Mean (Average) Introduction
The mean (or average) is one of the most commonly used measures in mathematics and daily life. It gives a single number that represents the "middle" or "typical" value of a group of numbers.
In Class 5, you learn to calculate the mean of a set of numbers and use it to solve word problems. Averages are used to find average marks, average temperature, average height, average speed, and much more.
When someone says "the average rainfall this month was 5 cm," they mean the total rainfall divided equally across all days.
What is Mean (Average) Introduction - Class 5 Maths (Data Handling)?
The mean (arithmetic mean or average) of a set of numbers is found by adding all the numbers together and dividing by how many numbers there are.
Mean = Sum of all values ÷ Number of values
The mean represents the value each item would have if the total were shared equally among all items.
Mean (Average) Introduction Formula
Mean = (Sum of all observations) ÷ (Number of observations)
Finding the total from the mean:
Sum = Mean × Number of observations
Solved Examples
Example 1: Example 1: Basic Average
Problem: Find the mean of 12, 18, 24, 30, and 16.
Solution:
Step 1: Sum = 12 + 18 + 24 + 30 + 16 = 100
Step 2: Number of values = 5
Step 3: Mean = 100 ÷ 5 = 20
Answer: Mean = 20
Example 2: Example 2: Average Marks
Problem: Ria scored 85, 92, 78, 88, and 97 in five tests. Find her average marks.
Solution:
Step 1: Sum = 85 + 92 + 78 + 88 + 97 = 440
Step 2: Number of tests = 5
Step 3: Average = 440 ÷ 5 = 88
Answer: Ria's average marks = 88
Example 3: Example 3: Average Temperature
Problem: The temperature over 4 days was 32°C, 35°C, 30°C, and 33°C. Find the average temperature.
Solution:
Step 1: Sum = 32 + 35 + 30 + 33 = 130
Step 2: Average = 130 ÷ 4 = 32.5
Answer: Average temperature = 32.5°C
Example 4: Example 4: Finding the Total from Average
Problem: The average weight of 6 students is 35 kg. What is their total weight?
Solution:
Step 1: Total = Mean × Number = 35 × 6 = 210
Answer: Total weight = 210 kg
Example 5: Example 5: Finding a Missing Number
Problem: The average of 4 numbers is 25. Three of the numbers are 20, 28, and 30. Find the fourth number.
Solution:
Step 1: Total = Mean × Number = 25 × 4 = 100
Step 2: Sum of three numbers = 20 + 28 + 30 = 78
Step 3: Fourth number = 100 − 78 = 22
Answer: The fourth number is 22.
Example 6: Example 6: Average Runs in Cricket
Problem: Aman scored 45, 32, 67, 28, and 53 runs in 5 cricket matches. What is his average score?
Solution:
Step 1: Sum = 45 + 32 + 67 + 28 + 53 = 225
Step 2: Average = 225 ÷ 5 = 45
Answer: Aman's average score = 45 runs
Example 7: Example 7: Average of Decimals
Problem: Find the average of 3.5, 4.2, 5.8, and 2.5.
Solution:
Step 1: Sum = 3.5 + 4.2 + 5.8 + 2.5 = 16.0
Step 2: Average = 16.0 ÷ 4 = 4.0
Answer: Average = 4.0
Example 8: Example 8: Average Height
Problem: The heights of 5 students are 130 cm, 142 cm, 138 cm, 135 cm, and 145 cm. Find the average height.
Solution:
Step 1: Sum = 130 + 142 + 138 + 135 + 145 = 690
Step 2: Average = 690 ÷ 5 = 138
Answer: Average height = 138 cm
Example 9: Example 9: Effect of Adding a Value
Problem: The average of 5 numbers is 40. If a new number 70 is added, what is the new average?
Solution:
Step 1: Original total = 40 × 5 = 200
Step 2: New total = 200 + 70 = 270
Step 3: New average = 270 ÷ 6 = 45
Answer: New average = 45
Example 10: Example 10: Average Pocket Money
Problem: Priya, Aditi, Kavi, and Meera receive pocket money of ₹150, ₹200, ₹180, and ₹170 respectively. Find the average pocket money.
Solution:
Step 1: Sum = 150 + 200 + 180 + 170 = 700
Step 2: Average = 700 ÷ 4 = 175
Answer: Average pocket money = ₹175
Key Points to Remember
- Mean = Sum of all values ÷ Number of values.
- The mean is also called the arithmetic average.
- The mean need not be one of the actual values in the data set.
- The mean can be a decimal, even if all values are whole numbers.
- To find the total from the mean: Total = Mean × Number of values.
- To find a missing value: Missing = Total − Sum of known values.
- Adding a value larger than the current mean increases the average; adding a smaller value decreases it.
Practice Problems
- Find the mean of 15, 25, 35, 45, and 30.
- Dev scored 72, 88, 64, 90, and 81 in 5 subjects. What is his average?
- The average of 8 numbers is 12. What is their total?
- The average weight of 4 bags is 6 kg. Three bags weigh 5 kg, 7 kg, and 8 kg. Find the weight of the fourth bag.
- The temperatures for 7 days are 28, 30, 32, 29, 31, 27, and 33. Find the average temperature.
- Neha's average score in 4 tests is 85. She scores 95 in the 5th test. What is her new average?
- The average of three numbers is 60. Two of the numbers are 55 and 70. Find the third number.
- Find the average of 2.4, 3.6, 4.8, and 5.2.
Frequently Asked Questions
Q1. What is the mean or average?
The mean is found by adding all values in a data set and dividing by the number of values. It represents the typical or central value of the data.
Q2. Is the mean always a whole number?
No. The mean can be a decimal. For example, the average of 3 and 4 is 3.5.
Q3. Can the mean be larger than all the values?
No. The mean always lies between the smallest and largest values in the data set.
Q4. How do you find a missing number when the average is given?
First find the total (Mean × Number of values). Then subtract the sum of the known values. The result is the missing number.
Q5. What happens to the average when you add a very large number?
The average increases. A very large number pulls the average upward, especially in a small data set.
Q6. Is average the same as median?
No. The average (mean) is the sum divided by count. The median is the middle value when data is arranged in order. They can be different.
Q7. Where is average used in daily life?
Average is used to calculate average marks, average temperature, batting average in cricket, average speed, and average monthly expenses.
Q8. What is the average of identical numbers?
If all numbers are the same, the average equals that number. For example, the average of 5, 5, 5, 5 is 5.
