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?
By how much does the replacement change the median age of the members of the orchestra?
To find the answer, we need to consider the average age and the median age of the members before and after the replacement.
1. Average Age:
Let's calculate the average age before the replacement. We know that the youngest member is 32 years old, so the total age before the replacement can be found by multiplying 32 by 25 (the number of members in the orchestra). This gives us 800.
To find the average age, we divide the total age by the number of members. So, 800 divided by 25 is 32. Therefore, the average age before the replacement is 32 years.
Now, let's calculate the average age after the replacement. We replace the youngest member (32 years old) with a new member who is 30 years old. This means the total age after the replacement is 800 - 32 + 30 = 798.
Again, we divide the total age by the number of members. So, 798 divided by 25 gives us 31.92. Therefore, the average age after the replacement is approximately 31.92 years.
To find the change in average age, we subtract the average age before the replacement from the average age after the replacement. Therefore, 31.92 - 32 = -0.08.
The replacement decreases the average age by approximately 0.08 years.
2. Median Age:
The median age is the middle value when the ages of all members are arranged in ascending order.
Before the replacement, the youngest member is 32 years old. Since the orchestra has an odd number of members (25), the median age is the age of the 13th member. Since the members' ages are not specified, we cannot calculate the exact median age.
After the replacement, the youngest member is replaced by a 30-year-old. In this case, since 25 is an odd number, the median age will still be the age of the 13th member. However, we cannot determine the exact value without more information.
Therefore, without additional information about the ages of the other members, we cannot calculate the change in the median age caused by the replacement.