Average Questions in maths is one of the most fundamental concepts in arithmetic, frequently used in academics, daily life, and competitive exams. Whether calculating the average score of students, the average speed of a journey, or the average income, this concept plays a crucial role in problem-solving. Practicing a variety of average questions enhances your understanding of the concept and improves accuracy and speed in calculations.

 

Table of Contents

• Origin and Importance of Averages
• What is Average in Maths?
• Average Formula Explained
• Solved Average Questions
• Benefits of Learning Averages
• Real-Life Use of Average Calculations
• Conclusion
• FAQs on Average Questions

 

Origin and Importance of Averages

The concept of average in mathematics is derived from statistical analysis. It is a measure of central tendency that represents the general value of a group of numbers. The idea of averages has been used since ancient times, even in trade and population studies, to understand common trends. In modern education and data analysis, the average is one of the most used statistical tools to describe data concisely.

Average Formula Explained

The basic average formula is:

Average = (Sum of Observations) / (Number of Observations)

There are also variations such as:

• Weighted Average = (Sum of weighted values) / (Sum of weights)

• Average Speed = Total distance / Total time

These formulas help solve a wide variety of average problems in different contexts.

  

Average Questions and Solutions

Here are some solved average questions to help you understand the application:

Q1. Find the average of 12, 15, 17, 20, and 21.

Solution: (12 + 15 + 17 + 20 + 21) / 5 = 85 / 5 = 17

 

Q2. The average of five numbers is 36. If four of the numbers are 30, 34, 40, and 38, find the fifth number.

Solution: Total sum = 36 × 5 = 180

Sum of four = 30 + 34 + 40 + 38 = 142

Fifth number = 180 - 142 = 38

 

Q3. A car travels 60 km at 30 km/h and another 60 km at 60 km/h. What is the average speed?

Solution:

Time1 = 60 / 30 = 2 hrs, Time2 = 60 / 60 = 1 hr

Total time = 3 hrs, Total distance = 120 km

Average speed = 120 / 3 = 40 km/h

 

Q4 .Find the average of the following set of numbers: 72, 88, 64, 96, and 120.

Solution: Given, the set of numbers is 72, 88, 64, 96, and 120.
Average = Sum of numbers / Total numbers
= (72 + 88 + 64 + 96 + 120) / 5
= 440 / 5
= 88

 

Q5.The sum of 8 numbers is 400. Find their average.

Solution: Given, the sum of 8 numbers = 400.
Average = Sum / Total numbers
= 400 / 8
= 50

Q6.What is the average of natural numbers from 1 to 51?

Solution: Given, natural numbers 1 to 51.
Average of n natural numbers = (n + 1)/2
Here, n = 51
Average = (51 + 1) / 2 = 52 / 2 = 26

 

Q7. The average of 5 consecutive numbers is 31. What is the largest of these numbers?

Solution: Let the 5 consecutive numbers be x, x+1, x+2, x+3, x+4.
Average = (x + (x+1) + (x+2) + (x+3) + (x+4)) / 5 = 31
⇒ (5x + 10) / 5 = 31
⇒ 5x + 10 = 155
⇒ 5x = 145
⇒ x = 29
Largest number = x + 4 = 33

 

Q6. The average of 12 numbers is 18. If each number is increased by 6, what will the new average be?

Solution: Average of 12 numbers = 18
Sum = 18 × 12 = 216
Increase in total = 6 × 12 = 72
New sum = 216 + 72 = 288
New average = 288 / 12 = 24

 

Q7. The average of 40 numbers is 25. If two numbers 35 and 45 are discarded, find the average of the remaining numbers.

Solution: Average of 40 numbers = 25
Sum = 40 × 25 = 1000
Sum of discarded numbers = 35 + 45 = 80
Remaining sum = 1000 – 80 = 920
Remaining numbers = 40 – 2 = 38
Average = 920 / 38 = 24.21

 

Q8. What is the average of the first six multiples of 7?

Solution: First six multiples of 7 are: 7, 14, 21, 28, 35, 42
Average = (7 + 14 + 21 + 28 + 35 + 42) / 6
= 147 / 6
= 24.5

 

Q9.The average age of three sisters is 18 years and their ages are in proportion 2:3:5. What is the age of the youngest sister?

Solution: Let the age of the youngest sister = 2x.
Then, ages = 2x, 3x, 5x.
Average = (2x + 3x + 5x)/3 = 18
10x / 3 = 18
10x = 54
x = 5.4
Youngest sister = 2x = 2(5.4) = 10.8 years

 

Q10. The average weight of a group of 8 students is 50 kg. The weights of 7 of them are 48, 55, 52, 49, 54, 47, and 56. Find the weight of the 8th student.

Solution: Average weight = 50 kg
Total weight = 50 × 8 = 400 kg
Sum of 7 students = 48 + 55 + 52 + 49 + 54 + 47 + 56 = 361 kg
Weight of 8th student = 400 – 361 = 39 kg

 

Q11.The mean of 20 numbers is 42. If the mean of the first 8 numbers is 38 and the mean of the last 8 numbers is 45, find the sum of the remaining 4 numbers.

Solution: Mean of 20 numbers = 42
Total sum = 42 × 20 = 840

Sum of first 8 numbers = 38 × 8 = 304
Sum of last 8 numbers = 45 × 8 = 360

Sum of 16 numbers = 304 + 360 = 664
Remaining sum = 840 – 664 = 176

Benefits of Learning Averages

• Builds a strong foundation in basic arithmetic

• Improves data interpretation and analysis skills

• Essential for aptitude-based entrance exams

• Enhances logical thinking and problem-solving speed

• Useful for comparing and summarizing data in real life

 

Real-Life Use of Average Calculations

• Household Budgeting: Estimating average monthly expenses

• Classroom Analysis: Understanding Class Performance Trends

• Business: Calculating average revenue or cost per unit

• Health: Monitoring average heart rate or calorie intake

• Travel: Estimating average speed or fuel consumption

 

Conclusion

Understanding the concept of average in maths is essential for both academic excellence and real-life utility. From calculating test scores to analyzing business profits, averages help simplify data and reveal trends. Practicing a wide range of average questions sharpens your speed, accuracy, and confidence in solving mathematical problems. With a grasp of the average formula, students are equipped to handle various math challenges with ease.
 

Frequently Asked Questions on Average Questions

1. What is the basic formula for the average?

Answer: The basic formula is: Average = Sum of values / Number of values

2. How is the average used in real life?

Answer: Averages are used in academics, sports, finance, health, and more to summarize and analyze data effectively.

3. What is the difference between average and weighted average?

Answer: An average gives equal importance to all values, while a weighted average assigns different weights based on importance or frequency.

4. Why is the average important in exams?

Answer: Average-based questions are common in aptitude tests and help assess analytical thinking and calculation speed.

5. Can averages be used for comparing groups?

Answer: Yes, averages are used to compare the performance, efficiency, or cost across different groups or categories.

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