Average
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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.
Topics
- Number System
- H.C.F. & L.C.M.
- Decimal Fractions
- Simplification
- Square Roots & Cube Roots
- Average
- Problems on Numbers
- Problems on Ages
- Surds & Indices
- Percentage
- Operations on Numbers
- Profit & Loss
- Ratio & Proportion
- Partnership
- Chain Rule
- Time & Work
- Pipes & Cistern
- Time & Distance
- Problems on Trains
- Boats & Streams
- Alligation or Mixture
- Simple Interest
- Compound Interest
- Logarithms
- Area
- Volume & Surface Areas
- Mensuration
- Races & Games of Skill
- Calendar
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- Permutations & Combinations
- Probability
- True Discount
- Banker’s Discount
- Heights & Distances
- Odd Man Out & Series
- Algebra
- Divisibility Rules & Remainder Theorem
- Factorials & Power Cycles
- Progressions (A.P., G.P., H.P.)
- Work & Wages
- Set Theory / Venn Diagrams
- Geometry (Lines, Angles, Triangles, Polygons)
- Coordinate Geometry
- Data Interpretation
- Trigonometry
- Statistics (Mean, Median, Mode)
- Arithmetic Operations
- Quadratic Equations
Other Subjects
- Prestressed Concrete
- Fluid Mechanics
- Geotechnical Engineering
- Ground Improvement Techniques
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