Lesson 118 — Reporting Findings: Shape and Summary Statistics
Strand: Statistics | Descriptor: AC9M7ST03 | Duration: 45 minutes
Block note. Stage 4 of the investigation. Students write the report from the analysis completed in Lesson 117; it is peer-reviewed in Lesson 119 and finalised for Lesson 120.
Learning Intentions
- To write a statistical report that communicates findings clearly and honestly.
- To state the limitations of an investigation.
Success Criteria
I can:
- Structure a report in four sections.
- Report findings using shape and summary statistics together.
- State the limitations of my investigation honestly.
- Draw a conclusion that my data actually supports.
Warmup
(6 minutes — which report is usable? pairs)
Two reports of the same investigation:
Report A: “We measured reaction times. The mean was
. Most people were quite fast. It was interesting.” Report B: “We measured the reaction times of
Year 7 students using a ruler-drop test, recording to the nearest cm and converting to milliseconds. The typical reaction time was ms (median), with most students between and ms. The distribution was right-skewed, and one reading of ms — possibly a mistimed trial — stretched the range to ms. Our sample was one class, so the findings describe Year 7 at this school rather than students generally.”
- Which could a reader actually use? Why?
- List four things Report A is missing.
- Which sentence in Report B is the most important, and why?
Answers: 1. B — it says what was measured, how, what was found, and what the limits are; 2. Units, sample size, method, spread, shape, and any limitation; 3. Arguably the last — it prevents the reader over-generalising, which is the commonest misuse of a statistic.
Activities
Activity 1 — Explicit Instruction: the Report Structure (14 min)
The four sections — the statistical counterpart to Lesson 76’s modelling report:
| Section | Contents |
|---|---|
| 1. Question and method | The statistical question; the variable and units; the population and sample; the collection procedure and precision |
| 2. Results | The display; all four summary measures; the four-feature description |
| 3. Interpretation | The answer to the question, citing evidence; comparison with the prediction |
| 4. Limitations | Sample size and representativeness; collection difficulties; anomalies; what the findings cannot support |
I do — model section 4, the least familiar and most valuable:
“Our sample of
students came from one Year 7 class, so the results describe this class and cannot be assumed to hold for all Year 7 students or other year levels. Three measurements were re-taken because the tape slipped, which may have introduced small inconsistencies. One student’s reading of ms was far outside the rest and may reflect a distraction rather than a genuine reaction time; we have kept it in the data but reported it separately. A larger sample collected at a consistent time of day would give a more reliable picture.”
Name the four moves that paragraph makes: it limits the population claim, discloses procedural problems, explains the anomaly’s treatment, and names an improvement.
The reporting-numbers rules:
- Give the centre and the spread together, never a centre alone.
- Name the measure used — “the median was
ms”, not “the average was “. - Include units on every figure.
- Report the sample size — a finding from
observations differs in weight from one from . - Describe the shape in words, not only in the display.
We do — improve a weak sentence, together:
Weak: “The average was about
.” Better: “The median number of siblings was
(mean ), with values ranging from to across our sample of students.”
(Ask what was added: the measure named, the units/variable named, the spread, and the sample size.)
Activity 2 — Write the Report (18 min)
Individually. The full four-section report, using the Lesson 117 analysis.
Length guide: one page. Section 1 about four sentences; section 2 a display plus four sentences; section 3 three sentences; section 4 three to four sentences.
Circulating prompts:
| Prompt | Purpose |
|---|---|
| Could a stranger repeat your investigation from section 1? | Reproducibility — the test of a method description. |
| Have you named which average you reported? | The “average” ambiguity from Lesson 109. |
| Where is your spread? | The commonest omission. |
| What is the biggest weakness of your study? | Drives a genuine limitations paragraph rather than boilerplate. |
| Does your conclusion claim more than your data shows? | Over-generalisation — the commonest fault. |
| Have you mentioned your sample size in the results? | Weight of evidence. |
The over-claiming check — display these paired examples:
| Over-claimed | Supportable |
|---|---|
| ”Year 7 students sleep | "In our sample of |
| "Musicians have faster reactions." | "In our sample, the |
The second row is worth reading aloud. Recognising that a difference is smaller than the variation within groups is genuine statistical maturity, and Year 7 students can see it when the spreads are laid side by side.
Activity 3 — Self-check against the Criteria (7 min)
Individually, before submission.
| Check | ✓ / ✗ |
|---|---|
| The statistical question is stated precisely | |
| The method could be repeated by a stranger | |
| Sample size and population are stated | |
| The display has a title, labels/key, and all intervals shown | |
| All four measures are given, with the chosen one named | |
| Shape, centre, spread and outliers are all described | |
| The question is answered directly | |
| The prediction is compared with the result | |
| Limitations name at least two specific issues | |
| The conclusion claims no more than the data supports |
Then: circle the weakest row and write one sentence on how you will fix it. That sentence becomes the focus of tomorrow’s peer review.
Checks for Understanding
(2 minutes — one question, collected with the report)
Reasoning. Write one sentence stating a conclusion your data supports, and one sentence stating a related conclusion it does not support — explaining the difference.
Expected form: e.g. “Supported: in our sample of
Common Misconceptions
| Misconception | How to pre-empt it |
|---|---|
| Reporting a centre with no spread. | The reporting rules; the circulating prompt. |
| Saying “the average” without naming which. | The Lesson 109 ambiguity, re-enforced. |
| Generalising a class sample to a whole year level. | The over-claiming table and the exit question. |
| Treating limitations as an admission of failure. | Modelled as the section that makes the report trustworthy. |
| Omitting sample size. | Named as a reporting rule; checked in the self-check. |
| Vague limitations (“we could have done better”). | Two specific issues required. |
Enrichment — Competition-Style Problems
E1 (Kangaroo style). A report states “the average height was
Answer
Which average — mean or median. With skewed data they can differ substantially, and the reader cannot judge the claim without knowing.
E2 (AMC Junior style). A report concludes “students who eat breakfast score higher on tests” from a sample of
Answer
The sample is small and from one group, so it may not represent the population; and the study shows only an association, not that breakfast causes higher scores — other factors (sleep, home support) could explain both.
E3 (Challenge). Group A’s median is
Answer
“Group B’s median was
E4 (Challenge). Why does a report’s limitations section make it more credible rather than less?
Answer
It shows the writer understands what the data can and cannot support, and lets the reader judge how far to trust the findings. A report claiming no limitations is either careless or overstating — and a reader who spots an unmentioned flaw doubts everything else too.
Homework
- Finalise your four-section report, incorporating the fix you identified in the self-check.
- Rewrite this sentence properly: “The average was 12 and it was pretty spread out.”
- For each, say whether the conclusion is supported by a
-student class sample: (a) “The median sleep in our class was hours.” (b) “Australian teenagers sleep hours.” (c) “Students in our class who play sport slept longer than those who do not.” - Write a limitations paragraph for an investigation that: used
students, relied on self-reported data, and was collected in the last five minutes of a lesson. - Name the four sections of a statistical report and one thing that belongs in each.
- Explain why a report must state its sample size.
- Write one supportable and one over-claimed conclusion from your own investigation.
- Reasoning. Explain why “the average” is an ambiguous phrase in a report.
- Reasoning. Explain the difference between an association and a cause, with an example.
- Challenge. Your investigation is to be repeated with
students across three schools. Write three sentences on what would improve and what would remain a limitation.
Answers: Q2 — e.g. “The median was