120i - Consolidation Statistical Investigations

Lesson 120 — Consolidation and Check: Statistical Investigations

Strand: Statistics | Descriptor: AC9M7ST03 | Duration: 45 minutes

Block note. Final lesson of the investigation project (115–120) and of the statistics strand. Reports are presented and submitted; the lesson closes with a synthesis of the whole strand.

Learning Intentions

• To present statistical findings clearly to an audience.
• To consolidate the complete statistical investigation cycle.

Success Criteria

I can:

1. Present my findings concisely and accurately.
2. Interpret and question another investigation’s findings.
3. Explain each stage of the investigation cycle.
4. Judge what a statistical claim does and does not support.

Warmup

(6 minutes — the cycle from memory, individually then check)

Write the four stages of a statistical investigation and one sentence on each. Then check against your Lesson 115 notes.

Answers: Pose — write a statistical question anticipating variability; define variable, population and sample. Collect — follow a precise procedure; record raw data with units and precision. Analyse — display the data; calculate summary measures; describe shape, centre, spread and outliers. Interpret — answer the question with evidence; state limitations.

The through-line: every stage constrains the next. A vague question produces uncollectable data; sloppy collection produces meaningless analysis; analysis without interpretation answers nothing.

Activities

Activity 1 — Findings Presentations (20 min)

Each pair presents for 90 seconds, then takes one question. Aim for 10–12 presentations.

The 90-second structure — display it:

1. Our question was… (one sentence)
2. We measured… from… (variable, sample size, method in one sentence)
3. We found… (centre with the measure named, spread, and shape)
4. This means… (the answer, with one limitation)

The audience’s job. Every listener writes one question they could ask. Only one is asked per presentation, but all are collected.

Question stems to display for the audience:

• “How did you decide…?”
• “What would have happened if…?”
• “Does your data support…, or only…?”
• “Why do you think the shape was…?”
• “How many students, and how did you choose them?”

Teacher’s role. Where a presentation over-claims, ask the sceptic’s question yourself — gently, and framed as curiosity: “Would that hold for Year 9 as well, do you think, or just for your sample?” The block’s whole ethic rests on this being a normal question, not a criticism.

Collect on the board as presentations run:

• The range of shapes found (symmetric, right-skewed, bimodal).
• Any variable whose shape surprised its investigators.
• The most common limitation named across the class.

Activity 2 — Cross-investigation Synthesis (12 min)

Whole class, using the board’s collected findings.

Looking across every investigation in the room:

1. Which variables gave right-skewed distributions? What do they have in common?
2. Which gave roughly symmetric distributions? What do they have in common?
3. Which limitation appeared in almost every report?
4. If the class repeated all these investigations with students, what would change and what would not?

Socratic scaffolding:

Prompt	Purpose
List the right-skewed variables.	Typically: times, waiting, screen time, siblings.
What do those share?	A floor with no ceiling — Lesson 117’s structural insight.
The symmetric ones?	Heights, arm spans, hand spans — physical measurements with deviations both ways.
Q3: the universal limitation?	Sample size and non-representativeness — every class investigation shares it.
Q4: what improves with ?	Shape clarity and reliability of the centre. What does not: the sample is still one school, and self-report or measurement error persists.
So is a bigger sample always the answer?	It fixes chance variation, not bias. A larger biased sample is confidently wrong.

The last point deserves the board. More data reduces randomness; it does not correct a flawed collection method. This is the single most useful statistical idea a Year 7 can take away.

Activity 3 — Strand Synthesis (5 min)

Whole class, closing all of ST01–ST03.

Complete from memory:

Question	Answer
Which measure is resistant to outliers?
Which measure works on categorical data?
What four features describe a distribution?
Which display keeps individual values?
What must accompany every centre in a report?
What does a bigger sample fix — and not fix?

Completed: median; mode; shape, centre, spread, outliers; stem-and-leaf (and dot plot); the spread; it reduces chance variation but not bias.

Checks for Understanding

(7 minutes — exit ticket, collected with the final report)

1. Name the four stages of a statistical investigation.
2. A report states: “Our median was minutes.” What two things must be added?
3. Data: . State the median, the mean, and which better represents the data, with a reason.
4. Why can a class sample not support a claim about all Year 7 students in Australia?
5. A study’s sample is increased from to . Name one thing that improves and one that does not.
6. Reasoning. Write one conclusion your own investigation supports and one it does not, explaining the difference.

Answers: 1. Pose, collect, analyse, interpret; 2. The spread (and the shape), and the sample size — with units already present; 3. Median ; mean ; the median, because the value is an outlier inflating the mean above every other value; 4. The sample was not drawn from that population — one class in one school cannot represent the variety of schools, regions and circumstances across the country; 5. Improves: the reliability of the centre and the clarity of the shape. Does not: bias from how the sample was chosen, or errors in the collection method; 6. Student’s own, marked on the reasoning.

Common Misconceptions

Misconception	How to pre-empt it
A bigger sample fixes everything.	Activity 2’s closing point — chance versus bias.
Presenting the centre without the spread.	Step 3 of the presentation structure requires both.
Treating an audience question as an attack.	The teacher models the sceptic’s question as curiosity.
Believing an unremarkable finding is a failed investigation.	Consistency is a result — carried from Lesson 117.
Generalising the sample to a population.	Exit Q4 and Q6, and the teacher’s live questioning.
Thinking statistics is about calculation.	The whole block: the calculation is the easy part; the judgement is the subject.

Enrichment — Competition-Style Problems

E1 (Kangaroo style). A survey of students finds a median of hours’ sleep. Which claim is supportable: “these students typically slept hours” or “teenagers need more sleep”?

Answer

The first. The second is a claim about need, not about the data collected — no amount of sleep-duration data establishes what people should have.

E2 (AMC Junior style). Two studies of the same question: Study A surveys students chosen at random; Study B surveys students, all from the school choir. Which is more trustworthy, and why?

Answer

Study A. Its randomness makes it representative despite the smaller size; Study B’s larger sample is drawn from a special subgroup, so it is confidently unrepresentative. Size does not repair bias.

E3 (Challenge). A student concludes: “Students who eat breakfast get better marks, so the school should provide breakfast.” Identify the two logical steps and say which the data can support.

Answer

Step 1: breakfast-eaters score higher (an association — potentially supported by data). Step 2: providing breakfast would raise marks (a causal claim, and a policy recommendation — not supported, since other factors could explain the association). The data can support step 1 only.

E4 (Challenge). Design, in four sentences, an investigation to test whether Year 7 students’ estimates of a cm length are too high or too low. State the question, the variable, the procedure, and one limitation.

Answer

Question: “Do Year 7 students at this school overestimate or underestimate a cm length?” Variable: the estimate minus cm, in centimetres (continuous, signed). Procedure: show an unmarked cm strip to each student individually, ask for a written estimate before any measuring, and record to the nearest centimetre. Limitation: students who see others’ estimates first may be influenced, so estimates must be given privately.

E5 (Challenge). Why is “we could have used a bigger sample” a weaker limitation than “our sample was drawn only from students who volunteered”?

Answer

The first names a problem that more time would fix and that applies to every study. The second names a specific mechanism by which the results may be systematically wrong — volunteers may differ from non-volunteers — which tells the reader in which direction to doubt the findings.

Homework

1. Submit your final report with the revision log attached.
2. Write a -word summary of your investigation for a school newsletter, using no technical vocabulary that a parent would not know.
3. Name the four stages of a statistical investigation, with one sentence each in your own words.
4. Data: . (a) Median and mean. (b) Which represents the data better, and why? (c) Describe the shape.
5. For each, say supported or not supported by a -student class sample, with a reason: (a) “Our class’s median screen time was hours.” (b) “Year 7 students spend hours on screens.” (c) “Screen time causes poor sleep.”
6. Rewrite as a specific limitation: “Our sample was a bit small.”
7. Explain the difference between what a larger sample fixes and what it does not.
8. Reasoning. Explain why a statistical question must anticipate variability, using an example of one that does not.
9. Reasoning. Explain, with an example, why an association is not a cause.
10. Challenge. Design a complete investigation (question, variable, sample, procedure, expected shape, one limitation) to answer: “Are Year 7 students better at estimating short lengths than long ones?”

Answers: Q4 — (a) median ; mean (b) the median, since is an outlier lifting the mean above all but one value (c) right-skewed, with one clear outlier. Q5 — (a) supported (b) not supported: one class is not a representative sample of all Year 7 students (c) not supported: this would require showing causation, not just association, and probably a controlled study. Q6 — e.g. “Our participants were all from one class and were measured in the last five minutes of a lesson, when many were restless.” Q7 — a larger sample reduces the influence of chance on the results, making the centre more reliable and the shape clearer; it does not correct bias in how the sample was chosen or errors in the measuring method. Q8 — without variability there is nothing to summarise: “How many students are in this class?” has one answer and needs no statistics. Q9 — e.g. ice cream sales and drowning rates rise together, but neither causes the other; hot weather increases both. Q10 — e.g. question: “Are Year 7 students’ percentage errors smaller when estimating a cm length than a m length?”; variable: percentage error (continuous); sample: our class, each student estimating both; procedure: show each length unmarked, collect written estimates privately, then measure; expected shape: right-skewed errors in both, with larger percentage errors for the long length; limitation: estimating the first length may inform the second, so the order should be varied between students.