Mathematics · Year 10

Active learning ideas

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.

• National Curriculum Attainment Targets
• GCSE: Mathematics - Statistics

• 30–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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.

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.

What to look for

Provide students with two small datasets, one with an obvious outlier and one without. Ask them to calculate both the range and IQR for each dataset. Then, ask: 'Which measure of spread, range or IQR, better represents the typical spread of data for the dataset with the outlier? Explain why.'

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 02

• 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.

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.

What to look for

Give students a frequency table showing the number of hours Year 10 students spent on homework per week. Ask them to calculate the IQR. On the back, have them write one sentence explaining why the IQR is a useful measure for this type of data.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 03

• 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.

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.

What to look for

Present a scenario: 'A teacher compares the test scores of two classes. Class A has a range of 60 marks and an IQR of 20 marks. Class B has a range of 30 marks and an IQR of 25 marks.' Ask students: 'What can you infer about the distribution of scores in each class? Which class had more consistent performance in the middle 50% of scores, and why?'

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 04

• 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.

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

What to look for

Provide students with two small datasets, one with an obvious outlier and one without. Ask them to calculate both the range and IQR for each dataset. Then, ask: 'Which measure of spread, range or IQR, better represents the typical spread of data for the dataset with the outlier? Explain why.'

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

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

  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.

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

  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.

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Methods used in this brief

• Collaborative Problem-Solving