Box Plots and Data Comparison

Active learning helps students grasp box plots because the abstract measures of quartiles and medians become concrete when they order real data and draw the plots themselves. Turning numbers into visual summaries reveals patterns and outliers in ways that passive study cannot.

• Year 10
• Mathematics
• 4 activities
• 25 min–45 min

Learning Objectives

1. Calculate the median, quartiles, and interquartile range for two or more datasets.
2. Construct accurate box plots representing given datasets, including whiskers and median lines.
3. Compare and contrast the central tendency and spread of two or more distributions using their box plots.
4. Justify the selection of box plots over other graphical representations for comparing specific datasets, considering skewness and outliers.

Collaborative Problem-Solving

⏱ 30 min·Pairs

Pairs Task: Heights Comparison

Pairs measure and record heights of 20 classmates, split by gender. Order data to calculate medians and quartiles, draw side-by-side box plots. Discuss which group has greater spread and why.

Prepare & details

Explain what each section of a box plot reveals about data distribution.

Facilitation Tip: During the Pairs Task: Heights Comparison, circulate and ask each pair to explain why they placed the median line where they did.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 45 min·Small Groups

Small Groups: Reaction Time Challenge

Provide stopwatch for groups to test 30 reaction times to a signal, split into two conditions like rested versus tired. Construct box plots and compare medians and ranges. Groups justify which condition performs better.

Prepare & details

Compare two datasets using their box plots, focusing on central tendency and spread.

Facilitation Tip: For the Small Groups: Reaction Time Challenge, supply stopwatches and printed data tables to ensure all students engage with the raw data before plotting.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 40 min·Whole Class

Whole Class: Sleep Survey Analysis

Conduct a 1-minute survey on weekly sleep hours. Collate data on board, split by day types. Class draws shared box plots, then votes on interpretations of spread and outliers.

Prepare & details

Justify the use of box plots for visual comparison of data distributions.

Facilitation Tip: In the Whole Class: Sleep Survey Analysis, display student-generated box plots side by side to encourage comparison and debate about data interpretation.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 25 min·Individual

Individual: Invent and Interpret

Students invent two small datasets from sports scores. Draw individual box plots, swap with a partner to interpret and critique. Share strongest comparisons with class.

Prepare & details

Explain what each section of a box plot reveals about data distribution.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Teaching This Topic

Teachers often start by having students order data physically with sticky notes on a board to visualise quartiles before moving to paper or digital plotting. Avoid rushing to formulas; focus on the meaning of the quartiles first. Research suggests that constructing box plots manually, even with imperfect scale, builds deeper understanding than pre-drawn templates.

What to Expect

Successful learning looks like students confidently calculating quartiles, identifying medians, and drawing accurate box plots with correct whiskers and outliers. Discussions should focus on comparing distributions rather than just listing values.

Watch Out for These Misconceptions

Common Misconception

During Pairs Task: Heights Comparison, watch for students confusing the median line with the mean.

What to Teach Instead

Have students calculate both the mean and median from their height data, then plot both on a number line to see where they differ. Ask them to explain which measure they think best represents the typical height in their sample.

Common Misconception

During Small Groups: Reaction Time Challenge, watch for students dismissing extreme reaction times as errors.

What to Teach Instead

Ask groups to research real-world examples of reaction times in sports or driving, then debate whether outliers reflect genuine differences or recording mistakes. Require them to justify their reasoning with data.

Common Misconception

During Whole Class: Sleep Survey Analysis, watch for students assuming box plots need large datasets to be valid.

What to Teach Instead

Use the class’ 15–20 survey responses to plot a box plot live on the board, then ask students to suggest how the plot would change (or stay the same) if five more responses were added.

Assessment Ideas

Quick Check

After Pairs Task: Heights Comparison, give each pair two new small datasets and ask them to calculate Q1, median, Q3, and IQR, then sketch the box plot on mini whiteboards. Ask them to hold up their plots for a quick class review.

Discussion Prompt

During Small Groups: Reaction Time Challenge, circulate and ask each group to present one insight about the spread or skewness of their data and how it relates to their experimental design.

Exit Ticket

After Whole Class: Sleep Survey Analysis, give each student a pre-drawn box plot of another class’s sleep data and ask them to interpret the median, IQR, and any outliers in writing before leaving.

Extensions & Scaffolding

• Challenge: Ask students to create a misleading box plot from a dataset, then have peers identify the manipulation.
• Scaffolding: Provide partially completed box plots with missing quartile labels for students to fill in.
• Deeper exploration: Introduce double box plots and ask students to write a short report comparing two related datasets.

Key Vocabulary

Median	The middle value in an ordered dataset, dividing the data into two equal halves.
Quartiles	Values that divide an ordered dataset into four equal parts; the lower quartile (Q1) is the median of the lower half, and the upper quartile (Q3) is the median of the upper half.
Interquartile Range (IQR)	The difference between the upper quartile (Q3) and the lower quartile (Q1), representing the spread of the middle 50% of the data.
Outlier	A data point that is significantly different from other observations in the dataset, often calculated as being more than 1.5 times the IQR below Q1 or above Q3.