6 In a large town there are three sports clubs. Here is some information about the ages of the people
who belong to each club.
Age of youngest
Club Number of people Mean age (years)
Age range (years)
person (years)
Football
46
23
9
24
32
29
32
7
Swimming
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?
Answers
Answer: 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.
Step-by-step explanation: (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=31years
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.