Olympiad topic · P4–P6
Averages
Averages appear in the Hua Xia Cup's P4 and P5 first rounds, qualifying rounds and finals.
Try one
★★ MediumA class sits a maths test in two groups.
Group A has 10 pupils with an average of 66; group B has 8 pupils with an average of 93.
What is the average for the whole class?
- Hint 1: The groups are different sizes, so you can't just average the two averages. Find each group's total first.
- Hint 2: The class total divided by the number in the class gives the class average.
- 1.Group A total: 66 × 10 = 660; group B total: 93 × 8 = 744.
- 2.Class: 10 + 8 = 18 pupils, total 660 + 744 = 1404.
- 3.Average: 1404 ÷ 18 = 78. The marks above the dashed line exactly fill the gap below it.
- ⚠️Common mistake: working out (66 + 93) ÷ 2. The bigger group pulls the class average more.
Answer: 78 marks
Four levels, step by step
- ★EasyFree2 question types · unlimited questionsFind the average or the total.
- ★★MediumFree2 question types · unlimited questionsA missing score, two groups combined.
- ★★★HardFree4 question types · unlimited questionsThe average changing after one more test, a score copied wrong.
- ★★★★Expert (competition level)VIP3 question types · unlimited questionsHighest and lowest left out, or the average changing every time.
Averages: what it is and how to solve it
Average = total ÷ how many; these problems use how the total and the count are linked.
For example: Four tests average 92; the first three were 86, 90 and 97. The fourth? 92 × 4 − (86 + 90 + 97) = 368 − 273 = 95.
The key idea: Find the total first (average × count), then follow how it changes. Or even out: what's above the average exactly fills what's below. The usual method, total ÷ count, is the same thing; each checks the other.
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