Lesson 115 — Planning a Statistical Investigation
Strand: Statistics | Descriptor: AC9M7ST03 | Duration: 45 minutes
Block note. Lessons 115–120 form one connected investigation project: plan (115), collect (116), analyse (117), report (118), review (119), consolidate (120). Students keep a single project folder throughout.
Learning Intentions
- To understand the statistical investigation cycle.
- To write a statistical question that data can actually answer.
Success Criteria
I can:
- Name and describe the four stages of a statistical investigation.
- Distinguish a statistical question from a non-statistical one.
- Define the variable, population and sample for my investigation.
- Write a practical data collection plan.
Warmup
(6 minutes — which can data answer? pairs)
Decide whether each question could be answered by collecting data, and if not, why not.
- How tall is our tallest student?
- Do Year 7 students spend more time on screens than Year 9 students?
- Is maths more important than art?
- How many hours of sleep does a typical Year 7 student get?
- What is the best colour?
Answers: 1. Yes, but trivially — one measurement, no variability; 2. Yes — a genuine statistical question; 3. No — a value judgement, not a measurable quantity; 4. Yes — “typical” implies variability; 5. No — a matter of taste.
The distinction to name: a statistical question anticipates variability in the answers. “How tall is Sam?” has one answer. “How tall are Year 7 students?” has many, and needs data to summarise.
Activities
Activity 1 — Explicit Instruction: the Investigation Cycle (12 min)
The four stages — the statistical counterpart to the modelling cycle from Lesson 74:
| Stage | What happens | Key question |
|---|---|---|
| Pose | Write a statistical question; define variable, population, sample | What exactly am I asking? |
| Collect | Plan and gather data accurately | Is my data trustworthy? |
| Analyse | Display and summarise the distribution | What does the data show? |
| Interpret | Answer the question; state limitations | What can I honestly conclude? |
A good statistical question has four properties:
- It anticipates variability — the answers will differ.
- It names a measurable variable.
- It specifies a population.
- It is answerable with data we can actually collect.
I do — improve a weak question, live:
Weak: “Do people like sport?”
- Variability ✓ but “like” is not measurable, “people” is not a population.
Better: “How many hours per week do Year 7 students at this school spend playing sport?”
- Variable: hours per week (continuous). Population: Year 7 at this school. Sample: our class. Answerable ✓
We do — improve these together:
- “Are boys taller?”
- “Is homework too much?”
- “What do students eat?”
(Sample improvements: “How does the arm span of Year 7 boys compare with that of Year 7 girls at this school?”; “How many minutes of homework do Year 7 students at this school do on a typical weeknight?”; “How many pieces of fruit do Year 7 students eat in a day?“)
Activity 2 — Pose Your Question (16 min)
Pairs. The project begins here; this plan is carried into Lesson 116.
Your investigation. Choose a question your class can answer with data collected in one lesson.
Suggested areas (or propose your own for approval):
- Reaction times (ruler-drop test)
- Arm span, height, or hand span
- Time spent on homework, sleep, or screens
- Number of letters in names; number of siblings
- Estimation accuracy (estimate then measure a length)
- Memory span (digits recalled)
Write your project plan, covering all six points:
- The question — precisely worded, anticipating variability.
- The variable — what exactly is measured, and its units.
- Discrete or continuous — with justification.
- Population and sample — who you want to know about, and who you will measure.
- Collection method — the exact procedure, including precision.
- Prediction — what you expect to find, and why.
Circulating prompts:
| Prompt | Purpose |
|---|---|
| Would two people measuring the same student get the same number? | Forces a precise procedural definition. |
| Could you collect this in one lesson? | Practicality — ambitious questions fail at the collection stage. |
| Who is your population, and is your sample really it? | Sample-versus-population honesty (Lesson 107). |
| What will your data look like if your prediction is right? | Makes the prediction testable, not decorative. |
| Is your variable a number? | Categorical variables limit the analysis to the mode only. |
Two comparison questions are worth encouraging — e.g. “Do students who play a musical instrument have faster reaction times?” — because they lead to back-to-back displays in Lesson 117. But warn: comparison needs two samples, doubling the collection.
Activity 3 — Inquiry: what Could Go Wrong? (11 min)
Pairs swap plans and stress-test them.
Read another pair’s plan and answer:
- Could you follow their collection method exactly, without asking questions?
- Name one thing that would make two measurers disagree.
- What is their population, and does their sample fairly represent it?
- Name one source of bias in how they plan to collect.
Socratic scaffolding — the bias discussion:
| Prompt | Purpose |
|---|---|
| If you ask only your friends, who is missing? | Selection bias — the sample is not representative. |
| If students report their own screen time, what might happen? | Under- or over-reporting — self-report bias. |
| If you measure reaction times only after lunch, what varies? | A confounding factor — time of day. |
| If the loudest students volunteer first, what happens? | Volunteer bias — willing participants may differ systematically. |
| Can bias always be removed? | Rarely. It can be reduced and must be reported — the honesty standard from Lesson 76. |
Then: each pair revises their plan in response to one comment received, and notes the revision.
Checks for Understanding
(5 minutes — exit ticket, collected with the plan)
- What makes a question statistical rather than not?
- Name the four stages of a statistical investigation.
- Rewrite as a statistical question: “Do students like reading?”
- For your own investigation, state the variable, its units, and whether it is discrete or continuous.
- Reasoning. Name one source of bias in your collection plan and how you will reduce it.
Answers: 1. It anticipates variability in the answers and names a measurable variable and a population; 2. Pose, collect, analyse, interpret; 3. E.g. “How many minutes per day do Year 7 students at this school spend reading for pleasure?”; 4–5. Student’s own, marked against the plan.
Common Misconceptions
| Misconception | How to pre-empt it |
|---|---|
| A question with one answer is statistical. | The warmup’s Q1 — no variability, no investigation. |
| Vague variables (“happiness”, “how much”). | The measurable-variable requirement and the two-measurers test. |
| Sample and population treated as the same. | Named separately in the plan; Lesson 107’s vocabulary. |
| Believing bias can always be eliminated. | It is reduced and reported, not erased. |
| Planning a question that cannot be collected in the time available. | The practicality prompt during circulation. |
| A prediction with no reasoning behind it. | Point 6 requires “and why”. |
Enrichment — Competition-Style Problems
E1 (Kangaroo style). Which is a statistical question: “How many students are in Year 7?” or “How many siblings do Year 7 students have?”
Answer
The second — it anticipates variability. The first has a single fixed answer.
E2 (AMC Junior style). A survey asks “Do you agree that our canteen is excellent?” Name the problem and rewrite it neutrally.
Answer
It is a leading question — the wording invites agreement. Neutral version: “How would you rate the canteen on a scale of
E3 (Challenge). A student surveys the school’s fastest runners about weekly exercise and concludes Year 7 students exercise for
Answer
Selection bias — the sample is drawn from an unusually active subgroup, so the estimate is far too high for the whole population. The conclusion is about fast runners, not Year 7 students.
E4 (Challenge). Two students investigate screen time. One asks students to estimate; the other collects phone screen-time reports. Which data is more trustworthy, and what does the other risk?
Answer
The phone reports — they are measured, not recalled. Estimates risk under-reporting (social desirability) and simple memory error. But phone data misses other screens, so neither is complete; the limitation should be stated either way.
Homework
- Explain in one sentence what makes a question statistical.
- Rewrite each as a good statistical question: (a) “Is our library popular?” (b) “Do people sleep enough?” (c) “Are Year 7s good at estimating?”
- For each of your Q2 questions, state the variable, its units, and whether it is discrete or continuous.
- For your class investigation, write out the full collection procedure so precisely that a stranger could follow it. Include the precision to be used.
- Name the four stages of a statistical investigation and write one sentence on each.
- Identify the bias in each: (a) surveying only students in the computer lab about screen time (b) asking “Don’t you agree homework is excessive?” (c) measuring reaction times only in the last five minutes of a lesson.
- Write a prediction for your investigation, with a reason.
- Reasoning. Explain the difference between a population and a sample, using your own investigation as the example.
- Reasoning. Why must a collection procedure state the precision to be used?
- Challenge. Design a study to answer: “Do Year 7 students underestimate short lengths?” Specify the question, variable, procedure, and one source of bias with a mitigation.
Answers: Q2 — e.g. (a) “How many times per week do Year 7 students visit the library?” (b) “How many hours of sleep do Year 7 students get on a typical school night?” (c) “How close are Year 7 students’ estimates of a