Quantitative Aptitude – Averages
Compute average, total, or term value quickly using formulas and shortcuts.
1. Definition & Formula
Average (Mean) of n terms = \( \frac{\text{Sum of terms}}{n} \).
Use this to find any one of the three elements if the other two are known.
2. Solving Related Problems
- When average changes after adding/removing terms: adjust total using \( \text{New Sum} = \text{New Avg} \times \text{New Count} \).
- For combined groups: use weighted average: \( \frac{n_1 a_1 + n_2 a_2}{n_1 + n_2} \).
3. Quick Tips
- Always form sum = average × count early.
- Use “difference method” when average shifts to avoid full sum.
- In MCQs, estimate and use elimination if exact values are messy.
4. Common Mistakes
- Forgetting to multiply average by number of elements.
- Applying weighted average incorrectly—watch group sizes.
5. Revision Checklist
- Memorize mean formula.
- Practice change-in-average problems.
- Use elimination and estimation to speed up MCQs.
Summary: Always link average and sum, use change patterns smartly, and estimate in MCQs to improve speed and accuracy.