Question

The following are the ages (years) of 5 people in a room:

17, 16, 15, 17, 22
A person enters the room.
The mean age of the 6 people is now 17.
What is the age of the person who entered the room

Answer 1

The age of the person who entered the room is 15

Explanation:

Ages of 5 people in a room are:

17, 16, 15, 17, 22

A person enters room, the mean age of 6 people is 17.

We need to find the age of person who entered the room.

We know that:
`Mean=(Sum\:of\:all\:data\:values)/(Number\:of\:data\:Values)`

Now, we have mean of 6 people that is 17

We know the age of 5 people while age of one person is unknown.

Let age of person which is unknown= x

So, we can write:

Sum of all data values = 17+16+ 15+ 17+ 22+x

where x is the age of person who enters the room.

Finding x

`Mean=(Sum\:of\:all\:data\:values)/(Number\:of\:data\:Values)\\17=(17+16+ 15+ 17+ 22+x)/(6)\\17=(87+x)/(6)\\17*6=87+x\\102=87+x\\x=102-87\\x=15`

So, we get the value of x: x=15

Therefore, the age of the person who entered the room is 15.