Question

5 of 8

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:

$\text{Mean}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}$

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

$26=\dfrac{\text{Sum of ages of 5 people}}{5}$

$26\times 5=\text{Sum of ages of 5 people}$

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

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

$33=\dfrac{\text{Sum of ages of 6 people}}{6}$

$33\times 6=\text{Sum of ages of 6 people}$

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

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.