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Averages, spread and comparing distributions

Averages problems

Q: What are the common mistakes in Averages problems?

Flipped the ratio Averaged the two means directly Assumed range shifts with the data

25 self-marking GCSE and IGCSE practice questions on Averages problems, written specifically for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Core and Extended tier. Instant marking with full worked solutions on every question.

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Sample Averages problems questions

A few of the 25 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

Question 13 marksGrade 3
The mean mass of a squad of 19 hockey players is 82 kg. A player of mass 93 kg joins the squad. Work out the mean mass of the squad now.
Show the worked solution
Original total mass = 19 × 82 = 1558 kg. M1
New total = 1558 + 93 = 1651 kg. M2
New mean = 1651 ÷ 20 = 82.55 kg. A1
Question 22 marksGrade 5
Three adults, Amos, Beth and Charlie, are comparing their age in years. Amos is 32. Beth is 48. The mean age of Amos, Beth and Charlie is 50. Work out the age of Charlie.
Show the worked solution
Total age of all three: 50 × 3 = 150. M1
Charlie's age: 150 − 32 − 48 = 70. A1

What are the common mistakes in Averages problems?

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

Flipped the ratio
Applied the ratio the wrong way round (used mean B : mean A = 2 : 5 instead of mean A : mean B = 2 : 5).
Averaged the two means directly
Took the mean of the two given means (18 and 24) instead of working with totals, ignoring that the two groups have different sizes.
Assumed range shifts with the data
Assumed the range must also increase by the same constant as every value, not recognising that the range (largest minus smallest) is unchanged when the same amount is added to every value.

Quick answers about Averages problems

How many Averages problems practice questions are there?: There are 25 self-marking GCSE and IGCSE Maths questions on Averages problems, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Core and Extended tier. Each one is marked instantly and has a full worked solution.
Do I need an account to practise Averages problems?: No. You can start practising Averages problems straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.