**Average in Maths** question is an important topic to be covered in competitive exams preparation be it for IBPS Clerk, PO, RRB, SO, or SBI Clerk or PO. The number of questions and the complexity of questions vary from exam to exam every year.

**Average in Maths questions** are complex in nature and require an understanding of Numbers Systems, Squares and Square roots, Cubes and Cube roots, and Math Tables. Example questions and **practice questions on Average in Maths** are given in this article.

Nowadays, questions in exams are mixed with multiple concepts and it requires practice and a deep understanding of basic concepts along with quickly identifying numbers.

## What is Average?

An average in maths is a single number that represents the central or middle number of a group of numbers. Average is calculated by summing up all the numbers and then dividing the sum by the number of numbers. Below is the **Formula for the average**:

### Average Formula

**Average = (Sum of Numbers) / Total Numbers**

**For example,** there are 20 students in a class who appeared for a test and got different marks than to represent the average marks obtained out of a total of 50. Marks obtained are as given below:

48, 45, 25, 15, 35, 48, 17, 28, 39, 34, 24, 37, 28, 26, 44, 46, 40, 20, 30, 41.

Now to calculate average marks obtained we first need to sum up all the numbers. Hence, Sum = 48 + 45 + 25 + 15 + 35 + 48 + 17 + 28 + 39 + 34 + 24 + 37 + 28 + 26 + 44 + 46 + 40 + 20 + 30 + 41 = 670

Now, as per the average formula:

=> Average = Sum of all numbers / Total Numbers

=> Total numbers is 20.

=> Sum of all numbers is 670.

=> Average = 670 / 20

=> Average = 33.5

## Use of Average

From the above example, it’s clear that we go average mark obtained by a class in a test is 33.5. Now if we have this average number for every test or for many years or classes then performance can be found out by improvement in average.

## Arithmetic Mean

Average in Maths is also known as **Arithmetic Mean** or simply known as **Mean**. Below is the formula for Arithmetic Mean (AM):

## Solved Example on Average in Maths

Below is the **solved example of the Average in Maths**:

**Example 1**: Find the average of all even numbers between 1 to 50.

**Solution 1**: Let’s first find out all the even numbers from 1 to 50:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50

Now let’s find the sum of all the above numbers: 650

Now the total even number are: 25

So, Average will be 650 / 25 = 26

**Short Trick**: When we’ve to find the average of continuous numbers then we can use the below formula:

Average = (First Number + Last Number) / 2

Applying above formula in example 1 we’ll get:

=> Average = (2 + 50) / 2

=> Average = 52 / 2

=> Average = 26

**Example 2**: Find the average of all even numbers between 10 to 60.

**Solution 2**: Let’s first find out all the even numbers from 10 to 60:

10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60.

Now let’s find the sum of all the above numbers: 910

Now the total even number is: 26

So, Average will be 910 / 26 = 35

**Short Trick**: When we’ve to find the average of continuous numbers then we can use the below formula:

Average = (First Number + Last Number) / 2

Applying above formula in example 2 we’ll get:

=> Average = (10 + 60) / 2

=> Average = 70 / 2

=> Average = 35

**Example 3**: Find the average of all numbers divisible by 3 between 10 to 50.

**Solution 3**: Let’s first find out all the numbers divisible by 3 from 10 to 50:

12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48

Now let’s find the sum of all the above numbers: 390

Now the total even number is: 13

So, Average will be 390 / 13 = 30

**Short Trick**: When we’ve to find the average of continuous numbers then we can use the below formula:

Average = (First Number + Last Number) / 2

Applying above formula in example 1 we’ll get:

=> Average = (12 + 48) / 2

=> Average = 60 / 2

=> Average = 30

**Example 4**: The average of five even numbers is 18. Find the sequence.

**Solution 4**: An easy way to find out numbers is finding 2 consecutive even numbers less than 18 and 2 consecutive even numbers greater than 18.

Hence Sequence is => 14, 16, 18, 20, 22

**Example 5**: The average of a 5-member family is 15 yrs. If a new member comes into the family and the new average is 16. Find the age of a new member?

**Solution 5**: Let’s first find sum of existing members

=> 15 x 5 = 75

Now, sum with new member

=> 16 x 6 = 96

Hence the age of new members will be different of both sum

=> Age of new member = 96 – 75

=> Age of new member = 21

## Practice Question on Average in Maths

Below are the **practice questions on Average in Maths**:

- Find the average of the first 50 odd numbers?
- Find the average of all odd numbers from 10 to 60?
- Find the average of all even numbers from 11 to 100?
- Find the average of all numbers that are divisible by 6 between 1 to 100?
- The total of six numbers is 108 and the average of the first 5 numbers is 20. Find the Sixth number?
- The Average of 5 Continous odd numbers is 23. Find the difference between the first and last numbers?
- The Average of 7 Continous even numbers is 28. Find multiple of the first and last numbers?
- The average of 4 continuous even numbers is 13. Find the biggest number?
- The average of 6 continuous odd numbers is 16. Find the square of the smallest number?
- In a class of 10 students, the average age of students is 12 years, and when added teacher the new average is 11. Find the age of the teacher?

## Final Words

Practicing the above questions for Average in Maths is not the end of your practice, but it’s the start of a new journey to apply logic to Average in Maths solutions with multiple approaches in a right and faster way.

For cracking competitive exams one must practice an Average in Maths without a calculator is a must. **At last**, during the exam, if a solution for the Average in Maths question cannot be found easily then mark that question to revisit and move ahead instead of wasting time and energy.