An orchestra consists of 25 members. The youngest member is 32 years old. She leaves and is replaced by a new member who is 30 years old. By how much does the replacement change the average age of the members of the orchestra?

Question

An orchestra consists of 25 members.  The youngest member is 32 years old.  She leaves and is replaced by a new member who is 30  years old.  By how much does the replacement change the average age of the members of the orchestra?

kropot72 · Answer

Let the original average age of the members = x
Then the sum of the original ages = 25x
The new sum of the ages = 25x - 32 + 30 = 25x -2
The new mean is therefore
$$\frac{25x-2}{25}=x-0.08$$
The replacement reduces the aveage age of the members by 0.08 year.

kropot72 · Answer

average*