The mean age of a family of 6 members is 25 years. What will the mean age of the family be after a 45 year old member leaves?
Understand the Problem
The question is asking to calculate the new mean age of a family after one member leaves. Initially, the family has 6 members with a mean age of 25 years. A 45-year-old member leaves, and we need to determine the mean age of the remaining 5 members.
Answer
21 years
Answer for screen readers
(b) 21 years
Steps to Solve
- Calculate the total age of the family initially
The mean age is the sum of the ages divided by the number of members. So, the total age of the family is the mean age multiplied by the number of family members. Total age $= \text{mean age} \times \text{number of members}$ Total age $= 25 \times 6 = 150$
- Calculate the total age of the family after one member leaves
Since a 45-year-old member leaves, we subtract 45 from the total age of the family. New total age $= \text{Original total age} - \text{Age of member who left}$ New total age $= 150 - 45 = 105$
- Calculate the new mean age of the family
Now that we have the new total age and the new number of family members (which is 5), we can find the new mean age. New mean age $= \frac{\text{New total age}}{\text{New number of members}}$ New mean age $= \frac{105}{5} = 21$
(b) 21 years
More Information
The mean age of the family after a 45-year-old member leaves is 21 years.
Tips
A common mistake is to forget to adjust the number of family members after one leaves. Another mistake might be subtracting the age of the leaving member from the mean instead of the total age.
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