Box Plots for Comparing Data

Active learning works for box plots because students build the visual themselves from raw data. When Year 9s collect measurements and mark their own medians and quartiles, the summary becomes meaningful, not abstract. This hands-on construction helps them trust the plot as a tool for comparing groups quickly and accurately.

• Year 9
• Mathematics
• 4 activities
• 20 min–45 min

Learning Objectives

1. Calculate the median, lower quartile, and upper quartile for two or more data sets.
2. Construct comparative box plots accurately on a numerical scale.
3. Compare the spread and central tendency of two or more data sets using their box plots.
4. Analyze the visual representation of quartiles and the interquartile range on a box plot.
5. Critique the suitability of box plots for representing skewed data distributions.

Decision Matrix

⏱ 35 min·Pairs

Pairs Survey: Heights Box Plots

Pairs survey 20 classmates' heights, order data, calculate median and quartiles, then draw box plots for boys and girls on shared graph paper. They note differences in spread and centre, presenting one key comparison to the class. Extend by identifying any outliers.

Prepare & details

How can we use box plots to visually compare the spread of two different groups?

Facilitation Tip: During the Pairs Survey, circulate to ensure students are ordering data before they find Q1, Q2, and Q3; unordered lists lead to incorrect medians.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Decision Matrix

⏱ 45 min·Small Groups

Small Groups Stations: Sports Data Comparison

Prepare four data sets on reaction times or jump heights from sports. Groups rotate through stations every 10 minutes: calculate stats, plot box plot, compare to another set, and critique skewness. Record findings on a group sheet.

Prepare & details

Analyze what the median and quartiles represent on a box plot.

Facilitation Tip: At the Sports Data Stations, give each group one set of data to plot and one to interpret so everyone contributes to both tasks.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Decision Matrix

⏱ 25 min·Whole Class

Whole Class Critique: Exam Scores Challenge

Display three pairs of box plots from mock exam data on the board. Class discusses in a think-pair-share: which shows greater spread, evidence of skewness, and why one set might mislead. Vote and justify best comparison method.

Prepare & details

Critique the effectiveness of box plots for identifying skewness in data.

Facilitation Tip: In the Whole Class Critique, deliberately overlay calculated means on box plots so students see how medians resist outliers compared to averages.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Decision Matrix

⏱ 20 min·Individual

Individual Plotting: Weather Data

Provide rainfall data for two UK cities over a month. Students independently order data, compute quartiles, plot box plots, and write two sentences comparing variability. Share digitally for class gallery walk.

Prepare & details

How can we use box plots to visually compare the spread of two different groups?

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Teaching This Topic

Teach box plots by starting with small, manageable data sets so students can manually order and split the data. Avoid rushing to software before they grasp how quartiles divide the data. Research shows that sketching builds spatial memory; students who draw their own plots retain the meaning of IQR and outliers better than those who only use digital tools. Emphasise that a box plot is a summary, not a raw display, so students learn to trust its ability to hide detail while revealing key patterns.

What to Expect

By the end of these activities, students should calculate quartiles correctly, plot box plots neatly, compare spreads with precise vocabulary, and explain skewness using the shape of the box and whiskers. Clear sketches and concise comparisons in pairs and groups signal solid understanding.

Watch Out for These Misconceptions

Common Misconception

During Pairs Survey: Heights Box Plots, watch for students who think all data points are shown inside the box and whiskers.

What to Teach Instead

Bring students back to their raw height measurements and have them mark each plotted value on the number line; they will see only five points define the plot, clarifying that the box and whiskers summarise the rest.

Common Misconception

During Whole Class Critique: Exam Scores Challenge, watch for students who say the median and mean are always the same.

What to Teach Instead

Ask groups to calculate the mean score from their data and overlay it on the box plot with a dotted line; the gap between the solid median line and dotted mean line in skewed data will show the difference visually.

Common Misconception

During Small Groups Stations: Sports Data Comparison, watch for students who extend whiskers to the absolute min and max regardless of outliers.

What to Teach Instead

Provide outlier cards at each station and have groups decide whether a point is beyond 1.5 times IQR; if yes, they redraw whiskers to the nearest non-outlier to practice the rule.

Assessment Ideas

Quick Check

After Pairs Survey: Heights Box Plots, give each pair two ordered tables of student heights and ask them to calculate median, Q1, Q3, and IQR for each class; collect these to check calculation accuracy.

Discussion Prompt

After Sports Data Comparison, display two box plots of race times from two teams and ask: 'Which team had the faster median time? Which team had more consistent times?' Listen for answers that reference median location and IQR length.

Exit Ticket

During Whole Class Critique, hand out a clearly right-skewed temperature box plot and ask students to write one sentence describing the skewness and one sentence explaining a limitation of using a box plot for skewed temperature data.

Extensions & Scaffolding

• Challenge early finishers to create a second box plot that hides one outlier and write a paragraph explaining how the summary changes.
• Scaffolding for struggling students: provide pre-sorted data cards and a blank plot frame so they focus on marking quartiles rather than reordering.
• Deeper exploration: ask students to design a question where a box plot would be more informative than a bar chart, then justify their choice in writing.

Key Vocabulary

Median	The middle value in an ordered data set. If there is an even number of data points, it is the average of the two middle values.
Quartiles	Values that divide an ordered data set 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). It represents the spread of the middle 50% of the data.
Box Plot	A graphical representation of data that shows the median, quartiles, and range of a data set using a box and whiskers.