Given:
The mean age of 5 people in a room is 26 years.
A person enters the room. The mean age is now 33.
To find:
The age of the person who entered the room.
Solution:
Formula for mean:
[tex]\text{Mean}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}[/tex]
The mean age of 5 people in a room is 26 years.
[tex]26=\dfrac{\text{Sum of ages of 5 people}}{5}[/tex]
[tex]26\times 5=\text{Sum of ages of 5 people}[/tex]
[tex]130=\text{Sum of ages of 5 people}[/tex]
The mean age is now 33. It means, the mean age of 6 people is 33.
[tex]33=\dfrac{\text{Sum of ages of 6 people}}{6}[/tex]
[tex]33\times 6=\text{Sum of ages of 6 people}[/tex]
[tex]198=\text{Sum of ages of 6 people}[/tex]
Now, the age of the person who entered the room is
Required age = Sum of ages of 6 people - Sum of ages of 5 people
= [tex]198-130[/tex]
= [tex]68[/tex]
Therefore, the age of the person who entered the room is 68 years.
