Measures of Spread: Range and Interquartile Range

Active learning helps students grasp measures of spread because moving data points and calculating values by hand builds intuitive understanding. Physical sorting and team-based tasks make abstract quartiles and ranges concrete, reducing confusion between range and IQR.

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

Learning Objectives

1. Calculate the range and interquartile range for a given set of raw data.
2. Calculate the range and interquartile range from data presented in frequency tables.
3. Compare the range and interquartile range of two different datasets, justifying the choice of measure for skewed data.
4. Explain how extreme values affect the range and interquartile range, using specific examples.
5. Analyze the robustness of the interquartile range compared to the range when dealing with datasets containing outliers.

Collaborative Problem-Solving

⏱ 35 min·Small Groups

Card Sort: Dataset Ordering

Provide printed cards with data values for two datasets, one with an outlier. In small groups, students sort cards by size, identify min/max for range, then mark Q1/Q3 for IQR. Groups compare results and discuss outlier impact on a shared poster.

Prepare & details

Explain why the interquartile range is a robust measure of spread for skewed data.

Facilitation Tip: During Card Sort: Dataset Ordering, circulate and ask groups to justify their placement of extreme values to reveal understanding of range versus IQR.

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·Small Groups

Frequency Table Relay: Team Calculation

Divide class into teams. Each member calculates range or a quartile from a frequency table section, passes to next for IQR. First team with correct box plot wins. Review errors as whole class.

Prepare & details

Differentiate between range and interquartile range in terms of data representation.

Facilitation Tip: During Frequency Table Relay: Team Calculation, require each team member to explain one step aloud to ensure collective understanding.

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

⏱ 30 min·Pairs

Outlier Investigation: Pairs Edit

Pairs receive raw data sets, calculate range/IQR, then add/remove outliers and recalculate. They sketch box plots before/after and note changes in a table. Share findings in plenary.

Prepare & details

Analyze how extreme values impact the range versus the interquartile range.

Facilitation Tip: During Outlier Investigation: Pairs Edit, provide colored markers so students can highlight quartiles and outliers, making boundaries visible.

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·Whole Class

Class Survey: Real Data Analysis

Collect class data on a topic like travel times. Whole class tallies into frequency table. Subgroups compute range/IQR, plot box plots, and present interpretations comparing to national data.

Prepare & details

Explain why the interquartile range is a robust measure of spread for skewed data.

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

Teach measures of spread by having students physically manipulate data. Start with small datasets to build confidence, then transition to frequency tables to address common calculation errors. Emphasize visual tools like box plots to anchor abstract quartile positions, as research shows tactile and visual approaches reduce misconceptions about spread.

What to Expect

Successful learning looks like students confidently distinguishing when to use range versus IQR. They should explain why IQR resists outliers and calculate both measures accurately from raw data and frequency tables.

Watch Out for These Misconceptions

Common Misconception

During Card Sort: Dataset Ordering, watch for students who assume range is always the best measure when an extreme value is present.

What to Teach Instead

Ask students to recalculate both range and IQR after moving the extreme value to different positions, then discuss which measure stays stable. This direct comparison helps them see IQR’s reliability.

Common Misconception

During Outlier Investigation: Pairs Edit, watch for students who include outliers in their IQR calculations.

What to Teach Instead

Have pairs use colored cards to mark Q1 and Q3 on their box plot, then physically cover the outliers to show they fall outside the IQR. Peer verification reinforces the quartile boundaries.

Common Misconception

During Frequency Table Relay: Team Calculation, watch for students who apply raw-data methods to frequency tables.

What to Teach Instead

In the relay, pause after the first team presents and ask others to explain why cumulative frequency guides quartile positions. This step-by-step discussion corrects table-specific errors.

Assessment Ideas

Quick Check

After Card Sort: Dataset Ordering, provide a follow-up task where students calculate range and IQR for two datasets—one with an outlier, one without—and justify which measure better represents the spread.

Exit Ticket

After Frequency Table Relay: Team Calculation, give students a frequency table on paper to calculate IQR independently. Collect responses to check for correct quartile identification and reasoning.

Discussion Prompt

After Outlier Investigation: Pairs Edit, present the scenario of two classes with different ranges and IQRs. Have students discuss in pairs what these numbers reveal about score consistency before sharing with the class.

Extensions & Scaffolding

• Challenge: Provide a dataset with multiple outliers and ask students to recalculate range and IQR after removing each outlier, then compare results.
• Scaffolding: Give students a partially completed frequency table with cumulative frequencies pre-filled to focus on quartile calculation.
• Deeper: Have students research real-world datasets (e.g., sports scores, exam results) and present their analysis, including why IQR is preferred over range in their chosen context.

Key Vocabulary

Range	The difference between the maximum and minimum values in a dataset. It provides a simple measure of spread but is sensitive to extreme values.
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 and is less affected by outliers.
Lower Quartile (Q1)	The value below which 25% of the data falls. It is the median of the lower half of the dataset.
Upper Quartile (Q3)	The value below which 75% of the data falls. It is the median of the upper half of the dataset.
Outlier	A data point that is significantly different from other observations in the dataset. Outliers can heavily influence the range.