The mean age of a family of 6 members is 25 years. What is the mean age of the family after a 45 year old member leaves?
Understand the Problem
The question asks to calculate the new mean age of a family after one member leaves. We start by finding the total age of the family, subtract the age of the leaving member, and then divide by the new number of family members to find the new mean age.
Answer
(b) 21 years
Answer for screen readers
(b) 21 years
Steps to Solve
- Calculate the initial total age
To find the total initial age of the family, multiply the mean age by the number of family members: $ \text{Total age} = \text{Mean age} \times \text{Number of members}$
$ \text{Total age} = 25 \times 6 = 150 $
- Subtract the age of the leaving member
Subtract the age of the member who leaves from the total age: $ \text{New total age} = \text{Total age} - \text{Age of leaving member} $
$ \text{New total age} = 150 - 45 = 105 $
- Calculate the new number of family members
Subtract 1 from the original number of members: $ \text{New number of members} = \text{Original number of members} - 1 $
$ \text{New number of members} = 6 - 1 = 5 $
- Calculate the new mean age
Divide the new total age by the new number of members: $ \text{New mean age} = \frac{\text{New total age}}{\text{New number of members}} $
$ \text{New mean age} = \frac{105}{5} = 21 $
(b) 21 years
More Information
The new mean age of the family is 21 years. This is lower than the original mean age because the member who left was older than the original mean age.
Tips
A common mistake is forgetting to reduce the number of family members after one member leaves. Also, one might mistakenly add the age of the leaving member instead of subtracting it.
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