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 need to add up all the ages and then divide by the 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 need to subtract each employee's age from the mean age:
Tom: 45 - 29 = 16
Melissa: 32 - 29 = 3
Rebecca: 26 - 29 = -3
Amber: 23 - 29 = -6
Jonathan: 19 - 29 = -10
To find the absolute deviation from the mean for each employee, we need to take the absolute value of the deviation:
Tom: |16| = 16
Melissa: |3| = 3
Rebecca: |-3| = 3
Amber: |-6| = 6
Jonathan: |-10| = 10
Therefore, the deviation from the mean and absolute deviation from the mean for each employee are:
Name Deviation from mean Absolute deviation from mean
Tom 16 16
Melissa 3 3
Rebecca -3 3
Amber -6 6
Jonathan -10 10
C. To find the mean absolute deviation for the data set, we need to add up all the absolute deviations from the mean and then divide by the 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.
Can anybody tell me, in steps, how to calculate mean absolute deviation?
Certainly, here are the steps to calculate the mean absolute deviation for a data set:
1. Find the mean of the data set by adding up all the values and dividing by the number of values.
2. For each value in the data set, subtract the mean. This will give you the deviation from the mean for each value.
3. Take the absolute value of each deviation. This will give you the absolute deviation from the mean for each value.
4. Add up all the absolute deviations from step 3.
5. Divide the sum of the absolute deviations by the number of values in the data set. This will give you the mean absolute deviation.
The formula for mean absolute deviation is:
Mean absolute deviation = ( Σ | Xi - X | ) / N
Where:
Σ = sum of
Xi = each value in the data set
X = mean of the data set
N = number of values in the data set
A. To calculate the mean age for the data set, you need to add up all the ages and divide the sum by the total number of employees. In this case, you have 5 employees.
Adding up the ages:
45 + 32 + 26 + 23 + 19 = 145
Calculating the mean age:
Mean age = Sum of ages / Number of employees
Mean age = 145 / 5
Mean age = 29
Therefore, the mean age for the data set is 29.
B. To calculate the deviation from the mean for each employee, you need to subtract the mean age from each employee's individual age. The deviation from the mean represents how much each employee's age differs from the average.
Deviation from the mean and absolute deviation for each employee:
For Tom:
Deviation from the mean = 45 - 29 = 16
Absolute deviation from the mean = |16| = 16
For Melissa:
Deviation from the mean = 32 - 29 = 3
Absolute deviation from the mean = |3| = 3
For Rebecca:
Deviation from the mean = 26 - 29 = -3
Absolute deviation from the mean = |-3| = 3
For Amber:
Deviation from the mean = 23 - 29 = -6
Absolute deviation from the mean = |-6| = 6
For Jonathan:
Deviation from the mean = 19 - 29 = -10
Absolute deviation from the mean = |-10| = 10
C. To calculate the mean absolute deviation for the data set, you need to find the average of the absolute deviations from the mean for each employee.
Calculating the mean absolute deviation:
Mean absolute deviation = (Sum of absolute deviations) / Number of employees
Mean absolute deviation = (16 + 3 + 3 + 6 + 10) / 5
Mean absolute deviation = 38 / 5
Mean absolute deviation = 7.6
Therefore, the mean absolute deviation for the data set is 7.6.