Answer: The average was 9 years old find the average age of both groups is 10 years old.
Step-by-step explanation:
Formula foe average : [tex]\text{Average} =\dfrac{\text{Sum of all observations}}{\text{Number of observations}}[/tex]
Given : The first group of students consists of 10 and their average age was 13 years old.
i.e. [tex]13=\dfrac{\text{Sum of ages of students of first group}}{10}\\\\\Rightarrow\ \text{Sum of ages of students of first group}=13\times10=130[/tex] (1)
The next group consisted of 30 students and their average was 9 years old.
i.e. [tex]9=\dfrac{\text{Sum of ages of students of next group}}{30}\\\\\Rightarrow\ \text{Sum of ages of students of nextgroup}=9\times30=270[/tex] (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 =[tex]\dfrac{\text{Sum of combined students}}{\text{combined students}}[/tex]
[tex]=\dfrac{400}{40}=10[/tex]
Hence, the average was 9 years old find the average age of both groups is 10 years old.
