CDS Mathematics · Teaching notes
Averages — CDS Elementary Mathematics
Averages has 47 past-year questions in CDS Elementary Mathematics, in 17 of the twenty-one sittings from 2016 (II) to 2026 (II). Working through the total accounts for 20 of them and combining groups for 19, and only four are HARD: turn each mean into a total, and the arithmetic does the rest. The pages go from totals to weighted averages and end with averages of consecutive numbers.
Every subtopic, worked example, formula and trap in one printable document — answers shown, ready to share.
Subtopic notes
Working Through the Total
20 PYQsAn average hides a total: sum = number of items × mean, and almost every average question is solved on the totals, not the means.
Weighted and Combined Averages
19 PYQsThe average of two groups together is weighted by their sizes, so it always lies between the two group averages, nearer the bigger group.
Averages of Consecutive Numbers
8 PYQsEqually spaced numbers average to their middle term, which is also the average of the first and the last.
Formula & revision sheet
5 formulas · 6 gotchas across all subtopics — the exam-eve cheat-sheet
Formula & revision sheet
5 formulas · 6 gotchas across all subtopics — the exam-eve cheat-sheet
Watch out for (3)
- A shared item is counted twice→ Sum = count × mean
- The new average, or the old one?→ Sum = count × mean
- Keep the signs→ Correcting a wrong entry
Watch out for (2)
- Not the plain average of the averages→ The combined average
- The ratio is inverted→ Ratio of group sizes
Formulas (1)
Watch out for (1)
- Only for equally spaced lists→ The middle term
PYQ weightage by concept
5 concepts · 47 PYQs — where the marks actually sit, so you know what to drill first
PYQ weightage by concept
5 concepts · 47 PYQs — where the marks actually sit, so you know what to drill first
| Concept | PYQs | Share |
|---|---|---|
| Sum = count × mean | 15 | 32% |
| Correcting a wrong entry | 5 | 11% |
| Concept | PYQs | Share |
|---|---|---|
| The combined average | 12 | 26% |
| Ratio of group sizes | 7 | 15% |
Test yourself on Averages
15 past CDS questions from this chapter, timed at 18 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.