Combining & Changing Means | OCR GCSE

Combining and changing means using one bridge identity: total = count × mean (used both ways). OCR GCSE Foundation, Year 10 Unit 7 Lesson 2. The cardinal error — averaging the means when groups are different sizes — is tackled head-on in three forms.

A direct prep for the exam’s classic “the mean of n values is m; one more is added…” question type. Every problem runs on the same identity, with the count as the variable pupils must track.

What’s included:

• Combining two groups — a worked example (20 pupils @ mean 15 with 30 @ mean 25 → 21, not 20) plus a reverse problem: find a missing group’s mean from the combined total
• Changing the mean — worked examples for both adding and removing a value, each on a clear count / mean / total ledger
• Spot the Mistake — three common misconceptions: averaging the means, treating the old mean as a single value when adding, and forgetting the count changes when you remove a value
• Four practice questions — two on combining (one forwards, one reversing to a missing group), two on changing a mean (one finds the added value, one finds the new mean)
• Going Deeper — a prediction task (an extreme 10-vs-90 size mismatch shows why the combined mean sits near the bigger group) and a work-backwards problem solvable by algebra or by reasoning
• Exit Ticket — a realistic test-average scenario that previews why a single extreme value moves a mean so much

Teacher answer key (4 pages):

• Full totals-ledger working for every question
• A suggested lesson timing guide (~55 min)
• Diagnostic notes linking each wrong answer to its underlying misconception
• Built-in sense-checks: a combined mean always lands between the two group means; removing a high value always lowers the mean
• A marking summary table for fast, consistent marking

EEF-structured, classroom-tested, OCR-aligned.

smartle. @Smartle-Maths