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Ignition Learning — Activity Sheet

Planning a fair statistical investigation

Mathematics · Year 8

Name: ______________________Date: ____________

A good statistical investigation follows a clear, ethical process. Start with a specific, answerable question. Choose a fair sampling method — random selection, not just asking whoever is convenient (which can bias results toward people similar to you). Collect data consistently, using the same method and questions for everyone. When reporting findings, be honest about uncertainty — a sample gives an estimate, not a certain fact, and ethical reporting acknowledges the sample size, method, and any limitations rather than overstating confidence in the result.

Example

Investigating "what proportion of Year 8 students at this school walk to school?" by only asking your own friends would bias the result toward students who live near you. A fairer method randomly selects students across the whole year level, then reports the result honestly: "based on a random sample of 40 students, an estimated 35% walk to school" — not an overstated "35% of students walk to school" stated as pure fact.

Key terms

Bias:
A systematic skew in results caused by an unfair sampling or collection method.
Ethical reporting:
Honestly acknowledging a result's sample size, method and limitations, rather than overstating certainty.

Questions

  1. 1. A good statistical investigation starts with:

    • A specific, answerable question
    • Guessing an answer first
    • Skipping straight to conclusions
    • No plan at all
  2. 2. A fair sampling method involves:

    • Random selection
    • Only asking whoever is convenient
    • Only asking your friends
    • Choosing people who agree with you
  3. 3. Bias in a survey means:

    • A systematic skew caused by an unfair method
    • A perfectly fair, random result
    • A type of data collection error that never happens
    • Nothing important
  4. 4. Only asking your own friends about a school-wide question would likely:

    • Bias the results
    • Guarantee a perfectly fair result
    • Have no effect on the results
    • Be the most accurate method possible
  5. 5. Ethical reporting of survey results means:

    • Being honest about sample size, method and limitations
    • Overstating confidence in the result
    • Hiding how the data was collected
    • Ignoring the sample size entirely
  6. 6. A sample gives you:

    • An estimate, not a certain fact
    • A guaranteed, exact fact
    • No useful information at all
    • The same as a full census always
  7. 7. Collecting data consistently means:

    • Using the same method and questions for everyone
    • Changing the question for each person
    • Only collecting data once from one person
    • Ignoring consistency entirely
  8. 8. Why might a survey question worded as "Don't you agree this policy is great?" be considered biased?

    • It leads respondents toward a particular answer rather than asking neutrally
    • This wording has no effect on how people respond
    • Leading questions always produce more accurate results
    • Bias can only occur in sampling, never in question wording
  9. 9. Why is randomly selecting participants generally fairer than choosing whoever is easiest to reach?

    • Convenient sampling can systematically over-represent certain types of people, skewing results
    • Convenience sampling always produces identical results to random sampling
    • Randomness has no effect on fairness
    • Ease of access has no connection to bias
  10. 10. Reporting "based on a sample of 40 students, an estimated 35% walk to school" rather than stating it as pure fact demonstrates:

    • Ethical, honest acknowledgement of uncertainty
    • Dishonest, misleading reporting
    • A meaningless distinction with no real difference
    • An error in the investigation
  11. 11. Why might using inconsistent questions for different survey participants make the results unreliable?

    • Comparing answers to different questions doesn't give a fair, consistent picture of the same thing
    • Inconsistent questions always produce more accurate results
    • Consistency in surveying has no bearing on reliability
    • Every participant should always be asked something different
  12. 12. A researcher only surveys people online, missing those without internet access. This is an example of:

    • A potential source of sampling bias
    • A perfectly representative sampling method
    • An ethical method with no drawbacks
    • A random sampling method
  13. 13. Why should a statistical investigation start with a specific question rather than a vague one?

    • A specific question can actually be answered clearly with collected data
    • Vague questions are always easier to answer with data
    • Specificity has no effect on the quality of an investigation
    • A vague question always produces more useful results
  14. 14. Why is acknowledging a small sample size an important part of ethical reporting?

    • It helps readers judge how much confidence to place in the finding, rather than assuming it as certain fact
    • Acknowledging sample size makes a result seem less trustworthy for no reason
    • Ethical reporting should hide the sample size to seem more confident
    • Sample size is irrelevant to how a result should be interpreted
  15. 15. Why might a company selectively reporting only the survey results that support their product be considered unethical?

    • It misleads the audience by hiding relevant, contradicting information
    • Selective reporting is always the most honest approach
    • Companies have no ethical obligations when reporting survey data
    • Hiding unfavourable results has no effect on how trustworthy the report seems
  16. 16. A student investigating "what percentage of students prefer online or in-person learning" surveys only students already enrolled in an online course. Why is this a flawed sampling method?

    • These students are likely to already prefer online learning, biasing the sample toward one answer
    • This sampling method perfectly represents the whole student population
    • Surveying a pre-selected group never introduces bias
    • This is actually the most representative approach possible
  17. 17. Why might a well-designed statistical investigation include a plan for how data will be analysed before collecting it, rather than deciding afterward?

    • Planning analysis in advance helps prevent selectively interpreting data in a way that fits a desired conclusion
    • Analysis plans have no effect on the fairness or ethics of an investigation
    • Deciding how to analyse data after seeing it is always the more rigorous approach
    • Pre-planning analysis makes an investigation less reliable
  18. 18. Why is transparency about a study's limitations (small sample, potential bias, method) considered a mark of good statistical practice, not weakness?

    • It allows others to fairly judge how much weight to give the findings, supporting trust in the research
    • Acknowledging limitations always makes a study worthless
    • Good research should hide any weaknesses to appear stronger
    • Transparency has no bearing on the credibility of research
  19. 19. A student's investigation into sleep habits only surveys classmates who are already awake and alert during a morning class. Why might this undercount how many students struggle with sleep?

    • Students who struggle most with sleep might be absent, late or less alert, making them less likely to be surveyed as usual
    • This sampling approach has no effect on the accuracy of the sleep data
    • Every possible sleep pattern would be equally represented in this classroom
    • This is the fairest, most representative way to investigate sleep habits
  20. 20. A council wants to know if residents support a new bike lane, and surveys people leaving a cycling club meeting. Why is this a flawed approach to planning the investigation?

    • Cyclists are far more likely to already support the bike lane, systematically skewing the result toward "yes"
    • Surveying any group of residents always gives an equally fair result
    • This is the most representative sample the council could choose
    • Sampling location has no effect on the fairness of a survey
  21. 21. Understanding how to plan a fair, ethical statistical investigation mainly helps you to:

    • Design and report research that genuinely and honestly reflects a population, not just a convenient or biased slice of it
    • Choose the sampling method that produces the most convenient result
    • Avoid ever acknowledging a study's limitations
    • Treat every survey result as an absolute, certain fact

Answer key (parent copy)

  1. 1. A specific, answerable question
  2. 2. Random selection
  3. 3. A systematic skew caused by an unfair method
  4. 4. Bias the results
  5. 5. Being honest about sample size, method and limitations
  6. 6. An estimate, not a certain fact
  7. 7. Using the same method and questions for everyone
  8. 8. It leads respondents toward a particular answer rather than asking neutrally
  9. 9. Convenient sampling can systematically over-represent certain types of people, skewing results
  10. 10. Ethical, honest acknowledgement of uncertainty
  11. 11. Comparing answers to different questions doesn't give a fair, consistent picture of the same thing
  12. 12. A potential source of sampling bias
  13. 13. A specific question can actually be answered clearly with collected data
  14. 14. It helps readers judge how much confidence to place in the finding, rather than assuming it as certain fact
  15. 15. It misleads the audience by hiding relevant, contradicting information
  16. 16. These students are likely to already prefer online learning, biasing the sample toward one answer
  17. 17. Planning analysis in advance helps prevent selectively interpreting data in a way that fits a desired conclusion
  18. 18. It allows others to fairly judge how much weight to give the findings, supporting trust in the research
  19. 19. Students who struggle most with sleep might be absent, late or less alert, making them less likely to be surveyed as usual
  20. 20. Cyclists are far more likely to already support the bike lane, systematically skewing the result toward "yes"
  21. 21. Design and report research that genuinely and honestly reflects a population, not just a convenient or biased slice of it