Statistical investigations

A statistical investigation follows a clear process: pose a question you want to answer, plan how to collect relevant data, collect the data carefully, analyse it using summary statistics and displays, and finally interpret the results to answer the original question. Good questions are specific and can actually be answered with data — "Do more students in my year prefer summer or winter?" is answerable; "Is summer good?" is too vague. The way you collect data (like who you ask) can affect how trustworthy your conclusions are.

Key terms

Statistical investigation:

A structured process of posing a question, collecting data, analysing it and interpreting results.

Representative sample:

A group chosen so that it fairly reflects the wider population being studied.

Questions

1. 1. A statistical investigation starts by:

   • Collecting data randomly
   • Posing a clear question
   • Drawing a graph
   • Guessing the answer

2. 2. After posing a question, the next step is usually to:

   • Interpret results
   • Plan how to collect data
   • Skip to conclusions
   • Ignore the question

3. 3. A good statistical question is:

   • Vague and general
   • Specific and answerable with data
   • Impossible to answer
   • About feelings only

4. 4. "Is summer good?" is a:

   • Good statistical question
   • Too vague to investigate well
   • Perfectly specific
   • The best kind of question

5. 5. A representative sample:

   • Includes everyone in the world
   • Fairly reflects the wider population being studied
   • Is always biased
   • Ignores the population

6. 6. After collecting data, you should:

   • Ignore it
   • Analyse it
   • Delete it
   • Guess instead

7. 7. The final step of a statistical investigation is to:

   • Collect more random data
   • Interpret the results to answer the question
   • Ignore the data
   • Start over

8. 8. "Do more students in my year prefer summer or winter?" is a:

   • Vague question
   • Specific, answerable statistical question
   • Question with no possible data
   • Trick question

9. 9. If you only survey your close friends about a school-wide issue, your sample is likely:

   • Perfectly representative
   • Not representative of the whole school
   • The best possible sample
   • Irrelevant

10. 10. Why does how you collect data matter?

    • It never matters
    • It can affect how trustworthy your conclusions are
    • Only the final graph matters
    • Data collection has no effect on results

11. 11. Displaying data visually (like a column graph) mainly helps:

    • Hide patterns
    • Show patterns at a glance
    • Make data harder to understand
    • Replace analysis entirely

12. 12. If your data doesn't clearly answer your original question, you should:

    • Ignore this and make up an answer
    • Reconsider your data or question
    • Publish it anyway
    • Delete the question

13. 13. A survey asking "What is your favourite subject?" to a random mix of students across all year levels is investigating:

    • Just Year 7 preferences
    • Preferences across a broader group
    • Nothing useful
    • Only maths

14. 14. Which is the best order for a statistical investigation?

    • Analyse, question, collect, interpret
    • Question, collect, analyse, interpret
    • Interpret, question, collect, analyse
    • Collect, interpret, question, analyse

15. 15. A survey about "favourite school lunch options" only surveys students who buy lunch from the canteen. This sample:

    • Is fully representative of all students
    • May be biased, missing students who bring lunch from home
    • Guarantees accurate results
    • Has no possible issues

16. 16. Why might a small sample size make conclusions less reliable?

    • Small samples are always more accurate
    • A small, unrepresentative sample may not reflect the wider group well
    • Sample size never matters
    • Small samples remove all bias automatically

17. 17. A question like "How many hours do Year 7 students spend on homework per week?" is well-suited to be answered by:

    • Opinions only
    • Collecting and analysing numerical data
    • Guessing
    • Ignoring data entirely

18. 18. After finding that the mean differs greatly from the median in a data set, a careful investigator should:

    • Ignore the difference
    • Consider whether outliers are affecting the mean
    • Assume the data is wrong
    • Only report the mean

19. 19. Why is interpreting results in terms of the original question an important final step?

    • It's optional and can be skipped
    • It connects the data analysis back to answering what was actually asked
    • Interpretation is irrelevant to investigations
    • Numbers speak for themselves with no need for context

20. 20. Two students investigate the same question but use different sampling methods and get different results. This mainly shows:

    • Statistics is always wrong
    • How data is collected can meaningfully affect conclusions
    • One student must have lied
    • Sampling method never matters