Understand what average (mean) means in everyday life
Calculate the average of a set of numbers using the formula
Find the sum when the average and number of values are known
Find a missing number when the average is given
Understand the relationship between average, sum, and count
Apply average to real-life situations (marks, runs, temperature, weight)
Solve word problems involving average with Indian context
Understand when average is useful and when it can be misleading
Introduction — What is Average?
Imagine your friend Arjun scored these marks in 5 Maths tests: 72, 85, 68, 91, and 84. His father asks, "How are you doing in Maths overall?" Arjun cannot list all 5 scores every time. He needs one single number that represents his overall performance. That single number is called the average (or mean).
The average is a number that represents the "middle" or "typical" value of a group of numbers. It tells us what each value would be if all values were equal. Think of it like sharing equally — if you have ₹100 and share it equally among 4 friends, each gets ₹25. That ₹25 is the average.
Image needed: Visual showing 5 stacks of different heights (representing different values) being levelled out to equal heights (representing the average). Use colourful blocks with Indian student characters. Style: Flat illustration, child-friendly, colourful Size: 700×400px
A Simple Way to Think About Average
Suppose Meena has 3 bags of mangoes. Bag 1 has 8 mangoes, Bag 2 has 4 mangoes, and Bag 3 has 6 mangoes. If she wants to redistribute so each bag has the same number:
Total mangoes = 8 + 4 + 6 = 18
Number of bags = 3
Equal share = 18 ÷ 3 = 6 mangoes per bag
So the average number of mangoes per bag is 6. This is what average does — it "levels out" unequal quantities into an equal share.
The Average Formula
Formula for Average
Average = Sum of all values ÷ Number of values
Or written as:
Average = (Sum of observations) ÷ (Number of observations)
From this formula, we can also derive two more useful formulas:
To Find
Formula
Average
Average = Sum ÷ Number of values
Sum
Sum = Average × Number of values
Number of values
Number = Sum ÷ Average
Image needed: A triangle diagram showing the relationship between Average, Sum, and Number (similar to speed-distance-time triangle). Average at top, Sum and Number at bottom. Style: Clean diagram with bold colours, educational Size: 500×400px
Understanding the Formula with an Example
Example 1: Priya scored 78, 85, 92, 88, and 77 in five subjects. Find her average marks.
Solution:
Step 1: Find the sum of all marks
Sum = 78 + 85 + 92 + 88 + 77 = 420
Step 2: Count the number of subjects = 5
Step 3: Apply the formula
Average = Sum ÷ Number = 420 ÷ 5 = 84
So Priya's average marks = 84
Example 2: The average weight of 6 students is 35 kg. What is the total weight of all 6 students?
Solution:
Given: Average = 35 kg, Number of students = 6
Sum = Average × Number = 35 × 6 = 210 kg
The total weight of all 6 students = 210 kg
Example 3: The sum of runs scored by Ravi in some innings is 288. His average is 48 runs per innings. How many innings did he play?
Solution:
Given: Sum = 288, Average = 48
Number of innings = Sum ÷ Average = 288 ÷ 48 = 6 innings
Step-by-Step: How to Calculate Average
Follow these steps every time you need to find the average:
Step
What to Do
Example (Heights: 120, 135, 128, 142, 130 cm)
1
List all the values
120, 135, 128, 142, 130
2
Add all values to find the sum
120 + 135 + 128 + 142 + 130 = 655
3
Count the number of values
5 values
4
Divide sum by count
655 ÷ 5 = 131
5
Write the answer with units
Average height = 131 cm
Think About It: Can the average ever be greater than the largest value? Can it be less than the smallest value? No! The average is always between the smallest and the largest value (or equal to them if all values are the same).
Worked Examples — Different Types
Type 1: Finding Average of Given Numbers
Example 4: Find the average of the first 5 multiples of 4.
Solution:
First 5 multiples of 4: 4, 8, 12, 16, 20
Sum = 4 + 8 + 12 + 16 + 20 = 60
Number of values = 5
Average = 60 ÷ 5 = 12
Example 5: The temperatures in Delhi for 7 days in January were: 12°C, 10°C, 14°C, 11°C, 13°C, 9°C, and 15°C. Find the average temperature.
Solution:
Sum = 12 + 10 + 14 + 11 + 13 + 9 + 15 = 84
Number of days = 7
Average = 84 ÷ 7 = 12°C
Type 2: Finding a Missing Value When Average is Known
Example 6: The average of 4 numbers is 25. Three of the numbers are 20, 28, and 30. Find the fourth number.
Solution:
Step 1: Find the total sum using Average × Number
Sum = 25 × 4 = 100
Step 2: Add the known numbers
Sum of known numbers = 20 + 28 + 30 = 78
Step 3: Subtract to find the missing number
Missing number = 100 − 78 = 22
Example 7: Sita's average score in 4 tests is 82. She scored 75, 88, and 79 in the first three tests. What did she score in the fourth test?
Solution:
Total marks needed = 82 × 4 = 328
Sum of first three = 75 + 88 + 79 = 242
Fourth test score = 328 − 242 = 86
Type 3: Effect of Adding or Removing a Value
Example 8: The average weight of 5 boys is 42 kg. A new boy weighing 48 kg joins the group. Find the new average.
Solution:
Original total weight = 42 × 5 = 210 kg
New total weight = 210 + 48 = 258 kg
New number of boys = 6
New average = 258 ÷ 6 = 43 kg
Example 9: The average of 8 numbers is 15. If one number (24) is removed, what is the new average?
Solution:
Original sum = 15 × 8 = 120
New sum = 120 − 24 = 96
New number of values = 7
New average = 96 ÷ 7 = 13.71 (approximately)
Average in Real Life — Indian Context
Average is used everywhere in daily life. Here are some real examples from India:
Situation
What We Average
Why It's Useful
School report card
Marks in all subjects
Find overall performance
Cricket batting average
Runs across innings
Compare batsmen's consistency
Monthly rainfall
Rainfall over days/months
Plan farming and water supply
Average temperature
Daily temperatures
Describe a city's climate
Family monthly expenses
Spending over months
Budget planning
Average speed
Distance ÷ Time
Plan travel time
Population density
People per square km
Urban planning
Image needed: Infographic showing 4 real-life uses of average in India — cricket scorecard, weather report, school report card, and a budget sheet. Each with a small icon and a simple average calculation. Style: Colourful infographic, child-friendly icons Size: 700×500px
Cricket Batting Average
In cricket, a batsman's average tells us how many runs they score per innings on average.
Example 10: Virat Kohli scored the following runs in 6 ODI innings: 82, 44, 107, 56, 73, and 92. Find his batting average for these innings.
Solution:
Total runs = 82 + 44 + 107 + 56 + 73 + 92 = 454
Number of innings = 6
Batting average = 454 ÷ 6 = 75.67 runs per innings
Average Monthly Expenditure
Example 11: A family in Bengaluru spent ₹22,000, ₹25,500, ₹19,800, and ₹24,700 in four months on groceries. Find their average monthly grocery expense.
Think About It: Suppose 5 friends have savings of ₹100, ₹120, ₹90, ₹110, and ₹5,000. The average is (₹100 + ₹120 + ₹90 + ₹110 + ₹5,000) ÷ 5 = ₹5,420 ÷ 5 = ₹1,084. But does ₹1,084 really represent the "typical" savings? Four out of five friends have much less than ₹1,084! One very large (or very small) value can pull the average up (or down). Such values are called outliers.
This is why in some situations, other measures like median (middle value) are more useful. You will learn about median in higher classes.
Image needed: A bar chart showing 5 friends' savings where 4 are around ₹100 and one is ₹5000, with a dashed line showing the average at ₹1084 — demonstrating how one outlier pulls the average up. Style: Clean bar chart with coloured bars and annotation Size: 600×400px
Key Words
Word
Meaning
Average
A single value that represents a group of values; found by dividing the sum by the count
Mean
Another name for average (arithmetic mean)
Sum
The total when all values are added together
Observation
Each individual value or data point in a set
Outlier
A value much larger or smaller than others that can make the average misleading
Data
A collection of numbers or information
Key Points to Remember
Average = Sum of all values ÷ Number of values
Sum = Average × Number of values
The average always lies between the smallest and largest values
If all values are equal, the average equals that value
Adding a value greater than the current average increases the average
Adding a value less than the current average decreases the average
To find a missing value: Missing = Total needed − Sum of known values
Average can be a decimal even if all original values are whole numbers
One extreme outlier can make the average misleading
Average is also called the arithmetic mean
Finished learning? Now test what you know!
🎯 Quick Quiz — Test Yourself!
Answer these questions right here. You get instant feedback — no paper needed!
Score: 0 / 8
1. How do you find the average of some numbers?
Average = Sum of values ÷ Number of values.
2. The average of 4, 6 and 8 is:
(4 + 6 + 8) ÷ 3 = 18 ÷ 3 = 6.
3. The average always lies:
The average is always somewhere between the smallest and largest values.
4. If the average of 5 numbers is 10, their sum is:
Sum = Average × Number = 10 × 5 = 50.
5. Find the average of 10, 20 and 30:
(10 + 20 + 30) ÷ 3 = 60 ÷ 3 = 20.
6. The average of 4 numbers is 25. What is their total sum?
Sum = Average × Number = 25 × 4 = 100.
7. Meena scored 12, 15 and 18 runs in three matches. What is her average score?
(12 + 15 + 18) ÷ 3 = 45 ÷ 3 = 15.
8. The average temperature over 5 days was 40°C. What was the total of all 5 temperatures? (digits only)
Total = Average × Number = 40 × 5 = 200.
Practice Questions
A. Find the Average
1. Find the average of 12, 18, 22, 28, and 30.
2. Find the average of 45, 50, 55, 60, and 65.
3. Find the average of 125, 140, 155, 130, and 150.
4. Find the average of the first 10 natural numbers.
5. Find the average of the first 5 multiples of 7.
6. Find the average of 3.5, 4.2, 5.8, 6.1, and 4.4.
B. Find the Sum
1. The average of 8 numbers is 42. What is their sum?
2. The average height of 12 students is 138 cm. What is the total of all their heights?
3. The average of some numbers is 75. If there are 6 numbers, find their sum.
4. A cricketer's batting average is 56 runs in 15 innings. How many total runs has he scored?
5. The average price of 5 books is ₹245. What is the total cost?
C. Find the Missing Number
1. The average of 5 numbers is 36. Four of the numbers are 28, 42, 35, and 40. Find the fifth number.
2. Arjun's average marks in 4 subjects is 87. He scored 92, 78, and 90 in three subjects. What did he score in the fourth subject?
3. The average of 6 numbers is 18. Five numbers are 15, 20, 12, 22, and 19. Find the sixth number.
4. The average weight of 5 bags is 8 kg. Four bags weigh 7 kg, 9 kg, 6 kg, and 10 kg. Find the weight of the fifth bag.
5. The average age of a family of 4 is 28 years. Three members are 35, 32, and 10 years old. How old is the fourth member?
D. Adding or Removing Values
1. The average of 4 numbers is 50. A fifth number 60 is added. Find the new average.
2. The average marks of 10 students is 72. A new student with 84 marks joins. What is the new average?
3. The average of 6 numbers is 30. If one number (18) is removed, what is the new average?
4. The average weight of 8 children is 32 kg. A child weighing 28 kg leaves the group. Find the new average weight.
5. The average of 5 numbers is 44. Two new numbers, 50 and 52, are added. Find the new average.
E. Word Problems
1. The average rainfall in Chennai during 5 months was 18 cm. The rainfall in 4 months was 12, 22, 15, and 20 cm. Find the rainfall in the fifth month.
2. A train covers 480 km in 6 hours. What is its average speed?
3. The average pocket money of 5 friends is ₹150. Ravi gets ₹120, Meena gets ₹180, Sita gets ₹140, and Priya gets ₹160. How much does the fifth friend get?
4. In a class of 30 students, the average marks in Science is 68. The boys' average is 72 (there are 18 boys). What is the girls' average?
5. A shopkeeper sold mangoes on 6 days. The numbers sold were: 45, 52, 38, 60, 47, and 50. What was his average daily sale?
6. The average age of 3 friends is 11 years. After 3 years, what will be their new average age?
F. Multiple Choice Questions
1. The average of 10, 20, 30, 40 is:
a) 20b) 25c) 30d) 100
2. If the average of 5 numbers is 12, their sum is:
a) 50b) 60c) 72d) 17
3. The average of the first 5 even numbers (2, 4, 6, 8, 10) is:
a) 5b) 6c) 7d) 8
4. The average of 3 numbers is 20. If two numbers are 15 and 25, the third number is:
a) 20b) 18c) 22d) 25
5. The average can NEVER be:
a) Equal to one of the valuesb) A decimalc) Greater than the largest valued) Zero
G. True or False
1. The average of 5, 5, 5, 5, and 5 is 5.
2. The average can be greater than the largest number.
3. If all numbers are increased by 10, the average also increases by 10.
4. Average and mean are two different things.
5. If one number in the set doubles, the average must also double.
H. Challenge Problems
1. The average of 5 consecutive numbers is 33. What are the numbers?
2. The average of 11 results is 60. The average of the first 6 results is 58 and the average of the last 6 results is 63. Find the 6th result.
3. A batsman has an average of 40 after 10 innings. How many runs must he score in the 11th innings to raise his average to 42?
4. The average marks of a class of 50 students is 72. Later, one student's marks are corrected from 48 to 84. What is the new average?
5. Three years ago, the average age of a family of 5 was 17 years. A baby was born one year ago. Find the present average age of the family.
Activity: Average Survey
Materials needed: Paper, pencil, ruler
Instructions:
Ask 8 friends or family members their height (in cm).
Record all 8 heights in a table.
Calculate the average height.
How many people are taller than the average? How many are shorter?
Now do the same with shoe sizes. Is the average shoe size a meaningful number?
Draw a bar chart showing all heights with a horizontal dashed line at the average.
Bonus: Ask 5 classmates how many books they read last month. Find the average number of books per person.
Want to review the lesson again?
Mathematics
Average (Mean)
Class 5 | CBSE / NCERT / ICSE
Name: Class: Date:
The average (or mean) is a single value that represents a group of values. It tells us what each value would be if all values were shared equally. For example, if Arjun scores 72, 85, 68, 91, and 84 in five tests, the average tells us his "typical" performance in one number.
The Average Formula
Average = Sum of all values ÷ Number of values
Sum = Average × Number of values
Number of values = Sum ÷ Average
Step-by-Step Method
Step
What to Do
Example (Heights: 120, 135, 128, 142, 130 cm)
1
List all values
120, 135, 128, 142, 130
2
Add all values
120 + 135 + 128 + 142 + 130 = 655
3
Count the values
5 values
4
Divide sum by count
655 ÷ 5 = 131
5
Write answer with units
Average height = 131 cm
Worked Examples
Example 1: Priya scored 78, 85, 92, 88, and 77 in five subjects. Find her average marks.
Sum = 78 + 85 + 92 + 88 + 77 = 420
Average = 420 ÷ 5 = 84 marks
Example 2: The average weight of 6 students is 35 kg. Find the total weight.
Sum = Average × Number = 35 × 6 = 210 kg
Example 3: The average of 4 numbers is 25. Three of them are 20, 28, and 30. Find the fourth.
Total sum = 25 × 4 = 100
Sum of known = 20 + 28 + 30 = 78
Missing number = 100 − 78 = 22
Example 4: The average weight of 5 boys is 42 kg. A new boy weighing 48 kg joins. Find the new average.
Old total = 42 × 5 = 210 kg. New total = 210 + 48 = 258 kg. New average = 258 ÷ 6 = 43 kg
Average in Real Life
Situation
What We Average
Why It's Useful
School report card
Marks in all subjects
Overall performance
Cricket batting average
Runs across innings
Compare batsmen
Monthly rainfall
Rainfall over months
Plan farming
Family expenses
Spending over months
Budget planning
Average speed
Distance ÷ Time
Travel planning
Key Points:
Average always lies between the smallest and largest values
If all values are equal, average = that value
Adding a value greater than the average increases the average
Adding a value less than the average decreases the average
One extreme outlier can make the average misleading
Mathematics
Average (Mean) — Practice
Class 5 | CBSE / NCERT / ICSE
A. Find the Average
1. Find the average of 12, 18, 22, 28, and 30.
2. Find the average of 45, 50, 55, 60, and 65.
3. Find the average of 125, 140, 155, 130, and 150.
4. Find the average of the first 10 natural numbers.
5. Find the average of the first 5 multiples of 7.
6. Find the average of 3.5, 4.2, 5.8, 6.1, and 4.4.
B. Find the Sum
1. The average of 8 numbers is 42. What is their sum?
2. The average height of 12 students is 138 cm. What is the total of all their heights?
3. A cricketer's batting average is 56 runs in 15 innings. Total runs?
4. The average price of 5 books is ₹245. What is the total cost?
C. Find the Missing Number
1. The average of 5 numbers is 36. Four are 28, 42, 35, and 40. Find the fifth.
2. Arjun's average marks in 4 subjects is 87. He scored 92, 78, and 90. Fourth subject?
3. The average of 6 numbers is 18. Five are 15, 20, 12, 22, and 19. Find the sixth.
4. The average age of a family of 4 is 28 years. Three are 35, 32, and 10. Fourth?
D. Adding or Removing Values
1. The average of 4 numbers is 50. A fifth number 60 is added. New average?
2. Average marks of 10 students is 72. A new student with 84 marks joins. New average?
3. The average of 6 numbers is 30. One number (18) is removed. New average?
4. Average of 5 numbers is 44. Two new numbers (50, 52) are added. New average?
Mathematics
Average (Mean) — Word Problems & Activity
Class 5 | CBSE / NCERT / ICSE
E. Word Problems
1. Average rainfall in Chennai during 5 months was 18 cm. Four months: 12, 22, 15, 20 cm. Fifth month?
2. A train covers 480 km in 6 hours. Average speed?
3. Average pocket money of 5 friends is ₹150. Four get ₹120, ₹180, ₹140, ₹160. Fifth friend?
4. A shopkeeper sold mangoes on 6 days: 45, 52, 38, 60, 47, 50. Average daily sale?
5. Average age of 3 friends is 11 years. After 3 years, new average age?
F. Multiple Choice Questions
1. The average of 10, 20, 30, 40 is:
a) 20b) 25c) 30d) 100
2. If the average of 5 numbers is 12, their sum is:
a) 50b) 60c) 72d) 17
3. The average of first 5 even numbers (2, 4, 6, 8, 10) is:
a) 5b) 6c) 7d) 8
4. Average of 3 numbers is 20. Two are 15 and 25. Third is:
a) 20b) 18c) 22d) 25
5. Average can NEVER be:
a) Equal to one valueb) A decimalc) Greater than the largestd) Zero
G. True or False
1. The average of 5, 5, 5, 5, and 5 is 5.
2. The average can be greater than the largest number.
3. If all numbers increase by 10, average also increases by 10.
4. Average and mean are two different things.
5. If one number doubles, the average must also double.
H. Challenge Problems
1. The average of 5 consecutive numbers is 33. What are the numbers?
2. A batsman has average 40 after 10 innings. How many runs in 11th to raise average to 42?
3. Average marks of 50 students is 72. One student's marks corrected from 48 to 84. New average?
Activity: Average Survey
Ask 8 friends their height (in cm). Record all heights, calculate the average. How many are taller than average? How many shorter? Draw a bar chart with a dashed line at the average.
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