What is Average in Maths?

Finding the average is a basic math skill required to summarise and compare large data sets. Learning core concepts based on average is not only important in academics but also holds significance in our daily lives. From calculating the average score of students to the average speed of a car, it is widely applied in our daily life. We use the concept of average in assessing academic performance, financial reports, sports statistics, etc. We have explained in detail about average, its formula, and the step-by-step calculation process to help students learn the topic clearly. 

Table of Contents

• What is Average?
• How to Calculate the Average?
• Formula for Calculating Average
• Application of Average
• Frequently Asked Questions on Average
• Solved Problems

What is Average?

Average is defined as the sum of all values in a dataset divided by the total number of values. It is used to find a middle or central value that represents the dataset. For example, if you scored 77, 80, 88, 85, and 90 in five different subjects your average score would be 

Average = (77 + 80 + 88 + 85 + 90) / 5 

This means your average performance across all five subjects was 84 marks.

How to calculate the average?

You can easily find the average using a simple formula that applies to both simple and large data sets. Let’s understand the steps to we need to follow to find the average of various numbers

Step 1: Write all the observations in the given data set to find the total number of observations (say n).

Step 2: Calculate the sum of all observations.

Step 3: The next step is to divide the sum of observations obtained in the 2nd step by the number of observations (n) calculated in the 1st step.

Step 4: Simplify the result to get the final value of the average.

Formula for Calculating Average

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.

 Applications of Average in Real Life

The concept of average in maths is applied in various fields:

• Academics: Average is used in academics to calculate the average marks or performance of students.

• Finance: In the financial sector, the concept of average is used in determining average income or expenditure and preparing reports.

• Sports: In sports, average helps to determine the average score, strike rate, or goals per match.

• Weather: Average temperature or rainfall over a period

• Business: Average sales, profit, or customer ratings

Solved Questions

Practising the problems based on this topic will help you build a strong foundation and conceptual fluency required for various competitive exams. Here are some solved average questions to help you understand the application:

Example 1. Find the average of 11, 12, 15, 20, and 21.

Solution: (11 + 14 + 18 + 20 + 22) / 5 = 85 / 5 = 17

Example 2. 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

The sum of four = 30 + 34 + 40 + 38 = 142

Fifth number = 180 - 142 = 38 

Example 3. A car travels 60 km at 30 km/h and another 60 km at 60 km/h. What is the average speed?

Solution: Time taken by car 1 = 60 / 30 = 2 hrs

Time taken by car 2 = 60 / 60 = 1 hr

Total time = 3 hrs, Total distance = 120 km

Average speed = 120 / 3 = 40 km/h

Benefits of Learning Averages

• It helps builds a strong foundation in basic arithmetic

• It improves our data interpretation and analysis skills

• It is essential for aptitude-based entrance exams

• Enhances logical thinking and problem-solving speed

• Useful for comparing and summarising data in real-life situations.

Conclusion

Understanding the concept of average in maths is essential for both academic excellence and real-life utility. From calculating test scores to analysing business profits, averages help simplify data and reveal trends. Practising 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

1. Define 'average' with an example.

Answer: Average is the measure of central value for a given set of values. For example, if 4 and 8 are the data values, the average will be calculated as (4+8)/2 = 6.

2. What is the formula used to calculate average?

Answer: The formula used to find the average of the given numbers is the sum of all values divided by the number of values: Average = sum of all values ÷ number of values. Let’s try to understand the application of this formula with an example: if the given set of numbers is {2, 8, 5}, then Average = (2 + 8 + 5) ÷ 3 = 5.