Comparing Box Plots

Overview

Students build on prior learning about ordering data, finding the median, lower quartile, upper quartile and interquartile range. They construct and interpret box plots, then compare two data sets using centre, spread and overall distribution.

Learning intentions

• WALT identify the five-number summary for a data set.
• WALT construct an accurate box plot on a number line.
• WALT compare distributions using the median and interquartile range.
• WALT explain what a box plot shows about a data set.

Success criteria

• I can order data and find the minimum, Q1, median, Q3 and maximum.
• I can plot the five-number summary correctly and join the sections to make a box plot.
• I can describe the centre and spread of a distribution.
• I can make a comparison using evidence from two box plots.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenge tasks are connected to relevant mathematical content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: opportunities to reason, justify and communicate mathematically.
• Statistical thinking: investigate, represent, interpret and compare numerical data in context.

Lesson structure (60 minutes)

1. 0–7 min · Hook and retrieval. Display the opening comparison slide showing two contrasting box plots with the labels hidden. Ask, “Which group appears to have the greater typical value, and how can we tell?” Students make an individual prediction, then recall the meanings of median, quartiles and IQR with a partner. Collect several explanations without confirming the answer immediately.

2. 7–18 min · Explicit teaching. Use the box plot teaching slides to model the complete process with the data set: 12, 13, 17, 18, 23, 24, 24, 29, 30, 33, 39. Think aloud while identifying the minimum, median, Q1, Q3 and maximum. Clarify that the median is excluded when splitting an odd-sized data set into lower and upper halves. Students record the five-number summary and check each value with a partner.

3. 18–30 min · Guided construction. Distribute the Box Plot and Five-number Summary Mat and use the guided construction slides. Model how to choose an even scale, mark the five values, draw the box from Q1 to Q3, add the median line and extend whiskers to the minimum and maximum. Students construct the box plot for the model data, then complete the mat’s quick checks. Pause to address common errors, such as joining Q1 to the maximum or using the mean instead of the median.

4. 30–45 min · Independent application. Distribute the box plot practice worksheet. Students order two small data sets, calculate each five-number summary, construct paired box plots and answer interpretation questions. They should describe which group has the higher median, which has the greater IQR, and whether either group has a greater overall range. Circulate and ask, “What evidence supports your comparison?” Students who finish check their scale, labels and calculations against the success criteria.

5. 45–54 min · Mathematical discussion. Display the comparison discussion slides with two completed box plots representing weekly television viewing for two groups. In pairs, students prepare a response to: “Which group’s viewing is more consistent?” and “Can we say every student in one group watches more television?” Invite pairs to justify their answers using median, IQR and overlap. Emphasise that a box plot summarises data and does not show every individual value.

6. 54–60 min · Plenary and exit check. Use the plenary slide to revisit the opening prediction. Students complete the final section of the box plot practice worksheet: write the five-number summary for a short data set and one evidence-based comparison sentence. Collect responses to identify who needs further support with quartiles, scale or interpretation.

Resources

• the box plot lesson slide deck
• the box plot practice worksheet
• the Box Plot and Five-number Summary Mat
• Projector or interactive whiteboard
• Rulers, pencils and erasers
• Calculators, if normally used for checking
• Board space for a worked example

Assessment

• Listen for accurate explanations of how the lower and upper halves are formed, particularly for an odd number of values.
• Check students’ five-number summaries, scales and box plot features during guided and independent work.
• Use the exit response to assess whether students can interpret median and IQR, not merely construct a diagram.

Differentiation

• Support students with a pre-ordered data set, colour-coded lower and upper halves, a partially completed number line and the sentence starters: “The median is higher for…” and “The IQR is smaller, so…”.
• Re-model quartiles using a smaller data set and allow students to work with a peer or teacher-led group. Provide dyslexia-friendly copies with clear sans-serif font, generous spacing, uncluttered layout and instructions read aloud.
• EAL learners may use labelled visual examples for minimum, maximum, median, Q1, Q3 and IQR, plus paired rehearsal before writing.
• Advanced learners compare box plots with similar medians but different IQRs, explain how changing one value affects the five-number summary, and respond to a Mathsteasers-style challenge: “Can two data sets have the same box plot but contain different individual values? Explain.”

Extension

• Students create two different data sets that produce the same five-number summary, then explain what information the box plot hides.
• Students write a short statistical conclusion comparing two groups, including a statement about what cannot be inferred from the box plots.