The mean age of 5 people in a room is 40 years.
A person enters the room.
The mean age is now 37.
What is the age of the person who entered the room?
Answers
Required Answer :
The age of the person who entered the room = 22 years
Given :
- Mean age of 5 people in a room = 40 years
- Mean becomes 37 after a person enters the room
To find :
- The age of person who entered the room
Concept :
Here, in this question we are given the mean age of 5 people which is 40 years and the new mean after a person enters the room is 37. We need to calculate the age of person who entered the room. So, for that firstly we will calculate the sum of the ages of the 5 people present in the room by using the formula of mean. Then to calculate the age of the person who entered the room, we will add any variable to the sum of the ages of the 5 persons. That variable will be the assumed age of the person who entered the room. So, by using the formula of mean we will get the value of that variable and hence it will be our required answer.
Formula of mean :
- Mean = Sum of the observations ÷ No. of observations
Solution :
Calculating the sum of ages of 5 persons :
⇒ Mean = Sum of ages ÷ No. of person
⇒ 40 = Sum of ages ÷ 5
⇒ 40 × 5 = Sum of ages
⇒ 200 = Sum of ages
- The sum of ages of the 5 persons = 200
Let the age of the person who entered the room be x years.
⇒ Sum of ages of 6 persons = 200 + x
⇒ No. of persons = 6
⇒ New mean = 37
⇒ Mean = Sum of ages of 6 persons ÷ No. of persons
⇒ 37 = (200 + x) ÷ 6
⇒ 37 × 6 = 200 + x
⇒ 222 = 200 + x
⇒ 222 - 200 = x
⇒ 22 = x
Therefore, the age of the person who entered the room = x = 22 years