Question

5 of 8

The mean age of 5 people in a room is 26 years.
A person enters the room.
The mean age is now 33.
What is the age of the person who entered the room?
years

Answer 1

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:

`\text{Mean}=\frac{\text{Sum of observations}}{\text{Number of observations}}`

The mean age of 5 people in a room is 26 years.

`26=\frac{\text{Sum of ages of 5 people}}{5}`

`26* 5=\text{Sum of ages of 5 people}`

`130=\text{Sum of ages of 5 people}`

The mean age is now 33. It means, the mean age of 6 people is 33.

`33=\frac{\text{Sum of ages of 6 people}}{6}`

`33* 6=\text{Sum of ages of 6 people}`

`198=\text{Sum of ages of 6 people}`

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

=
`198-130`

=
`68`

Therefore, the age of the person who entered the room is 68 years.