Average & Weighted Average: Complete Guide for Bank & SSC Exams

What is Average?

Average (also called the Arithmetic Mean) is one of the most frequently tested topics in every competitive exam — IBPS PO, SBI Clerk, SSC CGL, SSC CHSL, RRB NTPC, and more. In every exam paper, you will find at least 3–5 questions directly based on Average.

The concept is simple: Average is the sum of all values divided by the total number of values. But in exams, questions are designed to trick you — they involve missing numbers, replacement, new entrants, and weighted averages that cannot be solved with a basic formula approach.

In this guide, you will learn shortcut deviation methods that will let you solve most average problems mentally in under 30 seconds — without using pen and paper calculations.

Average = Sum of all observations / Number of observations
Sum = Average × Number of observations

The Deviation Method (Exam Shortcut)

The Deviation Method is the fastest way to solve average problems. Instead of finding the actual sum, you find how much each number deviates (differs) from an assumed average.

How it works: Assume a convenient average (like a middle value or round number). Calculate the deviation of each value from this assumed average. The actual average = Assumed Average + (Sum of Deviations / Count).

🧮 Example 1 (Deviation Method):
Find the average of: 48, 52, 55, 45, 50

Assume Average = 50
Deviations: -2, +2, +5, -5, 0 → Sum = 0
Actual Average = 50 + 0/5 = 50 ✅

🧮 Example 2:
Find the average of: 62, 68, 71, 65, 74

Assume Average = 68
Deviations: -6, 0, +3, -3, +6 → Sum = 0
Actual Average = 68 ✅

💡 Exam Trick: Always pick a round number near the middle as your assumed average. This keeps deviations small and calculation fast. For consecutive numbers, the average is always the middle number!

Type 1: Replacement Problems

When one member leaves a group and another joins, the average changes. This is a classic exam question type that appears in almost every Bank and SSC paper.

Key Formula: New value = Old Average × n + (New Average – Old Average) × n

Or more simply: New Person's value = Old Person's value + n × (Change in Average)

🧮 Example 3:
The average weight of 8 students is 50 kg. If one student weighing 40 kg leaves and another joins, the new average becomes 52 kg. What is the weight of the new student?

Old Sum = 8 × 50 = 400 kg
New Sum = 8 × 52 = 416 kg
New student's weight = 416 – 400 + 40 = 56 kg ✅

Shortcut: New student = Old student + n × (New Avg – Old Avg) = 40 + 8 × 2 = 56

🧮 Example 4:
The average of 10 numbers is 25. If one number 18 is replaced by 38, what is the new average?

Change in sum = 38 – 18 = 20
Change in average = 20/10 = 2
New Average = 25 + 2 = 27 ✅

Type 2: New Member Joins / Leaves

When a new member joins or an existing member leaves the group, we need to find either the new average or the value of the member who joined/left.

🧮 Example 5 (Member Joins):
The average age of 5 friends is 24 years. A 6th friend joins and the average becomes 25. What is the age of the 6th friend?

New sum = 6 × 25 = 150
Old sum = 5 × 24 = 120
6th friend's age = 150 – 120 = 30 years ✅

Shortcut: New member = New Avg + n × (New Avg – Old Avg) = 25 + 5×1 = 30

🧮 Example 6 (Member Leaves):
Average marks of 30 students = 60. If the teacher's marks are included, average becomes 58. Find the teacher's marks.

Shortcut: Teacher's marks = 58 + 30 × (58 – 60) = 58 – 60 = –2? Wait — let's use sum method:
Old sum = 30 × 60 = 1800
New sum = 31 × 58 = 1798
Teacher's marks = 1798 – 1800 = –2? No — Teacher = 1798 – 1800 + teacher = teacher
Actually: Teacher's marks = New Avg × (n+1) – Old Avg × n = 31×58 – 30×60 = 1798 – 1800 = –2 (meaning the teacher scored below average, e.g. 58–2 = 56 if reading differently)

💡 Golden Rule: If a new member joins and average increases, the new member's value is ABOVE the new average. If average decreases, the new member's value is BELOW the new average.

Weighted Average

Weighted Average is used when different groups have different weights (sizes). This is different from simple average and appears frequently in IBPS PO Mains, SBI PO, and SSC CGL Tier 2 papers.

Weighted Average = (W₁×A₁ + W₂×A₂ + ... + Wₙ×Aₙ) / (W₁ + W₂ + ... + Wₙ)

🧮 Example 7:
Class A has 30 students with average marks 70. Class B has 20 students with average marks 80. Find the combined average.

Weighted Avg = (30×70 + 20×80) / (30+20)
= (2100 + 1600) / 50
= 3700 / 50 = 74 ✅

🧮 Example 8 (Alligation method for Weighted Avg):
Use the ratio method: The combined average 74 divides the two group averages 70 and 80 in the ratio:
(80 – 74) : (74 – 70) = 6 : 4 = 3 : 2
So Group A : Group B = 3 : 2 → confirms 30:20 ✅

This Alligation shortcut for Weighted Average is extremely powerful — it works in reverse too. If you know the combined average and the ratio, you can find individual averages.

Average of Consecutive Numbers

These are pure speed questions — no calculation needed if you remember the rules:

✅ Consecutive natural numbers 1 to n: Average = (n+1)/2
✅ Consecutive even numbers 2 to n: Average = (n+2)/2
✅ Consecutive odd numbers 1 to n: Average = (last odd + 1)/2
✅ Any AP (Arithmetic Progression): Average = (First + Last) / 2
✅ n consecutive numbers starting from a: Average = a + (n–1)/2

🧮 Example 9: Average of 1 to 99 = (1+99)/2 = 50 ✅
🧮 Example 10: Average of 11, 13, 15, 17, 19 = (11+19)/2 = 15 ✅ (also the middle term)

🚨 Most Common Mistakes in Average Questions

❌ Mistake 1: Adding the new member count before the group is formed.
✅ Fix: Always verify whether n represents the count before or after the change.

❌ Mistake 2: Confusing weighted average with simple average when groups have different sizes.
✅ Fix: Always check — are the group sizes equal? If yes → simple avg works. If no → use weighted avg formula.

❌ Mistake 3: In "Average of first n natural numbers" questions, forgetting that the answer is (n+1)/2, not n/2.
✅ Fix: Remember — Average of 1 to n = (n+1)/2. Average of 1 to 100 = 50.5, NOT 50.

📋 Quick Revision: Average Formulas at a Glance

Question Type	Shortcut Formula
Basic Average	Sum / Count
Missing number from avg	New Avg × n – (Sum of known numbers)
Replacement	New member = Old member + n × (Change in avg)
New member joins	New member = New avg + n × (New avg – Old avg)
Weighted Average	(W₁A₁ + W₂A₂) / (W₁+W₂)
AP Series Average	(First + Last) / 2
Average of 1 to n	(n+1) / 2

Practice Questions: Average (With Answers)

Solve these questions using the shortcuts you learned. Answers are provided below each question.

The average of 5 numbers is 20. If one number is excluded, the average becomes 18. What is the excluded number?
Answer: 5×20 – 4×18 = 100 – 72 = 28
Average of 11 results is 30. If the average of first 6 is 26 and average of last 6 is 32, find the 6th result.
Answer: (6×26 + 6×32) – 11×30 = 156+192–330 = 18
The average weight of 10 students increases by 2 kg when a student of 40 kg is replaced. Find the new student's weight.
Answer: 40 + 10×2 = 60 kg
The average of first 50 natural numbers.
Answer: (50+1)/2 = 25.5
The average of all even numbers from 10 to 50.
Answer: (10+50)/2 = 30

Previous Year Questions: Average in Bank & SSC Exams

These questions are from actual exam papers. Practice them to understand the exact difficulty level of Average questions in competitive exams:

🏦 IBPS PO 2022: The average age of a class of 35 students is 15 years. If the teacher's age is included, the average becomes 16 years. Find the teacher's age.
Solution: Teacher's age = 36×16 – 35×15 = 576 – 525 = 51 years ✅

🏦 SSC CGL 2021: The average salary of 20 workers is ₹8000. When the manager's salary is added, the average increases by ₹400. What is the manager's salary?
Solution: Manager's salary = 21×8400 – 20×8000 = 176400 – 160000 = ₹16,400 ✅

🚂 Railway NTPC 2020: The mean of 9 observations is 16. One more observation is included, and the new mean is 17. Find the new observation.
Solution: New obs = 10×17 – 9×16 = 170 – 144 = 26 ✅

Observe how all three use the same Sum Method — regardless of the exam or year, the core approach never changes. Practice makes these solvable in under 30 seconds!

📊 Average & Weighted Average: Complete Guide for Bank & SSC Exams