Solved Examples on Average in Maths

Here are some numerical examples on average with solutions. These solved examples will help students understand and practice the concept of average.

Example 1: Find the average of the square of the first 16 natural numbers.

Solution:

Sum of square of first n natural number = n(n+1)(2n+1)/6 

Avg. of square of first n natural number = (n+1)(2n+1)/6 

Average = (16+1)(2×16+1)/6 

= 17 × 33 /6 

= 187/2 

Example 2: The average of 9 observations is 87. If the average of the first five observations is 79 and the average of the next three is 92. Find the 9th observation. 

Solution:

Average of 9 observations = 87 

Sum of 9 observations = 87 × 9 = 783 

Average of first 5 observations = 79 

Sum of first 5 observations = 79 × 5 = 395 

Sum of 6th,7th and 8th = 92 × 3 = 276 

9th number = 783 – 395 – 276 = 112 

Example 3: Five years ago the average of the Husband and wife was 25 years, today the average age of the Husband, wife, and child is 21 years. How old is the child? 

Solution:

H + W = 25 

Sum of ages of both 5 years before = 25×2 = 50 

Today, sum of their ages is = 50 + 5 + 5 = 60 

Today avg. of H + W + C = 21 

Sum of ages of H , W and C = 21×3 = 63 

Age of child = 63 – 60 = 3 years

Example 4: There are 42 students in a hostel. If the number of students increased by 14. The expense of mess increased by Rs 28 per day. While the average expenditure per head decreased by Rs 2. Find the original expenditure. 

Solution:

Total students after increment = 42 + 14 = 56 

Let the expenditure of students is A Rs/day. 

Increase in expenditure Rs 28/day. 

Acc. to question 

42A + 28 = 56(A – 2) 

42A + 28 = 56A – 112 

14A = 140 

A = 10 

Hence, the original expenditure of the student was Rs 10/day. 

Example 5: The average of 200 numbers is 96 but it was found that 2 numbers 16 and 43 are mistakenly calculated as 61 and 34. Find his correct average it was also found that the total number is only 190. 

Solution:

Average of 200 numbers = 96 

Sum of 200 numbers = 96 x 200 = 19200 

Two numbers mistakenly calculated as 61 and 34 instead of 16 and 43. 

So, 61 + 34 = 95 

16 + 43 = 59 

Diff = 95 – 59 = 36 

So, Actual sum of 200 numbers = 19200 – 36 = 19164 

Total numbers are also 190 instead of 200

So, correct average = 19164/190 = 100.86

Example 6: A batsman scored 120 runs in his 16th innings due to this his average increased by 5 runs. Find his current average. 

Solution:

Let the average of 15 innings is A

Acc. to question 

15A + 120 = 16(A + 5) 

15A + 120 = 16A + 80 

A = 40 

Hence, current average of the batsman is (40 + 5) = 45 

Example 7: There are three natural numbers if the average of any two numbers is added with the third number 48,40 and 36 will be obtained. Find all the natural numbers. 

Solution:

Let a, b and c are the numbers

Given 

• (a+b)/2 + c = 48

=> a + b + 2c = 96 ………(1) 

(b+c)/2 + a = 40 

=> 2a + b + c = 80 ……….(2) 

(c+a)/2 + b = 36 

=> a + 2b + c = 72 ……….(3) 

Add (1)(2)(3), we get 

4(a + b + c) = 248 

a + b + c = 62 

From 1, 2, and 3

(a+b+c) + c = 96 

62 + c = 96 

• c = 34

a + (a+b+c) = 80 

a + 62 = 80 

• a = 18

b + (a+b+c) = 72 

b + 62 = 72 

• b = 10

Example 8: A biker travels at a speed of 60 km/hr from A to B and returns at a speed of 40 km/hr. What is the average speed of the total journey? 

Solution:

Let a is the distance between A and B

Total distance travel in journey = 2a 

Time to travel from A to B = Distance/speed = a/60 

Time to travel from B to A = Distance/speed = a/40 

Total time of journey = a/60 + a/40 

Average speed = Total distance/Total time 

=2a / (a/60 + a/40) 

=240 × 2a /10a 

= 240/5 

= 48 

Hence, the average speed is 48 km/hr.

Average in Maths: An average is the middle value of a group of numbers. It’s calculated by adding up all the numbers and then dividing by how many there are. This is also known as the mean. For example, if you have the numbers 2, 3, and 4, you add them together to get 9. Then you divide by 3 (since there are 3 numbers), which equals 3. So, the average, or mean, of 2, 3, and 4 is 3. Finding the average helps us find the typical value in a group of numbers.

Average = Sum of Values/Number of Values

In this article, we’ll explore what is average in maths, including its symbol, average formula in maths, and how to calculate the average. We’ll also cover step-by-step instructions for calculating the average and several detailed examples.