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Lesson Example Discussion Quiz: Class Homework

Example

Title: Averages

Grade: 8-a Lesson: S3-L2

Explanation: Here are some examples of the topic with images and steps in sequence.

Examples:

Example: 1a

The average of 50 numbers is 20. If two numbers 37 and 43 are discarded, find the average of the remaining numbers.

Average of 50 numbers = 20
Sum of 50 numbers = \$20 \times 50 = 1000\$
Sum of discarded numbers = 37 + 43 = 80
Sum of remaining numbers = 1000 – 80 = 920
Now, total remaining numbers = 50 – 2 = 48
Average of remaining numbers = \$920 \div 48 = 19\$

Explanation: In the above problem, the average of 50 numbers is 20. If two numbers 37 and 43 are discarded, the average of the remaining numbers is 19.

Example: 2a

The average age of three boys is 15 years and their ages are in proportion of 3:5:7. What is the age in years of the youngest boy?

Average age of 3 boys = 15 years
Ages in proportion = 3:5:7
Let the age of youngest boy = x
Youngest boy age = \$(3x + 5x + 7x)/3\$ = 15
⇒ 15x = 45
⇒ x = \$45/15\$ =3
Age of the youngest boy is: 3x = 3(3) = 9 years

Explanation: In the above problem, the average age of three boys is 15 years and their ages are in proportion of 3:5:7. The age of the youngest boy is 9 years.

Example: 3a

Which is more, the average of the 4 even whole numbers from 8 to 15 or the average odd whole numbers from 8 to 15?

Average of 4 even numbers from 8 to 15 = \$(8 + 10 + 12 + 14)/4\$ = \$44/4\$ = 11
Average of 4 odd numbers from 8 to 15 = \$(9 + 11 + 13 + 15)/4\$ = \$48/4\$ = 12
Hence, the average of 4 odd whole numbers is more than 4 even whole numbers.

Explanation: In the above problem, the average 4 even numbers from 8 to 15 is 11 and average of 4 odd numbers from 8 to 15 is 12. Hence, the average of 4 odd whole numbers is more than 4 even whole numbers.