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
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.
A. The mean age for the data set can be calculated by adding up all the ages and dividing by the total number of employees.
Mean age = (45 + 32 + 26 + 23 + 19) / 5 = 145 / 5 = 29
Therefore, the mean age for the data set is 29.
B. To find the deviation from the mean for each employee, we take the difference between each employee's age and the mean age.
Deviation from the mean for Tom = 45 - 29 = 16
Deviation from the mean for Melissa = 32 - 29 = 3
Deviation from the mean for Rebecca = 26 - 29 = -3
Deviation from the mean for Amber = 23 - 29 = -6
Deviation from the mean for Jonathan = 19 - 29 = -10
To calculate the absolute deviation from the mean for each employee, we disregard the sign (positive or negative) of the deviation.
Absolute deviation from the mean for Tom = |16| = 16
Absolute deviation from the mean for Melissa = |3| = 3
Absolute deviation from the mean for Rebecca = |-3| = 3
Absolute deviation from the mean for Amber = |-6| = 6
Absolute deviation from the mean for Jonathan = |-10| = 10
C. The mean absolute deviation for the data set is calculated by finding the average of the absolute deviations.
Mean absolute deviation = (16 + 3 + 3 + 6 + 10) / 5 = 38 / 5 = 7.6
Therefore, the mean absolute deviation for the data set is 7.6.
To calculate the mean age for the data set, you need to find the average of the ages. To do this, add up all the ages and then divide by the number of employees.
A. The mean age for the data set:
Add up the ages: 45 + 32 + 26 + 23 + 19 = 145
Now divide the sum by the number of employees (5):
Mean age = 145 / 5 = 29
So, the mean age for the data set is 29.
To calculate the deviation from the mean and the absolute deviation from the mean for each employee, you need to subtract the mean age from each individual age and then take the absolute value of the result.
B. Deviation from the mean and absolute deviation from the mean for each employee:
Tom: Deviation = 45 - 29 = 16, Absolute Deviation = |16| = 16
Melissa: Deviation = 32 - 29 = 3, Absolute Deviation = |3| = 3
Rebecca: Deviation = 26 - 29 = -3, Absolute Deviation = |-3| = 3
Amber: Deviation = 23 - 29 = -6, Absolute Deviation = |-6| = 6
Jonathan: Deviation = 19 - 29 = -10, Absolute Deviation = |-10| = 10
So, the deviation from the mean and absolute deviation from the mean for each employee are as follows:
Tom: Deviation = 16, Absolute Deviation = 16
Melissa: Deviation = 3, Absolute Deviation = 3
Rebecca: Deviation = -3, Absolute Deviation = 3
Amber: Deviation = -6, Absolute Deviation = 6
Jonathan: Deviation = -10, Absolute Deviation = 10
Finally, to calculate the mean absolute deviation for the data set, you need to find the average of the absolute deviations.
C. The mean absolute deviation for the data set:
Add up the absolute deviations: 16 + 3 + 3 + 6 + 10 = 38
Now divide the sum by the number of employees (5):
Mean absolute deviation = 38 / 5 = 7.6
So, the mean absolute deviation for the data set is 7.6.