Comparing Data Sets – Average & Range | OCR

Comparing two datasets needs TWO measures (average + range) and TWO sentences — and the direction depends on context. OCR GCSE Foundation, Year 10 Unit 7 Lesson 10.

The most common mark loss isn’t arithmetic — it’s writing “A is higher” when the question is about times (where higher = slower). This lesson drills both the two-measure habit and the context-reading skill.

What’s included:

• I Do (goals per match — higher = better) and We Do (sprint times — lower = faster) — deliberately context-flipped
• Two independent practice tasks spanning the diagnostic spectrum: Task A “wins both” (Armand beats Renaud on both average AND consistency), Task B “mixed” (Riley sleeps more, Sam is more consistent — pupils must hold the tension and use however)
• Three-misconception Spot the Mistake — one-sentence thinking (forgets the range), context-direction error (“A is higher” for times), and the inverted range-consistency relationship (“larger range = more consistent”)
• Going Deeper: construct two lists with matching medians but contrasting ranges, plus the conceptual why range alone isn’t enough
• Exit Ticket with even n = 8 — median = average of 4th and 5th values, catches pupils still using the odd-n convention

Teacher key (3 pages):

• Full answers across all 5 comparisons
• Diagnostic patterns: pupils who only get “wins both” cases right have defaulted to bigger number = better
• Marking shortcuts: numbers without context-verb = ½ marks; context-verb without numbers = ½ marks; both needed for full credit
• Marking summary table with the “direction flip” cases called out explicitly

smartle. @Smartle-Maths