Statistic Problems on Aging of members of a club or group October 25, 2003
The following are problems that I have started to give to my statistics class. The problems
are based on my premise that in order for a club or a group to survive, it must maintain the
average age of its members constant, or reduce the average age. Any club failing to do so
is doomed. This premise holds for average ages in the region ≥50
Miguel Melgar
1. A social club of 50 people has an average age of its members at 65.3 years. A year
later, the oldest member of the club, age 89, died. What age should the new replacing
member of the club in order for the average age to remain at 65.3?
2. A social club of 100 people has an average age of its members of 70 years. The
oldest member, age 90, died. What is the average age of the remaining members?
3. A social club of 100 people has an average age of its members of 70 years. How
many new members of 35 years age must be recruited to reduce the average age to last
year’s 69 or below?
4. In problem 3, how many new members of age 50 years must be recruited to reduce
the average age to last year’s 69 or below?
5. Finally, a younger president was elected at a social club. The club has 100
members, with an average age of 76. The new president has declared that she is going to
start a campaign to recruit new younger members. She wants to double the membership
and bring the average age of the club members to 65. What is the maximum average age
of the new members in order to accomplish this goal?
6. In problem 6 the president also considered recruiting new members with an average
age of 50 years. How many new members would the club need in order to bring the
average age of the club member down to 65?
7. In problem 6 the new president failed to bring the average age down to 65. She
succeeded in increasing the membership by 50 and the average age of the new members
was 60 years. What was the new average age of the total members of the club?
8 The average age of a group of 6 tennis players was 72 years. About a year later the
84 year old player retires from the group because of illness. What is the maximum age that
should the replacement be in order to keep the average age at 72, that was the previous
year, or below.
The following are problems that I have started to give to my statistics class. The problems
are based on my premise that in order for a club or a group to survive, it must maintain the
average age of its members constant, or reduce the average age. Any club failing to do so
is doomed. This premise holds for average ages in the region ≥50
Miguel Melgar
1. A social club of 50 people has an average age of its members at 65.3 years. A year
later, the oldest member of the club, age 89, died. What age should the new replacing
member of the club in order for the average age to remain at 65.3?
2. A social club of 100 people has an average age of its members of 70 years. The
oldest member, age 90, died. What is the average age of the remaining members?
3. A social club of 100 people has an average age of its members of 70 years. How
many new members of 35 years age must be recruited to reduce the average age to last
year’s 69 or below?
4. In problem 3, how many new members of age 50 years must be recruited to reduce
the average age to last year’s 69 or below?
5. Finally, a younger president was elected at a social club. The club has 100
members, with an average age of 76. The new president has declared that she is going to
start a campaign to recruit new younger members. She wants to double the membership
and bring the average age of the club members to 65. What is the maximum average age
of the new members in order to accomplish this goal?
6. In problem 6 the president also considered recruiting new members with an average
age of 50 years. How many new members would the club need in order to bring the
average age of the club member down to 65?
7. In problem 6 the new president failed to bring the average age down to 65. She
succeeded in increasing the membership by 50 and the average age of the new members
was 60 years. What was the new average age of the total members of the club?
8 The average age of a group of 6 tennis players was 72 years. About a year later the
84 year old player retires from the group because of illness. What is the maximum age that
should the replacement be in order to keep the average age at 72, that was the previous
year, or below.
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