Coaching Centre
Statistical investigations and surveys
The statistical investigation process, writing a clear survey question, designing good survey questions and choices, and collecting data ethically.
Statistics isn't just calculating a mean. It starts much earlier, with a question worth answering, and it can go wrong long before any numbers appear. A badly worded survey produces data that no calculation can rescue.
The statistical investigation process
A statistical investigation follows a cycle. The NESA syllabus expects you to know the stages and to be able to criticise each one.
- Pose a question. Make it specific and answerable with data. "Do students sleep enough?" is vague. "How many hours do Year 11 students at our school sleep on a school night?" is a statistical question.
- Plan and collect the data. Decide the target population (the whole group you want to know about), whether to survey everyone or a sample, and how you'll collect: a survey, an observation, an experiment or existing data.
- Organise and display. Tables and graphs.
- Analyse. Summary statistics: centre, spread, shape, outliers.
- Interpret and communicate. Answer the original question in context, and say how confident you are.
- Reflect. What were the limitations? What would you do differently? Often this leads to a new question.
Mia wants to know whether using flashcards helps Year 11 students at her tutoring centre do better in maths tests. Write a statistical question, name the target population, and suggest how to collect the data.
Writing good survey questions
A good survey question means the same thing to everyone who reads it, and doesn't push them towards an answer. Watch for these faults:
| Fault | Example | Fix |
|---|---|---|
| Leading | "Don't you agree homework is too long?" | Use neutral wording |
| Double-barrelled | "Do you like maths and science?" | One idea per question |
| Vague | "Do you exercise often?" | Ask for a number or a clear time period |
| Overlapping choices | "0–2, 2–4, 4–6 hours" | "0 to under 2, 2 to under 4…" |
| Missing choices | "Train / Bus / Car" | Add "Other" or "None" |
| Too many choices | a list of $25$ options | Group them, keep it short |
Questions can be closed (a fixed set of choices, easy to graph and analyse) or open (any written answer, rich but harder to summarise). Most surveys are mainly closed questions with an optional open one at the end.
Rewrite the survey question "Wouldn't you say the new school timetable is worse than the old one and causes stress?"
Privacy, bias and ethics
People who give you data are trusting you with it. Before collecting:
- Consent: people should know what the survey is for and agree to take part. Students under 18 may need a parent's consent.
- Privacy and anonymity: don't collect names unless you need them, store data securely, and never share results that could identify a person. Sensitive topics (health, money, behaviour) must be anonymous or people won't answer honestly.
- Bias: a question, a sample or even the interviewer can push answers one way. You'll see sampling bias in the next section.
- Respect and cultural responsiveness: involve the community you're asking about, word questions respectfully, and offer choices that let everyone describe themselves.
Work through all six questions. For each, name the main fault before reading the fix.
Pick one question and write an even better version than the one suggested. What choices would you offer?
Your turn
A student surveys "How much do you spend on lunch each week? $\$0$–$\$10$ / $\$10$–$\$20$ / $\$20$–$\$30$". Give two faults and fix the choices.
Show the working
The choices overlap (someone spending exactly $\$10$ or $\$20$ fits two boxes), and they miss anyone spending more than $\$30$. Better: "less than $\$10$ / $\$10$ to less than $\$20$ / $\$20$ to less than $\$30$ / $\$30$ or more".
"Do you agree that our excellent library should open longer?" is:
"Our excellent library" invites agreement. It pushes people towards yes.
"How often do you read books and magazines?" is a poor question mainly because it is:
It asks about books and magazines together. Someone who reads books daily and magazines never can't answer accurately.
Which is the first step of a statistical investigation?
You need a clear question before you know what data to collect.
Which set of choices is best for "How many hours do you sleep on a school night?"
The last one doesn't overlap and covers every possible answer. The first overlaps and misses values, the second is vague, and the third overlaps.
Why should a survey about vaping at school be anonymous?
If answers can be traced back to a person, they may lie or refuse. That would bias the results.
An advantage of closed questions over open questions is that they:
Fixed choices can be counted and graphed straight away. Open questions give detail but must be read and grouped by hand.
Mia's flashcard investigation finds that flashcard users scored higher. Why can't she conclude flashcards caused the higher scores?
Students who use flashcards might also study more or attend more lessons. A survey can show a link, but not cause and effect.
Exam style: Which question would best investigate how Year 11 students travel to school?
It's neutral, about one thing, specific about the day and has complete choices. The others are leading, double-barrelled or vague.
Exam style: At the reflect stage of an investigation, a student should:
Reflecting means judging how reliable the conclusions are and what to change next time. Changing the question to fit the answer is not allowed.