How to Solve: Average Problems

How to Solve: Average Problems

(For SSC, Bank, Railway Exams – Ace Your Exam with Confidence!)

Introduction

"Master averages, and you unlock 5–10 marks in every SSC, Bank, or Railway exam—questions that look tricky but take less than 30 seconds if you know the shortcuts!

(On camera: Hold up a past paper with a circled average question.) "This one question could be the difference between a pass and a fail. Today, I’ll show you the exact steps to solve any average problem—fast, accurate, and without panic."

What You Need To Know First

Before diving in, make sure you understand:
1. Basic arithmetic (addition, subtraction, multiplication, division).
2. What an average means (the "central" value of a set of numbers).
3. How to solve simple equations (e.g., if Average = Sum / Number, then Sum = Average × Number).

(On camera: Pause, ask students to nod if they’re comfortable with these.)

Key Vocabulary

(On camera: Point to each term, say it aloud, and ask students to repeat.)

Formulas To Know

1. Basic Average Formula

Formula: Average = (Sum of all items) / (Number of items)

Variables: - Sum of all items = Total when you add all numbers. - Number of items = How many numbers are in the set.

MEMORISE THIS – This is the foundation of every average problem!

2. Sum of Items Formula

Formula: Sum of all items = Average × Number of items

Why it’s useful: If you know the average and how many items there are, you can find the total sum.

MEMORISE THIS – You’ll use this in 80% of average problems!

3. Weighted Average Formula

Formula: Weighted Average = (Sum of (Value × Weight)) / (Sum of Weights)

Variables: - Value = The number (e.g., a test score). - Weight = How much that number counts (e.g., "this test is worth 2x").

Given on exam sheet? Sometimes, but memorise it to save time.

4. Deviation Method (Shortcut for Changing Averages)

Formula: New Sum = Old Sum + (New Item – Old Average) × (New Number of Items)

When to use: When one item is added/removed, and the average changes.

MEMORISE THIS – Saves 2 minutes per question!

Step-by-Step Method

Follow these 5 steps for every average problem:

1. Read the question carefully. Underline:
2. What is given? (Average, sum, number of items?)

3. What is asked? (New average? Sum? Missing number?)

4. Write down the formula that fits the given data.

5. If you have the sum and number of items → Use Average = Sum / Number.

6. If you have the average and number of items → Use Sum = Average × Number.

7. Plug in the numbers and solve for the unknown.

8. If the question has multiple parts, solve step by step.

9. Check for tricks.

10. Are some numbers weighted differently?
11. Is one number being added/removed?

12. Is the question asking for a ratio or difference?

13. Verify your answer.

14. Does it make sense? (E.g., average should be between the smallest and largest number.)
15. Recalculate if unsure.

Worked Example Using the Steps

Question: The average of 5 numbers is 20. If one number is removed, the new average becomes 18. What is the removed number?

Step 1: Read carefully. - Given: 5 numbers, average = 20. - One number removed → 4 numbers left, new average = 18. - Asked: What is the removed number?

Step 2: Write the formula. - First, find the sum of 5 numbers: Sum = Average × Number = 20 × 5 = 100. - After removing one number, sum of 4 numbers = 18 × 4 = 72.

Step 3: Plug in the numbers. - Removed number = Original sum – New sum = 100 – 72 = 28.

Step 4: Check for tricks. - No weights or ratios here—just a simple removal.

Step 5: Verify. - If 28 is removed from 100, remaining sum is 72. - 72 ÷ 4 = 18 (matches the new average). ✅

Answer: 28

(On camera: Write each step on the board, explaining aloud.)

Worked Examples

Example 1 – Basic

Question: Find the average of 12, 15, 18, 21, and 24.

Solution:
1. Sum = 12 + 15 + 18 + 21 + 24 = 90.
2. Number of items = 5.
3. Average = Sum / Number = 90 / 5 = 18.

What we did and why: - Added all numbers to get the sum. - Divided by how many numbers there are. - No tricks—just the basic formula.

Example 2 – Medium (Missing Number)

Question: The average of 6 numbers is 15. If 5 of the numbers are 12, 14, 16, 18, and 20, what is the 6th number?

Solution:
1. Sum of 6 numbers = Average × Number = 15 × 6 = 90.
2. Sum of 5 known numbers = 12 + 14 + 16 + 18 + 20 = 80.
3. 6th number = Total sum – Sum of 5 numbers = 90 – 80 = 10.

What we did and why: - Found the total sum using the average. - Subtracted the sum of known numbers to find the missing one. - Common in exam questions—watch for "missing number" clues!

Example 3 – Exam-Style (Weighted Average)

Question: In a class, 30 students have an average score of 70. The remaining 20 students have an average score of 80. What is the average score of the whole class?

Solution:
1. Sum of first group = 30 × 70 = 2100.
2. Sum of second group = 20 × 80 = 1600.
3. Total sum = 2100 + 1600 = 3700.
4. Total students = 30 + 20 = 50.
5. Average = Total sum / Total students = 3700 / 50 = 74.

What we did and why: - Treated each group separately to find their sums. - Combined sums and divided by total students. - Weighted average—some students count more than others!

Common Mistakes

(On camera: Hold up a red pen, circle each mistake, and say:) "These mistakes cost marks. Avoid them by slowing down and double-checking!

Exam Traps

"Examiners love these traps. Spot them, and you’ll save 5 minutes per question!

1-Minute Recap

(On camera: Look directly at the student, speak naturally.)

"Okay, last-minute review—here’s what you need to remember:

1. Average = Sum / Number. Write this down now.
2. If you know the average and how many items, Sum = Average × Number.
3. For weighted averages, multiply each value by its weight before adding.
4. If a number is added/removed, use the deviation method to save time.
5. Never average averages directly—find sums first!
6. Common mistakes? Forgetting to divide, mixing up sum and average, ignoring weights.
7. Exam traps? Hidden weights, changing item counts, "average of averages."

You’ve got this. Take a deep breath, write down the formula, and solve step by step. Every average problem is just addition and division in disguise. Now go ace that exam!