Average
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Study MaterialAverage Cheat Sheet
Average is one of the most important and scoring topics in Quantitative Aptitude and is frequently asked in SSC, Banking, Railway, UPSC, Defence, Insurance, CAT, and other competitive examinations.
This cheat sheet helps candidates understand average formulas, weighted averages, average speed, arithmetic progression averages, age-based problems, replacement concepts, deviation methods, and shortcut techniques for solving questions quickly and accurately in exams.
About This Cheat Sheet
Complete guide to Average for competitive exams:
Basic Average Formula
- Average = Sum ÷ Number
- Finding Missing Values
- Total Sum Calculation
- Basic Problem Solving
Weighted Average
- Weighted Mean Formula
- Ratio Based Average
- Combined Average
- Application Problems
Average Speed
- Equal Distance Formula
- 2ab/(a+b) Shortcut
- Different Speeds
- Journey Problems
Natural Number Averages
Average of first n natural numbers, squares, cubes, and consecutive numbers.
Arithmetic Progression
- Average of AP Series
- Middle Term Method
- Consecutive Number Average
- Common Difference Concepts
Age Based Problems
- Present Age Average
- Past & Future Ages
- Family Average Problems
- Group Age Questions
Replacement Problems
- Person Joins Group
- Person Leaves Group
- Replacement Average
- New Average Calculation
Shortcut Tricks
Deviation method, fast average calculation, and exam-oriented shortcut techniques.
Topics Covered
| Topic | Description |
|---|---|
| Average Formula | Average = Sum of observations ÷ Number of observations |
| Weighted Average | Average based on weights or ratios |
| Combined Average | Average of two or more groups |
| Average Speed | Speed average for journeys and distances |
| Natural Numbers | Average of first n natural numbers |
| Squares & Cubes | Average of square and cube series |
| Consecutive Numbers | Average of consecutive even/odd numbers |
| Arithmetic Progression | Average of AP terms |
| Age Problems | Questions based on age averages |
| Replacement Problems | New average after replacing a member |
| Joining & Leaving | Average changes when a member joins or leaves |
| Deviation Method | Shortcut method for average calculation |
| Shortcut Tricks | Fast solving methods for exams |
Why This Cheat Sheet is Important
Understand Average Concepts
↓
Improve Calculation Speed
↓
Apply Shortcut Techniques
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Solve Word Problems Faster
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Score Better in Exams
Competitive Exams Covered
- SSC CGL
- SSC CHSL
- Bank PO & Clerk
- Railway Exams
- UPSC CSAT
- Defence Exams
- Insurance Exams
- State Government Exams
- MBA Entrance Exams
Quick Example
Example:
Find the average of 12, 18, 20, 25, and 30.
Sum of numbers:
12 + 18 + 20 + 25 + 30 = 105
Number of observations = 5
Average = 105 ÷ 5
Average = 21
Answer = 21
Final Takeaway
This Average Cheat Sheet provides complete revision material for all major concepts frequently asked in competitive examinations. Regular practice of weighted averages, speed averages, AP-based averages, age problems, and shortcut techniques can significantly improve speed, accuracy, and logical problem-solving ability.
It is highly useful for quick revision before exams and helps candidates strengthen the foundation of Quantitative Aptitude.
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