The names and ages for each person in a family of five follow:
Name Jane Kirk Jean Scott
Age 40 36 8 6 2
a. What is the mean age?
b. Find the mean of the ages 5 yr from now.
c. Find the mean 10 yr from now.
d. Describe the relationships among the means found in
(a), (b), and (c).
a. (40 + 36 + 8 + 6 + 2)/5 = ____
(It will not be an integer)
b. If everybody's age increases by 5, so does the average
c. Apply similar logic
d. If everybody's age increases by N, so does the average
Since we are dealing with a fractional average, the ages should have been given to the nearest tenth year. The computed average is probably low. A person who is "6" for example, could actually be 6.9 years old.
a. To find the mean age, you need to add up all the ages and divide by the total number of people.
Total age = 40 + 36 + 8 + 6 + 2 = 92
Number of people = 5
Mean age = Total age / Number of people = 92 / 5 = 18.4
b. To find the mean of the ages 5 years from now, you need to add 5 to each age, then find the new mean.
Age 5 years from now: 45, 41, 13, 11, 7
Total age (5 years from now) = 45 + 41 + 13 + 11 + 7 = 117
Number of people = 5
Mean age (5 years from now) = Total age (5 years from now) / Number of people = 117 / 5 = 23.4
c. To find the mean 10 years from now, you need to add 10 to each age, then find the new mean.
Age 10 years from now: 50, 46, 18, 16, 12
Total age (10 years from now) = 50 + 46 + 18 + 16 + 12 = 142
Number of people = 5
Mean age (10 years from now) = Total age (10 years from now) / Number of people = 142 / 5 = 28.4
d. The mean age is 18.4, the mean age 5 years from now is 23.4, and the mean age 10 years from now is 28.4. As time progresses, the mean age increases, indicating that the family members are getting older. The differences between the means in parts (a), (b), and (c) correlate with the amount of time added to the ages.
To find the mean age, add up all the ages and divide by the total number of people in the family:
a. The mean age = (40 + 36 + 8 + 6 + 2) / 5 = 92 / 5 = 18.4 years
b. To find the mean of the ages 5 years from now, we need to add 5 to each age first and then calculate the mean:
40 + 5 = 45
36 + 5 = 41
8 + 5 = 13
6 + 5 = 11
2 + 5 = 7
The mean of the ages 5 years from now = (45 + 41 + 13 + 11 + 7) / 5 = 117 / 5 = 23.4 years
c. Similarly, to find the mean of the ages 10 years from now, add 10 to each age first and then calculate the mean:
40 + 10 = 50
36 + 10 = 46
8 + 10 = 18
6 + 10 = 16
2 + 10 = 12
The mean of the ages 10 years from now = (50 + 46 + 18 + 16 + 12) / 5 = 142 / 5 = 28.4 years
d. The relationships among the means found in (a), (b), and (c) show that as time progresses, the mean age increases. The mean age gives an average representation of the current ages, while the mean of ages in the future represents the average ages after a certain amount of time has passed. As time goes on, the mean age will continue to increase.