Measures of Variability: Range and IQR

Measures of variability come alive when students manipulate real data rather than just compute numbers. Active learning lets students physically arrange values, compare spreads, and feel the impact of outliers on their measures. These hands-on tasks build intuition about range and IQR that static worksheets cannot match.

• 7th Grade
• Mathematics
• 3 activities
• 20 min–30 min

Learning Objectives

1. Calculate the range and interquartile range (IQR) for given numerical data sets.
2. Analyze the effect of outliers on the range and IQR of a data set.
3. Compare the variability of two data sets using their range and IQR.
4. Construct a data set with a specified range and IQR.
5. Explain how range and IQR describe the spread of data.

Stations Rotation

⏱ 30 min·Small Groups

Construct a Data Set: Variability Challenge

Give groups a constraint card specifying a required range and IQR (e.g., 'Create a 6-value data set with range = 20 and IQR = 8'). Groups work to build a valid data set and then compare solutions with other groups, discussing how multiple data sets can satisfy the same constraints.

Prepare & details

Explain how measures of variability describe the spread of a data set.

Facilitation Tip: During Construct a Data Set: Variability Challenge, remind students that the same range can hide very different inner spreads by asking them to build two sets with identical min/max but contrasting quartiles.

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: Outlier Impact

Students calculate range and IQR for a base data set, then add an extreme outlier. Individually, they predict and calculate how each measure changes. Partners compare and explain the difference in sensitivity before sharing findings with the class.

Prepare & details

Analyze the impact of outliers on the range and interquartile range.

Facilitation Tip: During Think-Pair-Share: Outlier Impact, circulate and listen for students who notice that adding one extreme value changes the range but barely moves the IQR.

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

Stations Rotation

⏱ 25 min·Small Groups

Data Card Sort: Ranking Consistency

Provide four data sets displayed as ordered lists. Groups rank them from most to least consistent using both range and IQR. When rankings differ across the two measures, groups discuss which ranking better reflects true variability and why.

Prepare & details

Construct a data set with a specific range or interquartile range.

Facilitation Tip: During Data Card Sort: Ranking Consistency, watch for groups that organize by visual spread before calculating, which shows emerging understanding of what variability really means.

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

Teaching This Topic

Teachers often start with range because it’s straightforward, but then pivot to IQR to show how ignoring extremes reveals typical variability. Research suggests students grasp variability better when they physically handle data cards and see quartiles as boundaries they can move. Avoid rushing to formulas; let students estimate quartiles from ordered lists first.

What to Expect

Successful learning looks like students explaining why a high range might hide a narrow middle spread, choosing the better measure for a given context, and justifying their choice with calculations. By the end, they should articulate which measure ignores extremes and which captures overall spread.

Watch Out for These Misconceptions

Common Misconception

During Construct a Data Set: Variability Challenge, watch for students who assume a higher range always means more variability without considering the inner spread.

What to Teach Instead

Prompt students to build two data sets with the same range but different quartiles, then calculate both measures to see that IQR reveals the true inner spread.

Common Misconception

During Data Card Sort: Ranking Consistency, watch for students who treat range and IQR as interchangeable.

What to Teach Instead

Have groups explain why the data set with the smallest IQR feels more consistent even if its range is larger, using their sorted cards as evidence.

Assessment Ideas

Quick Check

After Construct a Data Set: Variability Challenge, provide two small data sets and ask students to calculate range and IQR for each, then write one sentence comparing the spreads.

Exit Ticket

After Think-Pair-Share: Outlier Impact, present a data set with an outlier. Ask students to calculate the range and IQR, and explain in three sentences how the outlier affected each measure.

Discussion Prompt

During Data Card Sort: Ranking Consistency, pose the question: 'Which measure would you use to describe typical student screen time, and why?' Circulate to listen for students citing IQR because it ignores extreme outliers.

Extensions & Scaffolding

• Challenge: Ask students to create two data sets with the same mean and range but different IQRs, then explain which set has more consistent performance.
• Scaffolding: Provide pre-sorted strips of data with quartiles marked so students can focus on calculating IQR without ordering the values.
• Deeper exploration: Have students collect their own data (e.g., heights in class), calculate both measures, and present which best describes the group’s typical height.

Key Vocabulary

Range	The difference between the largest and smallest values in a data set. It gives a quick idea of the spread but can be affected by extreme values.
Interquartile Range (IQR)	The difference between the third quartile (Q3) and the first quartile (Q1) of a data set. It represents the spread of the middle 50% of the data and is less affected by outliers.
Outlier	A data point that is significantly different from other data points in a set. Outliers can greatly influence the range.
Quartiles	Values that divide a data set into four equal parts. Q1 is the median of the lower half, Q2 is the median of the entire set, and Q3 is the median of the upper half.