Question

the first group of students consists of 10 and their average age was 13 years old the next group consisted of 30 students and their average was 9 years old find the average age of both groups?

Answer 1

Answer: The average was 9 years old find the average age of both groups is 10 years old.

Explanation:

Formula foe average :
`\text{Average} =\frac{\text{Sum of all observations}}{\text{Number of observations}}`

Given : The first group of students consists of 10 and their average age was 13 years old.

i.e.
`13=\frac{\text{Sum of ages of students of first group}}{10}\\\\\Rightarrow\ \text{Sum of ages of students of first group}=13*10=130` (1)

The next group consisted of 30 students and their average was 9 years old.

i.e.
`9=\frac{\text{Sum of ages of students of next group}}{30}\\\\\Rightarrow\ \text{Sum of ages of students of nextgroup}=9*30=270` (2)

Then from (1) and (2) , the sum of both groups (first group and next group )students = 130+270 =400

Combined students of both groups (first and next group )= 10+30=40

Now , the average of both groups =
`\frac{\text{Sum of combined students}}{\text{combined students}}`

`=(400)/(40)=10`

Hence, the average was 9 years old find the average age of both groups is 10 years old.