Measures of Spread (Range, IQR)

Active learning works for measures of spread because students need to physically experience how data clusters or spreads to truly grasp the meaning behind range and IQR. When students step into a human box plot or debate sports statistics, they move from abstract numbers to concrete understanding of how spread reveals consistency or variability in real data.

• Year 9
• Mathematics
• 3 activities
• 35 min–50 min

Learning Objectives

1. Calculate the range and interquartile range (IQR) for a given data set.
2. Compare and contrast the range and IQR as measures of data spread, identifying their strengths and weaknesses.
3. Analyze how the addition of an outlier impacts the range and IQR of a data set.
4. Explain the meaning of the IQR in terms of data consistency and distribution.

Simulation Game

⏱ 40 min·Whole Class

Simulation Game: The Human Box Plot

The class collects data (e.g., number of siblings). Students line up in order. Five students are chosen to represent the 'five-point summary' and hold signs. The rest of the class uses a long rope to create the 'box' and 'whiskers' around them. This makes the quartiles physically visible.

Prepare & details

What does the spread of the interquartile range tell us about the consistency of a data set?

Facilitation Tip: During the Human Box Plot, stand at the quartile lines yourself to model the proportional spacing of data points.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Inquiry Circle

⏱ 50 min·Small Groups

Inquiry Circle: The Great AFL/NRL Stats Duel

Groups are given the scores from two different sports teams over a season. They must calculate the five-point summary, draw two box plots on the same scale, and then write a 'sports report' comparing the two teams' consistency and performance. This applies stats to a popular Australian context.

Prepare & details

Compare the range and IQR as measures of spread, highlighting their advantages and disadvantages.

Facilitation Tip: For the Great AFL/NRL Stats Duel, assign clear roles like 'data collector', 'calculator', and 'presenter' to keep groups focused.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Gallery Walk

⏱ 35 min·Pairs

Gallery Walk: Box Plot Detectives

Display several box plots representing different 'mystery' datasets (e.g., daily temperatures in Darwin vs. Hobart). Students move in pairs to match the 'story' to the plot based on the median and the spread (IQR). This builds data interpretation skills.

Prepare & details

Predict how adding an outlier affects the range and IQR of a data set.

Facilitation Tip: In the Gallery Walk, place sticky notes next to each box plot asking peers to note one insight about the data spread.

Setup: Wall space or tables arranged around room perimeter

Materials: Large paper/poster boards, Markers, Sticky notes for feedback

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

Teaching This Topic

Teach measures of spread by having students physically arrange themselves in order, which makes the concept of quartiles tangible. Avoid rushing to formulas; instead, build intuition first with small, relatable datasets. Research shows that students who manipulate data physically before calculating retain concepts longer.

What to Expect

Successful learning looks like students accurately calculating range and IQR, explaining what these measures reveal about data consistency, and justifying their conclusions using evidence from box plots. By the end, students should confidently compare datasets and interpret measures of spread in context.

Watch Out for These Misconceptions

Common Misconception

During the Human Box Plot, watch for students assuming a longer box or whisker means more data points. The correction is to have students count the people in each section to see that each quartile contains exactly 25% of the data, regardless of length.

What to Teach Instead

During the Human Box Plot, pause the activity and ask each quartile group to count their members. Then, have students physically spread out within their section to show how the same number of people can occupy more space when data is spread out.

Common Misconception

During the Great AFL/NRL Stats Duel, watch for students confusing the median with the mean. The correction is to use the small dataset provided to physically find the middle person before calculating anything.

What to Teach Instead

During the Great AFL/NRL Stats Duel, give students a small dataset printed on cards. Have them line up in order and physically remove the highest and lowest values until one remains to find the median, reinforcing that it’s about position, not calculation.

Assessment Ideas

Quick Check

After the Human Box Plot, provide two small datasets on the board and ask students to calculate the range and IQR for both. Then, ask them to explain which measure of spread is more affected by an outlier and why.

Discussion Prompt

During the Great AFL/NRL Stats Duel, pose the question: 'Class A has a range of 40 and an IQR of 15. Class B has a range of 30 and an IQR of 20. Which class is more consistent, and how do you know?' Have groups discuss and present their reasoning using their plotted data.

Exit Ticket

After the Gallery Walk, give students a dataset printed on their exit ticket. Ask them to calculate the range and IQR, then write one sentence explaining what the IQR reveals about the middle 50% of the data.

Extensions & Scaffolding

• Challenge: Ask students to create a dataset where the range is 30 but the IQR is only 5, explaining their choices.
• Scaffolding: Provide a partially completed five-point summary table for students to fill in before plotting.
• Deeper: Have students research a real-world dataset (like daily temperatures) and compare its box plot to another location’s, explaining why spreads differ.

Key Vocabulary

Range	The difference between the maximum and minimum values in a data set. It provides a simple measure of the total spread of the data.
Interquartile Range (IQR)	The difference between the upper quartile (Q3) and the lower quartile (Q1) of a data set. It represents the spread of the middle 50% of the data.
Quartiles	Values that divide a data set into four equal parts. Q1 is the 25th percentile, Q2 is the median (50th percentile), and Q3 is the 75th percentile.
Outlier	A data point that is significantly different from other observations in the data set. Outliers can heavily influence the range but have less impact on the IQR.