Range and Variation

Overview

In this sixteenth lesson of Mapping Data and Change, students investigate how the range describes the spread of a data set. They calculate and interpret range, compare spread with centre, identify unusual values, and use evidence to describe what data suggests.

Learning intentions

• WALT order data and find the range.
• WALT compare the centre and spread of data sets.
• WALT identify unusual values and explain their effect.
• WALT describe what data suggests using mathematical evidence.

Success criteria

• I can find the smallest and largest values in a data set.
• I can calculate the range by subtracting the smallest value from the largest.
• I can compare data sets using centre and spread.
• I can explain how an unusual value affects the data and support my ideas with numbers.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: applying statistical ideas through relevant, connected mathematical challenges.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: reasoning, interpreting and communicating mathematical thinking.

Lesson structure (45 minutes)

1. 0–5 min · Hook and notice. Open with the hook and learning intention slides and display two data sets showing the number of minutes five students spent travelling to school: Set A: 12, 13, 14, 15, 16; Set B: 5, 10, 14, 18, 23. Ask, “Which group has more variation, and how can you prove it?” Students make a quick individual prediction, then compare ideas with a partner. Record language such as spread, clustered, centre and unusual.

2. 5–13 min · Explicit teaching. Use the range teaching slides to model ordering a data set, identifying the minimum and maximum, and calculating range: maximum − minimum. Work through 12, 13, 14, 15, 16 (range 4) and 5, 10, 14, 18, 23 (range 18). Emphasise that range describes spread, not the typical or central value. Students calculate both examples on mini-whiteboards and explain which set is more spread out.

3. 13–18 min · Guided reasoning. Display three data sets on the comparison discussion slide: A: 7, 8, 8, 9, 8; B: 4, 7, 8, 9, 12; C: 8, 8, 8, 8, 20. Ask students to find each range and discuss: “Which set is most consistent?”, “Which has an unusual value?”, and “Can two sets have the same centre but different spread?” Students share answers using the sentence frame: “Set ___ has a range of ___, so the values are ___.”

4. 18–33 min · Collaborative investigation. Distribute the range and variation investigation worksheet to pairs. Students calculate range for several age-appropriate data sets, compare centre and spread, circle possible unusual values, and answer interpretation questions. Pairs must justify one conclusion with numerical evidence. Circulate and check that students subtract the minimum from the maximum rather than counting intervals; ask, “What does this range tell us about the data?” and “Would your conclusion change if the unusual value were removed?”

5. 33–40 min · Challenge and discussion. Return to the reasoning challenge slides. Present two data sets with the same range but different clustering, such as A: 2, 3, 4, 5, 12 and B: 2, 5, 6, 9, 12. Ask, “Is range alone enough to describe variation?” Students discuss in groups of four and prepare a response using at least two pieces of evidence. Invite several groups to share; clarify that range is useful but does not show how all values are distributed.

6. 40–45 min · Plenary and exit check. Use the plenary and exit-ticket prompt. Students independently answer: “Data set A is 14, 15, 15, 16, 17. Data set B is 10, 14, 15, 16, 22. Find both ranges. Which set has greater variation? Identify one unusual value and explain its effect.” Students hand in their response as they leave.

Resources

• the introduction, teaching, discussion, challenge and plenary slide deck
• the range and variation investigation worksheet
• Mini-whiteboards and pens
• Pencils and rulers
• Prepared data sets for modelling
• Board or digital display
• Calculators for selected learners who need calculation support

Assessment

• Check mini-whiteboard responses for accurate identification of minimum, maximum and range.
• Confer with pairs during the investigation, listening for comparisons that use both centre and spread.
• Use the exit check to identify students who need further support with calculating range or interpreting unusual values.

Differentiation

• Support learners by highlighting the minimum and maximum in worked examples, providing a range formula card, and using the sentence frame “The range is ___ because ___ − ___ = ___.”
• Allow students to order data physically on a number line or use a calculator after identifying the two end values.
• Pair students strategically and read worksheet instructions aloud; provide enlarged data tables and uncluttered layout for learners with visual, literacy or processing needs.
• Extend confident learners by asking them to create two data sets with the same range but different variation, then explain why range alone may not give a complete picture.