Measures of Spread: Range and IQR

Active learning helps students grasp measures of spread because these concepts require hands-on calculation and comparison to make sense. When students manipulate real datasets, they move beyond abstract formulas to see how spread reflects consistency and reliability in practical contexts.

• Secondary 4
• Mathematics
• 3 activities
• 20 min–50 min

Learning Objectives

1. Calculate the range and interquartile range for a given dataset.
2. Compare the spread of two datasets using both range and IQR.
3. Explain how the IQR provides a measure of spread for the middle 50% of data.
4. Evaluate the impact of outliers on the range versus the IQR.
5. Interpret the meaning of range and IQR in the context of a real-world scenario.

Ready-to-Use Activities

Inquiry Circle

⏱ 40 min·Small Groups

Inquiry Circle: The Consistency Challenge

Groups are given the 'scores' of two fictional archers. Both have the same average, but one is very consistent and the other is erratic. Students calculate the standard deviation for both and debate which archer they would hire for a competition.

Prepare & details

Explain what the interquartile range reveals about the consistency of data compared to the overall range.

Facilitation Tip: During the Collaborative Investigation, circulate and ask groups to explain their reasoning for choosing which class performed more consistently.

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

Stations Rotation

⏱ 50 min·Small Groups

Stations Rotation: Measures of Spread

Set up stations with different data types (e.g., house prices, temperatures, heights). At each station, students calculate the range, interquartile range, and standard deviation, discussing which measure best describes that specific set of data.

Prepare & details

Compare the robustness of the range versus the interquartile range to extreme values.

Facilitation Tip: For the Station Rotation, set up a timer at each station to keep groups focused and ensure they rotate efficiently.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Think-Pair-Share

⏱ 20 min·Pairs

Think-Pair-Share: The 'Mean' Trap

Show two datasets with the same mean but vastly different spreads. Students individually write down why the mean alone is misleading, then share their reasoning with a partner to develop a more complete statistical description.

Prepare & details

Assess the spread of two different datasets using both range and IQR to draw conclusions.

Facilitation Tip: In the Think-Pair-Share activity, model how to phrase a clear and concise response before students begin working in pairs.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Teaching This Topic

Teachers often introduce measures of spread by connecting them to real-world contexts students care about, like comparing test scores or product quality. Avoid rushing to formulas—instead, build intuition with concrete examples. Research shows that students retain these concepts better when they first experience variability through physical or visual representations before moving to calculations.

What to Expect

Successful learning looks like students confidently calculating range and IQR, explaining when each measure is appropriate, and recognizing how outliers affect these values. They should also justify their choices when comparing datasets, using precise mathematical language.

Watch Out for These Misconceptions

Common Misconception

During the Collaborative Investigation, watch for students who believe a standard deviation of zero is impossible.

What to Teach Instead

Ask them to create a dataset with identical values (e.g., 4, 4, 4, 4) and calculate its standard deviation to see that zero spread is valid when all data points match.

Common Misconception

During the Station Rotation, watch for confusion between standard deviation and the range.

What to Teach Instead

Have students compare two datasets with identical ranges but different standard deviations to demonstrate that range only considers extremes, while standard deviation accounts for all data points.

Assessment Ideas

Quick Check

After the Station Rotation, provide two small datasets and ask students to calculate the range and IQR for each. Collect their work to check calculations and interpretations of spread.

Discussion Prompt

During the Think-Pair-Share, pose the question about two datasets with different ranges and IQRs. Listen for students who recognize that IQR is more robust to outliers when comparing consistency.

Exit Ticket

After the Collaborative Investigation, give students a dataset with an outlier. Ask them to calculate both range and IQR, then explain in writing which measure better represents typical spread and why.

Extensions & Scaffolding

• Challenge students to create two datasets with the same range but different IQRs, then calculate both measures to compare their spreads.
• For students who struggle, provide partially completed tables where they fill in missing data points to achieve a given range or IQR.
• Deeper exploration: Have students research how measures of spread are used in quality control industries and present their findings to the class.

Key Vocabulary

Range	The difference between the highest and lowest values in a dataset. It provides a simple measure of the total spread of the data.
Interquartile Range (IQR)	The difference between the third quartile (Q3) and the first quartile (Q1) of a dataset. It represents the spread of the middle 50% of the data.
Quartiles	Values that divide a dataset 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 dataset. Outliers can heavily influence the range.