Box Plots (Box-and-Whisker Plots)

Active learning works well for box plots because students need to physically order and measure data to see how quartiles divide the set. Moving numbers and drawing lines helps them connect abstract values to visual representations, which builds lasting understanding beyond memorizing steps.

• Grade 6
• Mathematics
• 4 activities
• 25 min–45 min

Learning Objectives

1. Calculate the five-number summary (minimum, Q1, median, Q3, maximum) from a given data set.
2. Construct accurate box plots on a number line using a five-number summary.
3. Analyze and interpret the spread and center of a data set as represented by a box plot.
4. Compare and contrast the distributions of two different data sets by analyzing their respective box plots.
5. Explain the specific advantages of using a box plot over a histogram for displaying certain data characteristics.

Museum Exhibit

⏱ 30 min·Pairs

Pairs Plotting: Student Heights

Pairs measure and record classmates' heights in centimetres, then find the five-number summary. Each pair sketches a box plot on grid paper and compares it to a partner's plot. Discuss differences in medians and spreads during share-out.

Prepare & details

Explain what specific information a box plot can show that a histogram cannot.

Facilitation Tip: During the Pairs Plotting: Student Heights activity, circulate to ensure pairs order data sets in ascending order before marking quartiles on the number line.

Setup: Tables or desks arranged as exhibit stations around room

Materials: Exhibit planning template, Art supplies for artifact creation, Label/placard cards, Visitor feedback form

• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Museum Exhibit

⏱ 45 min·Small Groups

Small Groups: Sports Data Comparison

Provide data sets on basketball free throws for two teams. Groups calculate summaries, draw box plots side by side, and note which team has greater consistency via interquartile range. Present findings to class with one insight each.

Prepare & details

Construct a box plot from a five-number summary.

Facilitation Tip: During the Small Groups: Sports Data Comparison activity, ask groups to explain why one box plot seems more stretched out than another, focusing on IQR differences.

Setup: Tables or desks arranged as exhibit stations around room

Materials: Exhibit planning template, Art supplies for artifact creation, Label/placard cards, Visitor feedback form

• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Museum Exhibit

⏱ 35 min·Whole Class

Whole Class: Poll and Plot

Conduct a class poll on minutes spent on screens daily. Record data on board, compute summary as a class using a number line. Draw a large box plot together and interpret median versus range.

Prepare & details

Compare two different data sets using their box plots.

Facilitation Tip: During the Whole Class: Poll and Plot activity, have students predict where quartiles will fall before calculating to build intuition about data shape.

Setup: Tables or desks arranged as exhibit stations around room

Materials: Exhibit planning template, Art supplies for artifact creation, Label/placard cards, Visitor feedback form

• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Museum Exhibit

⏱ 25 min·Individual

Individual: Mystery Data Analysis

Give five-number summaries for three data sets. Students construct box plots individually, then rank sets by spread. Pair up to verify calculations and explain one comparison.

Prepare & details

Explain what specific information a box plot can show that a histogram cannot.

Facilitation Tip: During the Individual: Mystery Data Analysis activity, provide a partially completed plot so students focus on interpreting rather than drawing errors.

Setup: Tables or desks arranged as exhibit stations around room

Materials: Exhibit planning template, Art supplies for artifact creation, Label/placard cards, Visitor feedback form

• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Teaching This Topic

Teach box plots by having students first sort small, real-world data sets by hand to see quartiles emerge naturally. Avoid rushing to formulas; instead, use the physical act of grouping and measuring to build the concept of quartiles as natural dividers. Research suggests this kinesthetic approach reduces confusion about median placement and whisker meaning compared to abstract calculations alone.

What to Expect

Successful learning looks like students accurately identifying quartiles, constructing clean plots, and explaining what the box and whiskers show about data spread and center. They should also compare two plots to discuss consistency and typical values with precise terms like median and interquartile range.

Watch Out for These Misconceptions

Common Misconception

During the Pairs Plotting: Student Heights activity, watch for students who assume the box spans the entire data range. Correction: Have pairs measure the box on their number line and compare it to the whiskers, then ask them to recount how many data points fall inside versus outside the box to reinforce that the box covers only the middle 50%.

Common Misconception

During the Small Groups: Sports Data Comparison activity, watch for students who assume the median is always centered in the box. Correction: Ask groups to physically fold their data sets in half to find the median, then slide the halves apart to show how skewness shifts the median within the box.

Common Misconception

During the Individual: Mystery Data Analysis activity, watch for students who dismiss points outside the whiskers as errors. Correction: Provide real data with an unusual value (e.g., a student height of 6 feet in a class where most are under 5 feet) and ask students to calculate the IQR before deciding if the point is an outlier, linking the rule to the data context.

Assessment Ideas

Quick Check

After the Pairs Plotting: Student Heights activity, provide each pair with a new small data set and ask them to calculate the five-number summary and sketch the box plot on a provided number line. Collect these to check quartile accuracy and whisker placement.

Discussion Prompt

After the Small Groups: Sports Data Comparison activity, display two box plots side by side from different sports teams. Ask the class to discuss which team had more consistent scores and how the IQR and range support their answer, calling on students to point to specific features of the plots.

Exit Ticket

After the Whole Class: Poll and Plot activity, give each student a printed box plot with no labels. Ask them to write the minimum, median, and IQR on the back, then add one observation about the data spread to assess their interpretation skills.

Peer Assessment

During the Individual: Mystery Data Analysis activity, have students swap their box plots with a partner and write one compliment and one question about the plot’s accuracy, focusing on quartile placement and whisker lengths.

Extensions & Scaffolding

• Challenge: Provide a data set with an outlier and ask students to redraw the box plot after deciding whether to keep or remove it, justifying their choice with evidence.
• Scaffolding: Give students a five-number summary table to plot, so they focus on box construction rather than quartile calculations.
• Deeper exploration: Have students collect their own data (e.g., number of siblings) and create two box plots comparing different classes or grade levels, writing a paragraph about what the comparisons reveal.

Key Vocabulary

Five-Number Summary	A set of five key values that describe a data distribution: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
Median	The middle value in a data set when the data is ordered from least to greatest. It divides the data into two equal halves.
Quartiles	Values that divide a data set into four equal parts. Q1 is the median of the lower half, and Q3 is the median of the upper half.
Interquartile Range (IQR)	The difference between the third quartile (Q3) and the first quartile (Q1), representing the spread of the middle 50% of the data.