Average — Study Notes for IBPS Clerk Prelims
Overview
Average is one of the most straightforward yet frequently tested topics in the Numerical Ability section of IBPS Clerk Prelims. The good news: formulas are simple, and with practice, most questions take under 30 seconds.
The core idea is finding a single value that represents an entire group. IBPS Clerk focuses on averages of numbers, ages, runs scored, marks obtained, and weights. Questions typically involve finding the average, finding a missing value when average is given, or calculating how the average changes when elements are added or removed.
Master the basic formula, learn the shortcut for weighted average, and practice the "new member added/removed" variation — these three skills cover 90% of Clerk-level average questions.
Key Concepts
- Basic Average: Sum of all observations divided by the number of observations. This is your default starting point for every problem.
- Sum = Average × Count: Rearranging the formula lets you find total sum when average and count are known — critical for most exam questions.
- Weighted Average: When groups have different sizes, you cannot simply average the averages. Multiply each group's average by its size, add them, then divide by total count.
- Effect of Adding a New Element: If a new value is added and average increases by k, the new value = Old Average + k × (New Count).
- Effect of Removing an Element: If one value is removed and average changes, the removed value = Old Average − (Change × New Count).
- Average of Consecutive Numbers: For any arithmetic progression, the average equals the middle term (or average of two middle terms if count is even).
- Age-Based Problems: When time passes, everyone's age increases equally. If average age of a group increases by t years, then t years have passed.
Formulas / Key Facts
Average = Sum of Observations ÷ Number of Observations Use this to find average when all values are given.
Sum = Average × Number of Observations Use this to find total when average is known.
Weighted Average = (n₁ × A₁ + n₂ × A₂) ÷ (n₁ + n₂) Use when combining two groups with different averages.
New Average after Adding a Value = (Old Sum + New Value) ÷ (Old Count + 1) Shortcut: If average increases by k, New Value = Old Average + k × New Count.
Average of First n Natural Numbers = (n + 1) ÷ 2 Quick formula for 1, 2, 3, ..., n.
Average of First n Even Numbers = (n + 1) For 2, 4, 6, ..., 2n.
Average of First n Odd Numbers = n For 1, 3, 5, ..., (2n − 1).
Average of Consecutive Numbers from a to b = (a + b) ÷ 2 Works for any arithmetic sequence.
Worked Examples
Example 1: Basic Average Calculation
Problem: The marks of 5 students are 72, 85, 68, 90, and 75. Find the average marks.
Solution:
- Sum = 72 + 85 + 68 + 90 + 75 = 390
- Number of students = 5
- Average = 390 ÷ 5 = 78 marks
Example 2: Finding Missing Value
Problem: The average of 6 numbers is 24. If five of them are 20, 25, 30, 18, and 22, find the sixth number.
Solution:
- Total sum = Average × Count = 24 × 6 = 144
- Sum of five numbers = 20 + 25 + 30 + 18 + 22 = 115
- Sixth number = 144 − 115 = 29
Example 3: New Member Added
Problem: The average age of 8 persons is 25 years. A new person joins, and the average becomes 26 years. Find the age of the new person.
Solution:
- Old sum = 25 × 8 = 200 years
- New count = 9, New average = 26
- New sum = 26 × 9 = 234 years
- Age of new person = 234 − 200 = 34 years
Shortcut: Average increased by 1, new count is 9. New person's age = Old Average + (Increase × New Count) = 25 + (1 × 9) = 34 years
Example 4: Weighted Average
Problem: Section A has 30 students with average marks 60. Section B has 20 students with average marks 75. Find the combined average.
Solution:
- Total marks of A = 30 × 60 = 1800
- Total marks of B = 20 × 75 = 1500
- Combined total = 1800 + 1500 = 3300
- Total students = 30 + 20 = 50
- Combined average = 3300 ÷ 50 = 66 marks
Example 5: Replacement Problem
Problem: The average weight of 10 persons increases by 2.5 kg when a person weighing 45 kg is replaced by a new person. Find the weight of the new person.
Solution:
- Total increase in weight = 2.5 × 10 = 25 kg
- Weight of new person = 45 + 25 = 70 kg
Logic: The extra 25 kg must have come from the new person being heavier than the one who left.
Common Mistakes
Mistake 1: Averaging the averages directly Wrong: "Average of group A is 60, group B is 80, so combined average is 70." Fix: Use weighted average. Simple averaging works only when both groups have equal size.
Mistake 2: Using old count instead of new count Wrong: When a person joins, students use old count (8) instead of new count (9) in calculations. Fix: After addition, always use new total count. After removal, use reduced count.
Mistake 3: Forgetting direction of change Wrong: Confusing whether to add or subtract when average increases or decreases. Fix: If average increases after addition, new element is above old average. If decreases, below.
Mistake 4: Calculation errors in large sums Wrong: Adding 5–6 numbers incorrectly under time pressure. Fix: Add in pairs that make round numbers (e.g., 72 + 28 = 100). Verify by rough estimation.
Mistake 5: Misreading "average increases by" vs "new average is" Wrong: Treating "increases by 3" as "new average is 3." Fix: Read carefully. "Increases by 3" means New Average = Old Average + 3.
Quick Reference
- Average = Sum ÷ Count; rearrange to find any unknown.
- When a new member joins: New Value = Old Avg + (Change × New Count).
- When combining groups: always use weighted average, never simple average of averages.
- Average of consecutive numbers a to b = (a + b) ÷ 2.
- In replacement problems: Weight difference = Change in average × Total count.
- First n natural numbers: Average = (n + 1) ÷ 2.