Question

The ages of 5 employees of a small business are shown in the table.
Name Age
Tom 45
Melissa 32
Rebecca 26
Amber 23
Jonathan 19
Calculate the following:
A. The mean age for the data set
B. The deviation from the mean and absolute deviation from the mean for each employee
C. The mean absolute deviation for the data set

Answer 1

A. To find the mean age, we add up all of the ages and divide by the total number of employees:

Mean age = (45 + 32 + 26 + 23 + 19) / 5 = 29

Therefore, the mean age for the data set is 29.

B. To find the deviation from the mean for each employee, we subtract the mean age from each employee's age:

Tom's deviation from the mean = 45 - 29 = 16
Melissa's deviation from the mean = 32 - 29 = 3
Rebecca's deviation from the mean = 26 - 29 = -3
Amber's deviation from the mean = 23 - 29 = -6
Jonathan's deviation from the mean = 19 - 29 = -10

To find the absolute deviation from the mean for each employee, we take the absolute value of their deviation:

Tom's absolute deviation = |16| = 16
Melissa's absolute deviation = |3| = 3
Rebecca's absolute deviation = |-3| = 3
Amber's absolute deviation = |-6| = 6
Jonathan's absolute deviation = |-10| = 10

C. To find the mean absolute deviation for the data set, we add up all of the absolute deviations and divide by the total number of employees:

Mean absolute deviation = (16 + 3 + 3 + 6 + 10) / 5 = 7.6

Therefore, the mean absolute deviation for the data set is 7.6.