Question

In a large town there are three sports clubs. Here is some information about the ages of the people who belong to each club.

Club	Number of people	Mean age (years)	Age range (years)	Age of youngest person (years)
Football	46	24	23	9
Swimming	32	29	32	7
Athletics	23	18	11	12

Use the information in the table to answer these questions. Give reasons for your answers.
a. Work out the age of the oldest person in each club.
b. Which club has the highest average age?
c. Which club has the greatest variation in ages?

Answer 1

Hint: We will first calculate the age of the oldest person by adding the age of the youngest person to the corresponding range of ages. Next, we have to find the highest average age which is equal to the mean age, so just find the club which has the highest mean age from the given data. Also, the greatest variation is the highest range, which can be seen from the given data.

Complete step by step answer:

(i) We are given that the age of the youngest person in the football club is 9 years and the range of the ages is 23 years.
The range is the difference between the highest and the lowest value.
Therefore, the age of the oldest person in football is calculated by adding the age of the youngest person to the range.
Hence, age of oldest person is $23 + 9 = 31$years
Next, we will calculate the age of the oldest person in the Swimming Club.
The youngest age of the person is 7 and the range of age is 32.
Hence, the age of the oldest person in the Swimming club is $32 + 7 = 39$ years.
Similarly, we have the age of the youngest person in the Athletics club as 12 years and the range of ages is 11 years.
So, the age of the oldest person is $12 + 11 = 23$ years.
(ii) From the given data, the highest average age is of the Swimming Club, which is 29 years.
(iii) Next, we are asked to find out the sports club with the greatest variation in ages.
That is, we have to find a club which has the largest range of age.
From the given data, we can see the maximum range is of the Swimming Club, thus it has the greatest variation in ages.


Note: The range is calculated by subtracting the lowest value from the highest value. The data with the highest range has the greatest variation. The mean is the average of the numbers. It is calculated by dividing the sum of all the quantities by the total number of quantities.