📘 Average (Mean) – Complete Concept Guide
For School Students & Competitive Exams
1️⃣ What is Average?
The Average (also called Mean) is a measure of central tendency. It tells us the typical value in a group of numbers.
Average = (Sum of all observations) ÷ (Number of observations)
It helps simplify large data into one meaningful value.
2️⃣ Basic Formula
Average = Total Sum / Total Number
Example:
Find the average of 2, 4, 6, 8, 10
Sum = 2 + 4 + 6 + 8 + 10 = 30
Number of values = 5
Average = 30 ÷ 5 = 6
3️⃣ Important Average Formulas
- Sum = Average × Number
- New Average = New Total ÷ Total Number
- If one value is replaced: New Sum = Old Sum − Old Value + New Value
4️⃣ Exam-Based Solved Examples
Example 1: Average of 3 numbers is 20. Two numbers are 15 and 25.
Total sum = 20 × 3 = 60
Third number = 60 − 15 − 25 = 20
Example 2: Average of 5 numbers is 12. Two numbers are 10 and 15.
Total sum = 12 × 5 = 60
Sum of remaining three = 60 − 10 − 15 = 35
Example 3: Average weight of 10 students is 60 kg.
Total = 600 kg
Replace 70 kg with 50 kg
New total = 600 − 70 + 50 = 580
New average = 580 ÷ 10 = 58 kg
Example 4: Average of 4 numbers is 25. One number is 30.
Total sum = 100
Remaining sum = 100 − 30 = 70
Average of remaining 3 = 70 ÷ 3 = 23.33
Example 5: Average age of 5 members = 40
Total age = 200
Youngest = 20
Remaining total = 180
Average of remaining 4 = 180 ÷ 4 = 45
Example 6: Average of 5 consecutive even numbers is 24.
Middle number = 24
Numbers = 20, 22, 24, 26, 28
Largest = 28
5️⃣ Special Tricks for Exams 🎯
- ✔ In consecutive numbers, average = middle number
- ✔ Use Sum = Average × Number formula for fast solving
- ✔ When one value changes → adjust total directly
- ✔ For even number of terms → average lies between middle values
6️⃣ Real-Life Applications
- ✔ Average marks in exams
- ✔ Average salary in companies
- ✔ Average temperature reports
- ✔ Sports statistics (batting average)
🔥 Final Revision Box
✔ Average = Sum ÷ Number
✔ Sum = Average × Number
✔ Replace method: New Sum = Old Sum − Old Value + New Value
✔ Consecutive numbers → Average = Middle Number
