Estimating the Mean — GCSE Foundation

Complete 4-page Year 10 Foundation lesson on estimating the mean from grouped frequency tables — midpoints, ∑f×m ÷ ∑f, and why the answer is always ≈.

Inside the pack

• Retrieval Do Now with separate Retrieval section — arithmetic warm-up then four targeted items seeding today’s procedure (midpoints, mean, multiplication)
• Rule box: midpoint formula + ∑f×m ÷ ∑f step by step
• I Do → We Do examples (minutes late to lesson; homework hours per week)
• Spot the Mistake — three OCR exam traps: upper bound as midpoint, dividing by row count, writing = instead of ≈
• Independent Practice — two grouped tables (TV hours; texts sent per day)
• Going Deeper Q1: find a missing frequency given an estimated mean of 50 (algebraic inverse reasoning)
• Going Deeper Q2: explain in 2–3 sentences why the answer is always ≈
• Exit Ticket + metacognitive reflection

Why “estimate” matters on OCR papers: pupils who write = instead of ≈ lose the conceptual mark. This lesson makes the distinction explicit three times — including one example where the arithmetic gives a clean integer, specifically to challenge the “looks exact, must be exact” instinct.

Curriculum: OCR GCSE Maths J560 Foundation — Unit 7 Averages, Lesson 8. Also suitable for AQA and Edexcel Foundation statistics.

Format: Two PDFs — student worksheet (4 pages) and teacher answer key (6 pages, with worked solutions, teaching notes, and a marking summary table).