Module 1 · Arithmetic
Chapter 4: Averages
Arithmetic
4 topics
What this chapter covers
The 4 topics below make up Averages on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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Notes, worked examples and hint-guided practice for every topic.
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🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
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📝 Chapter test
25 fresh mixed-difficulty questions, timed, with full solutions.
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Formula Reference Sheet
This chapter
Core average relations
| Arithmetic mean | Average = (Sum of observations) / (Number of observations) |
|---|---|
| Sum from average | Sum = Average × Count |
| Average of first n natural numbers | (n + 1) / 2 |
| Average of an arithmetic progression | (First term + Last term) / 2 |
| Deviation (shift) method | Average = Assumed mean + (Sum of deviations) / Count |
Weighted, speed & replacement tools
| Weighted average | (w₁a₁ + w₂a₂ + …) / (w₁ + w₂ + …) |
|---|---|
| Alligation (ratio of weights) | w₁ : w₂ = (A₂ − Avg) : (Avg − A₁) |
| Average speed (whole journey) | Total distance / Total time |
| Equal-distance two speeds | 2xy / (x + y) (harmonic mean) |
| Change in average on replacement | New value = Old value ± (Change in average × Count) |
CAT reference
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