about a third of students want more nets, not most.
Try it
Name the population.
Who do you want to know about?
Spot possible bias.
Who would be easiest to ask? How might they differ?
Plan a random sample.
Number everyone and pick numbers by chance.
Choose a size.
Bigger samples vary less. What can you manage?
Write the plan.
Population, method, size, and the biases you avoided.
What you make (paper or offline)
Your sampling plan
Population and sample size.
How you will choose at random.
Biases you checked for.
Make it on paper. Keep it with you. Nothing to upload.
Check yourself
Five questions about what this page teaches. Choose an answer and press Check answer, or open "See the answer and why". Nothing is saved or sent: your choices stay on this screen and disappear when you leave or reload the page.
How do you want to answer? You choose, and you can change at any time.
See the answer and why
- A. A fair test Not this one. A fair test is about changing one variable, not choosing people.
- B. Sampling bias Correct. The cricket team is not like the whole school.
- C. A random sample Not this one. They were chosen because they were easy to ask, not at random.
- D. A larger sample Not this one. The team is small, and the problem is who, not how many.
See the answer and why
- A. 60 volunteers who answer a poster about the survey Not this one. Volunteers are often the most interested.
- B. 60 names picked at random from the full register Correct. Everyone has the same chance of being chosen.
- C. 60 students who walk past the canteen first Not this one. Those who pass first may differ from others.
- D. 60 students from Class 11 only Not this one. One class does not represent all classes.
See the answer and why
- A. 15% Not this one. 15 is the sample size.
- B. 87% Correct. 13 ÷ 15 = 0.866..., about 87%.
- C. 13% Not this one. 13 is the number agreeing, not the percentage.
- D. 65% Not this one. Divide 13 by 15, then multiply by 100.
See the answer and why
- A. 39% Not this one. Divide 21 by 60: 0.35.
- B. 21% Not this one. 21 is the count, not the percentage.
- C. 60% Not this one. 60 is the sample size.
- D. 35% Correct. 21 ÷ 60 = 0.35.
See the answer and why
- A. Remove the need to choose at random Not this one. Size does not replace random choice.
- B. Vary less from one sample to another Correct. Bigger random samples give steadier results.
- C. Remove all bias, even if chosen unfairly Not this one. A big biased sample is still biased.
- D. Make the result 100% certain Not this one. Samples always leave some uncertainty.
Think back
Where have you seen a survey that only asked one kind of person?
How big a sample could you manage in your school?
Investigate further
- Find a poll in the news. Who was asked, and how many?
- Try picking 10 random numbers from 1-100 with a die or slips.
For grown-upsTap a heading to open it. The safety notes are at the top of the page.
Before you start
- A numbered list (no names) and a way to pick numbers by chance.
Questions that help
- "Who did you ask, and who did you miss?"
- "Would a different group answer differently?"
What's really going on
Sampling bias is why some polls get elections wrong; random sampling is the main protection.
Other ways to do it
- Sample sweets from a mixed packet to estimate the share of each colour.
For teachersLearning aims, classroom ideas and what to look for.
Learning aims
- Identify sampling bias and plan a random sample.
- Explain the effect of sample size.
Subject links
- Mathematics: statistics and percentages.
- Social science: surveys and polls.
These links are general. They have not been checked against a specific board syllabus.
In the classroom
- Compare class results from a "convenience" sample and a random sample on the same question.
What to look for
- Defines the population.
- Random method and a realistic size.