Mathematics · Year 11

Active learning ideas

Box Plots and Interquartile Range

Active construction of box plots helps Year 11 students move beyond abstract definitions to see how quartiles partition data. When learners order raw scores and mark Q1, median, and Q3 themselves, the five-number summary becomes a tool they trust, not just a formula they memorize.

• National Curriculum Attainment Targets
• GCSE: Mathematics - Statistics

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Gallery Walk
• 30 min · Pairs

Pair Plotting: Class Test Scores

Provide pairs with two lists of 20 test scores each. They order data, find quartiles and median, then sketch box plots side-by-side. Pairs note differences in spread and outliers before sharing with the class.

Justify why the median is often a better measure of central tendency than the mean for skewed data.

Facilitation Tip

During Pair Plotting, have students swap datasets before plotting so they must read each other’s ordered lists aloud, reinforcing precision.

What to look for

Provide students with a dataset of exam scores. Ask them to calculate the five-number summary and then construct a box plot. Check for accuracy in calculations and plot construction.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Gallery Walk
• 45 min · Small Groups

Small Group Comparison: Athlete Performances

Give small groups datasets on 100m sprint times for two teams. Groups construct box plots, calculate IQRs, and discuss which team has greater consistency. They present findings using key questions on a whiteboard.

Differentiate between the range and the interquartile range as measures of spread.

Facilitation Tip

In Small Group Comparison, assign each group one class’s scores and one athlete’s performance measures so debates focus on concrete numbers rather than assumptions.

What to look for

Present two box plots comparing the heights of Year 11 boys and girls. Ask students: 'Which group has a greater spread in heights? How do the medians compare? Based on these box plots, what can you conclude about the typical height of a boy versus a girl in this sample?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 03

• Gallery Walk
• 35 min · Whole Class

Whole Class Outlier Hunt: Real Data Challenge

Display a large dataset on the board, such as household incomes. Class votes on potential outliers, then constructs a box plot together to verify using IQR rule. Discuss impacts on mean versus median.

Compare two datasets using box plots, drawing conclusions about their distributions.

Facilitation Tip

For Whole Class Outlier Hunt, give three different IQR multipliers (1.0, 1.5, 2.0) on the same dataset so students see how threshold choices change the outlier list.

What to look for

Give students a small dataset. Ask them to calculate the IQR and identify any potential outliers. Then, ask them to write one sentence explaining why the median might be a better measure of central tendency for this specific dataset if it were skewed.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 04

• Gallery Walk
• 25 min · Individual

Individual Interpretation: Skewed Distributions

Students receive printed box plots of skewed data like incomes or ages. Individually, they justify median use over mean and compare spreads. Follow with pair shares to refine explanations.

Justify why the median is often a better measure of central tendency than the mean for skewed data.

What to look for

Provide students with a dataset of exam scores. Ask them to calculate the five-number summary and then construct a box plot. Check for accuracy in calculations and plot construction.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Start with a human box plot on the floor using students’ heights or shoe sizes; this kinesthetic hook makes quartiles tangible. Avoid rushing to the formula—instead, let learners derive Q1 and Q3 from medians of halves, which reduces later confusion about quartile placement. Research shows that students who physically arrange data before plotting score higher on interpretation tasks.

Students will confidently order data, compute quartiles and IQR, and draw accurate box plots by the end of the sequence. They will also interpret spread and skewness and justify decisions about outliers using clear reasoning.

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Watch Out for These Misconceptions

• During Pair Plotting: Class Test Scores, watch for students who assume the box plot’s box height equals the number of students in that quartile.

  Have students label the quartile boundaries with the actual minimum, Q1, median, Q3, and maximum values, then count how many data points fall in each section to prove the box height does not reflect frequency.

• During Small Group Comparison: Athlete Performances, watch for students who interpret a wider box as higher overall performance rather than greater spread.

  Ask groups to calculate the median heights of both distributions and compare them before discussing box width, reinforcing that spread and center are separate features.

• During Whole Class Outlier Hunt: Real Data Challenge, watch for students who treat any value beyond 1.5×IQR as an automatic error to remove.

  Direct students to write a one-sentence context-based justification for each outlier, such as ‘A 10-second 100m time could be valid for an elite sprinter,’ before deciding whether to investigate further.

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Methods used in this brief

• Gallery Walk