WORKSHEET ON AVERAGE 

Problem 1 :

Find the average of first 20 natural numbers.

Problem 2 :

Find the average of first 15 odd numbers. 

Problem 3 :

Find the average of first 20 natural numbers which are the multiples of 7. 

Problem 4 :

The average of four consecutive odd numbers is 10. Find the smallest of these numbers. 

Problem 5 :

The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. Find the ratio of the number of boys to the number of girls in the class. 

Answers

1. Answer :

Step 1 :

Use 1 + 2 + 3 + ........ + n = n(n + 1)/2, to find the sum of first 20 natural numbers. 

1 + 2 + 3 + ........ + 20 = 20(20 + 1)/2

= 20(21)/2

= 10(21)

= 210

Step 2 :

Average of first 20 natural numbers : 

= (Sum of first 20 natural numbers)/20

= 210/20

= 10.5

2. Answer :

Step 1 :

Formula for sum of first n odd numbers. 

S_n = n²

Step 2 :

Use the formula in step 1 to find the sum of first 15 odd numbers. 

S₁₅ = 15²

= 225

Step 3 :

Find the average of first 15 odd numbers. 

Average of first 15 odd numbers :

= (Sum of first 15 odd numbers)/15

= 225/15

= 15

3. Answer :

Step 1 :

The first natural number which is a multiple of 7 is 7.

The next numbers which are the multiples of 7 are

14, 21, 28, ........

Step 2 :

Write the first twenty natural numbers which are the multiples of 7.

7, 14, 21, 28, ........ to 20 terms

Step 3 :

Find the sum of all the above numbers. 

= 7 + 14 + 21 + 28 + ......... to 20 terms

= 7(1 + 2 + 3 + 4 +......... to 20 terms)

= 7(1 + 2 + 3 + 4 +......... + 20)

Using 1 + 2 + 3 + ........ + n = n(n + 1)/2, 

= 7[20(20 + 1)/2]

= 7[10(21)]

= 7[210]

= 1470

Step 4 : 

Average = (Sum of all 20 numbers)/20 

= 1470/20

= 73.5 

4. Answer :

Step 1 :

Let x be the smallest of four consecutive odd numbers. 

Then the four consecutive odd numbers are

x, x + 2, x + 4, x + 6 

Step 2 :

Given : Average of the four consecutive odd numbers is 10. 

(x + x + 2 + x + 4 + x + 6)/4 = 10

(4x + 12)/4 = 10 

Multiple each side by 4. 

4x + 12 = 40

Subtract 12 from each side. 

4x = 28

Divide each side by 4.

x = 7

The smallest of four consecutive odd numbers is 7.

5. Answer :

Step 1 :

Let x be the number of boys and y be the number of girls. 

We have to find the ratio x : y. 

Step 2 :

Given : The average age of students in the class is 15.8 years.

(Sum of the ages  of all students)/no. of students = 15.8

(Sum of the ages of all students)/(x + y) = 15.8

Sum of the ages of all students = 15.8(x + y) ----(1)

Step 3 :

Given : The average age of boys of in the class is 16.4 years.

(Sum of the ages of all boys)/no. of boys = 16.4

(Sum of the ages of all boys)/x = 16.4

Sum of the ages of all boys = 16.4x ----(2)

Step 4 : 

Given : The average age of girls of in the class is 15.4 years.

(Sum of the ages of all girls)/no. of boys = 15.4

(Sum of the ages of all girls)/y = 15.4

Sum of the ages of all girls = 15.4y ----(3)

Step 4 : 

Sum of the ages of boys and girls is equal to the total ages of all students

(2) + (3) = (1)

16.4x + 15.4y = 15.8(x + y)

16.4x + 15.4y = 15.8x + 15.8y

Simplify.

0.6x = 0.4y

x/y = 0.4/0.6

x/y = 4/6

x/y = 2/3

x : y = 2 : 3

The ratio of the number of boys to the number of girls in the class is 2 : 3. 

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.