Measures of Spread: Range and Interquartile Range

Active learning helps students grasp measures of spread because variability is best understood through hands-on data work. When students collect, order, and manipulate real data sets, they move beyond abstract formulas to see how range and IQR reveal different stories about consistency and outliers. This kinesthetic approach makes the shift from computing numbers to interpreting meaning immediate and memorable.

• 3rd Class
• Mathematical Explorers: Building Number and Space
• 4 activities
• 25 min–45 min

Learning Objectives

1. Calculate the range for various data sets, including student heights and class test scores.
2. Determine the interquartile range (IQR) for ordered data sets, identifying Q1 and Q3.
3. Compare the spread of two different data sets using both range and IQR.
4. Explain how a larger range or IQR indicates greater variability in a data set.
5. Design a simple survey question that could be answered by analyzing the range or IQR of the collected data.

Inquiry Circle

⏱ 45 min·Small Groups

Survey Stations: Spread Calculations

Set up stations for data collection on arm spans, jump distances, or favorite numbers. Small groups order data at each station, compute range and IQR, then plot on mini box plots. Rotate stations and compare spreads across topics.

Prepare & details

Evaluate the most significant finding from a given data set, considering both central tendency and spread.

Facilitation Tip: During Survey Stations, circulate to prompt groups to explain why they chose range or IQR for their data, not just compute the numbers.

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

Inquiry Circle

⏱ 30 min·Pairs

Data Duel Pairs: Team Scores

Provide pairs with two sports team score data sets. Calculate range and IQR for each, discuss which shows more consistency. Pairs create posters explaining findings with visuals.

Prepare & details

Hypothesize why certain trends appear in the data, relating to its spread.

Facilitation Tip: In Data Duel Pairs, ask teams to swap results and check each other’s Q1, Q3, and IQR calculations before moving to comparisons.

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

Inquiry Circle

⏱ 40 min·Whole Class

Trend Hunt: Whole Class Analysis

Conduct a class survey on travel times to school. Order data together, compute range and IQR as a group. Hypothesize trend causes and vote on key insights.

Prepare & details

Design a question that can be answered by analyzing the range or IQR of a data set.

Facilitation Tip: For Trend Hunt, assign roles so every student contributes to the box plot construction, ensuring no one is left observing.

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

Inquiry Circle

⏱ 25 min·Individual

Outlier Challenge: Individual Modifications

Give students a data set with outliers. Individually recalculate range and IQR after adjustments, note changes. Share in pairs why spread measures differ.

Prepare & details

Evaluate the most significant finding from a given data set, considering both central tendency and spread.

Facilitation Tip: During Outlier Challenge, provide rulers and colored pencils to help students visualize how adding an outlier changes the range but barely shifts the IQR.

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

Teaching This Topic

Teach measures of spread by alternating between quick mini-lessons and sustained data work. Start with a concrete example, such as student heights, to show why range alone can mislead. Model the step-by-step process for finding IQR, then immediately give students their own small data set to practice. Reinforce the concept of middle half by physically cutting ordered data into halves and quarters before calculating. Avoid rushing to abstract definitions; let students discover why IQR is robust against outliers through guided surprises, like adding a very large or small value and observing the effect.

What to Expect

Students will confidently explain when to use range versus IQR, justify their choices with evidence, and recognize how outliers distort range but not IQR. They will also articulate why the IQR focuses on the middle half of data, not the extremes. Look for clear labeling of Q1, Q3, and IQR in written or visual work, and discussions that reference real data examples.

Watch Out for These Misconceptions

Common Misconception

During Survey Stations, watch for students treating range as a general measure of spread across all data points.

What to Teach Instead

Have students plot their data on a number line and circle the highest and lowest values. Ask them to explain why the gap between these extremes doesn’t tell the full story of variability.

Common Misconception

During Data Duel Pairs, watch for students confusing IQR with the median or mean.

What to Teach Instead

Ask each pair to present their Q1, median, and Q3 side by side on a whiteboard so the class can visually separate measures of center from measures of spread.

Common Misconception

During Trend Hunt, watch for students assuming data sets with identical ranges must have the same variability.

What to Teach Instead

Provide two ordered data sets with the same range but different distributions. Ask groups to modify one set to match the other’s IQR and explain how the values are spread differently.

Assessment Ideas

Quick Check

After Survey Stations, ask each group to show their range and IQR calculations on a mini-whiteboard. Circulate to check for correct identification of Q1 and Q3 and proper subtraction.

Discussion Prompt

During Data Duel Pairs, ask teams to present their findings on which class had more consistent scores. Listen for references to range or IQR, and prompt them to explain why one measure was more helpful.

Exit Ticket

After Outlier Challenge, give students a short list of numbers and ask them to calculate the range and IQR. Then have them write one sentence explaining what the IQR tells them about the typical spread of the data.

Extensions & Scaffolding

• Challenge students to create two data sets with the same range but different IQRs, then justify which measure better describes the spread in a short written reflection.
• For students who struggle, provide pre-sorted data strips and labeled quartile guides to scaffold the process of identifying Q1 and Q3.
• Deeper exploration: Ask students to research real-world contexts where IQR is preferred over range (e.g., income data) and present their findings to the class.

Key Vocabulary

Range	The difference between the highest and lowest values in a data set. It gives a quick idea of the total spread of the data.
Interquartile Range (IQR)	The difference between the third quartile (Q3) and the first quartile (Q1) of an ordered data set. It represents the spread of the middle 50% of the data.
Quartiles	Values that divide an ordered data set into four equal parts. Q1 is the median of the lower half, Q2 is the overall median, and Q3 is the median of the upper half.
Variability	A measure of how spread out or clustered the data points are in a data set. Range and IQR are measures of variability.