Australian Curriculum v9 / ACiQ Year 7 Mathematics - Unit 0 - Statistical investigation, displays and summaries

Statistical investigation, displays and summaries

Plan investigations, acquire numerical data, create displays and interpret distributions with suitable summary statistics.

Updated 2026-07-24 - 9 min read

Plan investigations, acquire numerical data, create displays and interpret distributions with suitable summary statistics. This draft teaching resource is aligned to the cited Year 7 content descriptions and still requires named human curriculum approval.

Keep the investigative question connected to the data, display and conclusion so the final claim cannot exceed the evidence.

1. Plan a statistical investigation

A statistical question anticipates variation. The plan defines the variable, group, measurement method and how results will be recorded.

Decision check: Apply this lesson's rule to the worked example: Match the data-collection method and variable to the question. Identify the exact value, label or property that satisfies the rule.

2. Discrete, continuous and organised data

Discrete data are counted in separate values; continuous data are measured and can take intermediate values.

Decision check: Apply this lesson's rule to the worked example: Ask whether a value between two recorded values could be meaningful. Identify the exact value, label or property that satisfies the rule.

3. Construct, read and describe distributions

A display should preserve the data and make its distribution readable. For a stem-and-leaf plot, choose place values for the stem and leaf, order every leaf, retain repeats and provide a key. For a dot plot, use an evenly spaced number scale and place one dot for every observation.

Text-equivalent representation: Text stem-and-leaf example: 1 | 2 5 8; 2 | 1 1 4. Key: 1 | 2 means 12. Equivalent ordered data: 12, 15, 18, 21, 21, 24.

Decision check: Apply this lesson's rule to the worked example: Construct first; audit that every data value appears exactly once; then describe the display using context, centre, spread, shape and unusual values. Identify the exact value, label or property that satisfies the rule.

4. Summarise and report findings

Mean uses every value and is sensitive to outliers. Median depends on order and is resistant to extreme values; mode reports frequency.

Decision check: Apply this lesson's rule to the worked example: Justify a centre by referring to the distribution, not by naming a favourite measure. Identify the exact value, label or property that satisfies the rule.

Worked examples with complete reasoning

Worked example 1

Question: Construct a stem-and-leaf plot for 12, 15, 18, 21, 21 and 24. Use the format “1 | ...; 2 | ...” and order every leaf.

  1. Use the tens digits as stems and the ones digits as leaves.
  2. Order leaves within each row: 1 | 2 5 8; 2 | 1 1 4. A key would read 1 | 2 = 12.

Answer: 1 | 2 5 8; 2 | 1 1 4

Check: Keep repeated values as repeated leaves and order the leaves from least to greatest.

Worked example 2

Question: Find the mean of 4, 7, 7, 10.

  1. Sum = 28.
  2. Divide by 4: mean = 7.

Answer: 7

Check: Mean = total ÷ number of values.

Worked example 3

Question: Which plan best investigates how many minutes Year 7 students read on a school night?

  1. The question names a population and a numerical variable that should vary.
  2. A consistent night, unit and recording method make the data interpretable.

Answer: Ask a defined Year 7 group for minutes read on one specified night and record each numerical response consistently.

Check: Match the participants, variable, unit and collection method to the statistical question.

Method map for this topic

  1. Plan a statistical investigation: Match the data-collection method and variable to the question.
  2. Discrete, continuous and organised data: Ask whether a value between two recorded values could be meaningful.
  3. Construct, read and describe distributions: Construct first; audit that every data value appears exactly once; then describe the display using context, centre, spread, shape and unusual values.
  4. Summarise and report findings: Justify a centre by referring to the distribution, not by naming a favourite measure.

Common mistakes and how to correct them

  • mean calculation: Not yet. Mean = total ÷ number of values. Recheck the mean calculation step, then try again.
  • median order: Not yet. Always order data before locating the median. Recheck the median order step, then try again.
  • mode range: Not yet. Mode is about frequency; range is about distance between extremes. Recheck the mode range step, then try again.
  • data type: Not yet. Match the participants, variable, unit and collection method to the statistical question. Recheck the data type step, then try again.
  • centre choice: Not yet. Check for outliers and skew before choosing a centre. Recheck the centre choice step, then try again.
  • display construction: Not yet. Keep repeated values as repeated leaves and order the leaves from least to greatest. Recheck the display construction step, then try again.
  • display interpretation: Not yet. Use the key to reconstruct the ordered dataset before finding its centre. Recheck the display interpretation step, then try again.

Guided interactive lesson studio

The Learn lesson for this topic includes a structured action rather than asking you only to read an explanation or select an answer.

School-night reading investigation

Work through the investigation cycle for the fixed pilot dataset: define the variable, audit the data, construct a display, calculate summaries and write a bounded conclusion.

You will complete: Variable type; Ordered stem-and-leaf display; Mean, median and range; Conclusion for this class and night.

Accessible route: All six observations are provided in a semantic table and plain-text description. The stem-and-leaf display can be completed through labelled fields.

Evidence boundary: the automatically checkable fields give immediate formative feedback. Explanation and reflection fields remain formative and require rubric or teacher review; this action cannot create mastery evidence by itself.

Practice

  1. Construct a stem-and-leaf plot for 12, 15, 18, 21, 21 and 24. Use the format “1 | ...; 2 | ...” and order every leaf.
  2. A stem-and-leaf plot reads “1 | 2 5 8; 2 | 1 1 4”, with key 1 | 2 = 12. What is the median?
  3. Find the mean of 4, 7, 7, 10.
  4. Find the mean of 3, 5, 8, 8, 11.
  5. Which plan best investigates how many minutes Year 7 students read on a school night?
  6. Classify the numerical variable “number of books borrowed by each student”.

<details> <summary>Answers and reasoning</summary>

  1. 1 | 2 5 8; 2 | 1 1 4 — Use the tens digits as stems and the ones digits as leaves. Order leaves within each row: 1 | 2 5 8; 2 | 1 1 4. A key would read 1 | 2 = 12.
  2. 19.5 — Read the ordered values as 12, 15, 18, 21, 21, 24. There are six values, so median = (18 + 21) ÷ 2 = 19.5.
  3. 7 — Sum = 28. Divide by 4: mean = 7.
  4. 7 — Sum = 35. Divide by 5: mean = 7.
  5. Ask a defined Year 7 group for minutes read on one specified night and record each numerical response consistently. — The question names a population and a numerical variable that should vary. A consistent night, unit and recording method make the data interpretable.
  6. discrete — Ask whether measurements can take values between recorded values. This variable is discrete.

</details>

Checklist and vocabulary

| Skill | Observable evidence | | --- | --- | | choose useful graph small dataset | Choose and create a useful display for a small numerical dataset, including a stem-and-leaf plot. | | explain outlier changes mean median | Calculate summary statistics and explain how an outlier affects the mean and choice of median. | | acquire discrete continuous data | Distinguish discrete and continuous numerical variables and acquire suitable data. |

Retrieval prompts

  • State the defining relationship for each method above without looking.
  • Give one example where two visually similar representations mean different things.
  • Diagnose one misconception from the list and explain the first corrective step.
  • Name a check that is independent of simply repeating the same calculation.

Teach-back and self-check

Close the worked examples and explain statistical investigation, displays and summaries as if you were helping another Year 7 student. Begin by naming the clue that tells you which relationship, representation or operation is needed. Then show one complete example with labels and units where they matter. At each line, explain what stayed equivalent and why the next step is allowed.

Use this four-part check before calling the method secure:

  1. Identify: What information is given, and what must be found or justified?
  2. Represent: Which number line, diagram, table, expression, graph or organised list makes the relationship visible?
  3. Reason: Which rule connects the representation to the required answer?
  4. Verify: Can you check by estimation, substitution, an inverse operation, a second representation or the original context?

If the explanation depends on “I just knew”, return to the method map and name the missing decision. A durable method is one you can explain, check and use in a changed context after a delay.

Transfer task

Design a small investigation or simulation using statistical investigation, displays and summaries. Record the data or outcomes in an accessible text format, analyse them, and write a conclusion that does not claim more than the evidence supports.

Sources