- explain the central idea: Compare continuous numerical distributions using boxplots and other displays, discussing centre, spread, shape and outliers.
- choose and apply an appropriate method without relying on keyword matching
- check results using units, substitution, estimation, a second representation or contextual reasonableness
- justify a conclusion and communicate limitations where the context requires them
Year 10 Mathematics · AC9M10ST02
Boxplots and Comparing Continuous Distributions
Compare distributions by centre, spread, shape and unusual values, and choose a display that answers the statistical question rather than one that merely looks familiar
Ready to project and teach
Learning goalsSay it simply
Key conceptTeach from the board
A boxplot summarises a distribution using minimum, Q1, median, Q3 and maximum (with outlier conventions where used). IQR=Q3−Q1 measures middle-50% spread. Boxplots are excellent for comparison but hide detailed modality/frequency patterns that histograms or dot plots can show.
Five-number summary
min, Q1, median, Q3, max.
Spread
IQR=Q3−Q1; range=max−min.
Compare
Centre → spread → shape → outliers → context.
Outlier rule
Common convention: below Q1−1.5IQR or above Q3+1.5IQR.
Worked examplesWe do
Worked examples
AC9M10ST02 - Boxplots and Comparing Continuous Distributions
Example 1
Five-number summary min, Q1, median, Q3, max.
Example 2
Spread IQR=Q3−Q1; range=max−min.
Example 3
Compare Centre → spread → shape → outliers → context.
Example 4
Outlier rule Common convention: below Q1−1.5IQR or above Q3+1.5IQR.
Curriculum examplesCopied content
Australian Curriculum: AC9M10ST02 — Year 10 Statistics. Compare continuous numerical distributions using boxplots and other displays, discussing centre, spread, shape and outliers.
Victoria: VC2M10ST01 — Level 10 Statistics
NSW: Stage 5 Core — Data classification, visualisation and analysis; Path — Data analysis and statistical enquiry
Alignment explanation: The explicit teaching and worked examples address the Australian Curriculum concept directly. The Victorian mapping follows the current Version 2.0 descriptor structure; where Victoria combines or extends content, that difference is stated rather than hidden. NSW uses a Stage 5 Core–Paths structure, so this page maps to the relevant content group(s) and Working mathematically processes instead of inventing a Year 10 one-to-one code.
| Lesson component | Australian Curriculum | Victoria | NSW |
|---|---|---|---|
| Explicit concept teaching and worked examples | AC9M10ST02 | VC2M10ST01 — Level 10 Statistics | Stage 5 Core — Data classification, visualisation and analysis; Path — Data analysis and statistical enquiry |
| Guided and independent practice | Builds fluency and application for AC9M10ST02 | Practises the mapped Level 10/10A knowledge as applicable | Practises the mapped Stage 5 Core/Path content |
| Reasoning and assessment tasks | Applies reasoning/problem solving in the descriptor context | Supports Victorian reasoning and modelling expectations | Embeds Working mathematically: reasoning, problem solving and communication |
Australian Curriculum elaborations
AC9M10ST02: compare continuous-data distributions using displays including boxplots and discuss centre, spread, shape and outliers in context.
- E1: construct/interpret boxplots and compare datasets. Examples 1–4.
- E2: compare distribution shapes using boxplots, histograms, cumulative-frequency graphs and dot plots, including symmetry/skew/modality. Examples 6–8.
- E3: use digital tools to compare boxplots/histograms according to statistical question. Example 7.
- E4: use five-number summary/boxplot for numerical and visual centre/spread comparisons. Examples 1–4.
- E5: compare stories/information from continuous/discrete datasets displayed in different ways. Examples 7–9.
- E6: explore identifying/handling outliers in machine learning. Example 10.
Questions and answersWith answers
- Find median of 3,5,8,10,11.
- 8.
- If Q1=12,Q3=21 find IQR.
- 9.
- Find outlier fences for Q1=20,Q3=28.
- IQR=8; fences 8 and 40.
Practice and reviewReady for practice
- Comparing only medians and ignoring spread.
- Assuming a boxplot reveals exact frequencies or modes.
- Calling every extreme value an error.
- Using range when IQR better represents middle spread.
- Describing “higher/lower” without interpreting what it means in context.
Curriculum alignmentStart here
- explain the central idea: Compare continuous numerical distributions using boxplots and other displays, discussing centre, spread, shape and outliers.
- choose and apply an appropriate method without relying on keyword matching
- check results using units, substitution, estimation, a second representation or contextual reasonableness
- justify a conclusion and communicate limitations where the context requires them
- Australian Curriculum Version 9 — ACARA
- Victorian Curriculum Mathematics Version 2.0 — VCAA
- NSW Mathematics K–10 Syllabus (2022) — NSW Curriculum/NESA
Official wording is paraphrased on SkillrHub; use the linked curriculum sites as the source of record.
Other curriculum comparisons retained
US CCSS HSS-ID.A.1–3; UK GCSE box plots/distribution comparison; NSW Stage 5 and Victorian Level 10 statistics; comparable Canadian/NZ secondary distributions.
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