Mathematics · Year 9

Active learning ideas

Measures of Spread: Range and Interquartile Range

Active learning helps students grasp measures of spread because these concepts rely on spatial reasoning and repeated calculation. Students need to physically arrange data, compare spreads visually, and test how changes affect results to truly understand range and IQR. Hands-on tasks make abstract ideas concrete and reveal relationships between data points that static worksheets cannot.

• National Curriculum Attainment Targets
• KS3: Mathematics - Statistics

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Gallery Walk
• 25 min · Pairs

Pair Sort: Dataset Comparison

Provide pairs with printed data sets on heights or test scores. Students order data, calculate range and IQR step-by-step, then compare spread. Pairs swap sets with neighbours to verify calculations and discuss differences.

What does the range or interquartile range tell us about the consistency of a data set?

Facilitation Tip

During Pair Sort, have students verbally justify their groupings using both range and IQR calculations to reinforce reasoning.

What to look for

Provide students with two small data sets, one with an obvious outlier. Ask them to calculate the range and IQR for both sets. Then, pose the question: 'Which measure, range or IQR, better represents the typical spread of data in each set and why?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Gallery Walk
• 35 min · Small Groups

Small Group: Outlier Investigation

Distribute cards with data sets to small groups. Groups add or remove an outlier, recalculate range and IQR, and record changes on mini-whiteboards. Share findings in a class gallery walk.

Compare the advantages and disadvantages of using the range versus the interquartile range.

Facilitation Tip

In Outlier Investigation, ask groups to plot their data before and after adding outliers to observe visual changes in spread.

What to look for

Present a scenario: 'A teacher is comparing the test scores of two classes. Class A has scores ranging from 45 to 95, with an IQR of 15. Class B has scores ranging from 65 to 85, with an IQR of 20.' Facilitate a discussion using prompts like: 'What do these measures tell you about the consistency of scores in each class? Which class has more consistent scores overall? Why might the range be misleading here?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 03

• Gallery Walk
• 30 min · Whole Class

Whole Class: Measure Debate

Project two data sets with outliers. Class votes on best spread measure, calculates both range and IQR together, then debates pros and cons using evidence from screenshared workings.

Predict how an outlier might affect the range but not the interquartile range.

Facilitation Tip

For Measure Debate, provide sentence stems on the board to scaffold students’ arguments about which measure is more reliable.

What to look for

Give each student a data set. Ask them to calculate the range and IQR. On the back, have them write one sentence explaining what the IQR of their data set signifies and one sentence about how an outlier would affect the range but not the IQR.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 04

• Gallery Walk
• 20 min · Individual

Individual: Real Data Challenge

Students collect personal data like step counts from fitness trackers. Individually order data, compute range and IQR, then annotate how outliers from one day affect results in journals.

What does the range or interquartile range tell us about the consistency of a data set?

What to look for

Provide students with two small data sets, one with an obvious outlier. Ask them to calculate the range and IQR for both sets. Then, pose the question: 'Which measure, range or IQR, better represents the typical spread of data in each set and why?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Teach this topic through iterative practice, starting with small, clean data sets to build confidence, then introducing outliers to challenge assumptions. Always connect calculations back to the meaning of the numbers, asking students to interpret what a range of 20 or an IQR of 10 tells them about the data. Research shows that repeated, varied practice with immediate feedback corrects misconceptions faster than abstract explanations alone.

Successful learning looks like students confidently calculating range and IQR, explaining when each measure is appropriate, and recognizing how outliers influence spread. They should articulate why IQR is robust against extremes and justify their choice of measure for different data sets. Clear, evidence-based discussions show deep understanding.

---

Watch Out for These Misconceptions

• During Pair Sort, watch for students assuming the range is always the best measure of spread.

  After students calculate both range and IQR for each pair of data sets, ask them to present which measure they trust more and why. Have peers challenge their reasoning using the outlier’s impact as evidence.

• During Outlier Investigation, watch for students believing the IQR includes all data points.

  During the activity, have students physically mark Q1 and Q3 on number lines and count the data points between them. Ask them to compare this to the total number of points to reinforce that IQR covers only the middle 50%.

• During Measure Debate, watch for students confusing Q1 and Q3 with the median.

  Have pairs plot their data on box plots and label Q1, Q2 (median), and Q3 together. Circulate and ask targeted questions like, 'How does Q2 split the data? Where do Q1 and Q3 sit relative to Q2?'

---

Methods used in this brief

• Gallery Walk