Average – General Aptitude for GATE, PSU, ESE, AE/JE

Average is one of the most important and frequently asked topics in General Aptitude. It is simple yet powerful and helps solve questions related to marks, age, speed, and data interpretation.

What is Average?

The average of a set of numbers is defined as:

Average = (Sum of all observations) / (Number of observations)

Basic Formula

If there are n numbers: x₁, x₂, x₃, ... xₙ

Average = (x₁ + x₂ + x₃ + ... + xₙ) / n

Important Concepts

1. Sum = Average × Number

This is the most important shortcut:

Sum = Average × Number of observations

2. Change in Average

If a number is replaced:

New Sum = Old Sum + (New Value – Old Value)

3. Combined Average

If two groups are given:

Combined Average = (Sum₁ + Sum₂) / (n₁ + n₂)

Solved Examples

Example 1

Find the average of 10, 20, 30, 40, 50

Sum = 10 + 20 + 30 + 40 + 50 = 150
Number of terms = 5
Average = 150 / 5 = 30

Example 2

The average of 5 numbers is 20. Find the total sum.

Sum = Average × Number = 20 × 5 = 100

Example 3

The average of 4 numbers is 25. One number (20) is replaced by 40. Find new average.

Old sum = 25 × 4 = 100
New sum = 100 + (40 – 20) = 120
New average = 120 / 4 = 30

Example 4 (GATE Level)

Average marks of a class of 20 students is 60. If 5 new students join with average 50, find new average.

Old sum = 20 × 60 = 1200
New sum = 1200 + (5 × 50) = 1450
Total students = 25
New average = 1450 / 25 = 58

Shortcut Tricks

• Use Sum = Average × Number directly to save time
• For replacement questions, avoid recalculating full sum
• In combined average, always find individual sums first
• Practice mental calculations to improve speed

Practice Questions

Q1. The average of 8 numbers is 15. What is the sum?

Answer: 8 × 15 = 120

Q2. Average of 10 numbers is 25. If one number is removed, average becomes 24. Find removed number.

Old sum = 10 × 25 = 250
New sum = 9 × 24 = 216
Removed number = 250 – 216 = 34

Exam Tips

• Average questions are easy scoring – do not skip
• Focus on shortcut formulas
• Practice previous year questions
• Maintain calculation speed

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