Average

1. What is Average?

Average is the value obtained by dividing the total sum of observations by the number of observations. It represents the central or typical value in a group of numbers.

Central Value of Data Set

Tests Speed & Logical Thinking

Represents Typical Value

Common in Competitive Exams

Simple Definition: Average = (Sum of all quantities) ÷ (Number of quantities)

Examples:

Example 1: Average of 5, 10, 15 = (5 + 10 + 15) ÷ 3 = 30 ÷ 3 = 10

Example 2: Average marks of 4 subjects = (80 + 75 + 85 + 90)/4 = 330/4 = 82.5

2. Important Concepts & Formulas

Concept	Formula / Description	Example
Basic Formula	Average = Sum / Number	(12 + 18 + 24)/3 = 54/3 = 18
Finding Total	Total = Average × Number	Avg = 20, No. = 5 → Total = 100
Finding Missing Value	Missing = (New Total – Known Sum)	5 Nos avg = 10 → total = 50 → if 4 sum = 40 → 5th = 10
Adding New Quantity	New Avg = (Old Total + New Value) / New No.	(40 + 20)/3 = 20
Equal Difference Series	Average = (First + Last)/2	For 2,4,6,8,10 → (2+10)/2 = 6
Weighted Average	(a₁w₁ + a₂w₂ + …) / (w₁ + w₂ + …)	Avg of boys & girls using ratio
Change in Average	Total change = Change × No. of terms	Avg ↑ by 5 for 8 students → total ↑ by 40

3. Step-by-Step Method for Solving

Step	Description
Step 1	Find total of all given quantities
Step 2	Divide total by number of quantities
Step 3	Apply formula if missing or new values are added
Step 4	Check if the numbers form a series (arithmetic)
Step 5	Simplify and double-check calculations for errors

4. Real-Life Analogy

Think of Average as your overall performance score

Individual Scores

80, 70, 90 in three tests

(individual performances)

Average Score

80 shows typical performance

(balanced middle point)

If you scored 80, 70, 90 in three tests, the average (80) shows your typical performance. Even if one mark is high or low, the average gives the balanced middle point.

5. Common Delhi Police / SSC Exam Facts

Average questions are frequent and scoring

Common types: missing number, new value added, group average

Shortcut: For consecutive numbers, average = middle number

Often combined with topics like Time & Work, Speed, or Ratio

Be careful with decimals and units (marks, km/hr, rupees, etc.)

Equal difference series questions are common

6. Practice Questions (Exam-Type)

No.	Question	Solution	Answer
1	Find average of 10, 20, 30, 40, 50	(10+20+30+40+50)/5 = 150/5	30
2	Average of 5 numbers is 20. Find total	20×5 = 100	100
3	Average of 4 numbers is 25. One number is 35. Find new average	(25×4 + 35)/5 = 135/5	27
4	Find average of first 7 even numbers	(2+14)/2 = 8	8
5	Average of 10 students increased by 4 marks. Find total increase	10×4 = 40	40 marks

7. Quick Recap

Concept	Summary
Average	Sum ÷ Number of terms
Key Formula	Total = Average × Number
Series Tip	Average = (First + Last)/2
Shortcut	For consecutive numbers → Middle term
Exam Tip	Watch for "added/removed" type questions

You've completed Average Concepts!

Courage Tip: Practice average problems regularly, focusing on different types like missing numbers, weighted averages, and series-based questions. Remember the key formulas and shortcuts to solve problems quickly in exams.