AIN3701 ASSESSMENT 4 Ac/vity 5,8 Due 14 August 2023
This is a guidance on how to answer ASSESSMENT 4 Ac/vity 5,8
Before proceeding, it is important to note that plagiarism is a serious offence, and users must
not copy this solu/on in its en/rety. Instead, this solu/on should only be used as a guide,
and users should incorporate their own style of response in line with their school guide.
Furthermore, users should write their own findings and not replicate the provided text.
To ensure that all requirements are met, it is recommended that users employ a rubric to
check if all expecta/ons are sa/sfied.
I. Introduction
The maintenance department of our company plays a pivotal role in ensuring the smooth
operation of our production lines. As our product managers presented their annual budgets, it
became evident that there was a discrepancy in the calculation of maintenance fees. The standard
practice had been to use a flat rate for maintenance service per machine. However, the complexity
of maintenance tasks, especially concerning the ovens, and the variability in staff availability
necessitate a more nuanced approach to costing.
II. Problem Statement
The current flat rate of R130 for maintenance service per machine does not accurately reflect the
actual maintenance costs incurred by the department. This discrepancy may lead to budgeting
inaccuracies and potential underfunding of critical maintenance activities.
III. Descriptive Statistics
We'll provide a statistical summary of the data, which includes measures like mean, median,
standard deviation, and range for each column in the data.
Summarised statistics for the provided data:
Metric Output Nr employees Direct labour Total cost (R
hours
Count 12 12 12 12
Mean 525.83 35.00 5,510 70,800
Std Dev 222.73 4.805 1,231.10 21,191.68
Min 250 28 3,960 43,626.67
25% 315 31.50 4,645 53,213.33
Median 515 34 5,135 69,320
75% 757.5 39.50 6,600 91,860
Max 820 41 7,300 101,066.67
IV. Commentary on Descriptive Statistics
, 1. Output: On average, 525.83 machines are serviced each month, with a variation (standard
deviation) of about 222.73 machines.
2. Nr employees: The mean number of employees available for maintenance is 35, with a
variation of approximately 4.8 employees.
3. Direct labour hours: The average direct labour hours spent on maintenance monthly is 5,510
hours, with a standard deviation of 1,231.10 hours.
4. Total cost: The average monthly maintenance cost is R70,800, with a standard deviation of
R21,191.68, highlighting a significant fluctuation in monthly costs.
The widespread in data, especially in 'Output' and 'Total cost', signifies variability in the number of
machines serviced and the associated costs. It underscores Mr. Mashaba's assertion that a flat
maintenance fee does not truly represent the actual costs incurred.
V. Scatterplots
a. Relationship between Output and Total Cost
The scatterplot illustrates the relationship between the number of machines serviced (Output) and
the Total Cost. A positive trend is visible, indicating that as the number of machines serviced
increases, the total cost also rises. The coefficient of determination (\( R^2 \)) is 0.90, suggesting
that approximately 90% of the variance in the Total Cost can be explained by the number of
machines serviced.
*b. Relationship between Number of Employees and Total Cost
The scatterplot showcases the relationship between the number of employees and the Total Cost.
Again, a positive trend is observed, indicating that as the number of employees increases, the total
cost also goes up. The coefficient of determination (\( R^2 \)) for this relationship is 0.83, implying
that about 83% of the variance in the Total Cost can be attributed to the number of employees.
This is a guidance on how to answer ASSESSMENT 4 Ac/vity 5,8
Before proceeding, it is important to note that plagiarism is a serious offence, and users must
not copy this solu/on in its en/rety. Instead, this solu/on should only be used as a guide,
and users should incorporate their own style of response in line with their school guide.
Furthermore, users should write their own findings and not replicate the provided text.
To ensure that all requirements are met, it is recommended that users employ a rubric to
check if all expecta/ons are sa/sfied.
I. Introduction
The maintenance department of our company plays a pivotal role in ensuring the smooth
operation of our production lines. As our product managers presented their annual budgets, it
became evident that there was a discrepancy in the calculation of maintenance fees. The standard
practice had been to use a flat rate for maintenance service per machine. However, the complexity
of maintenance tasks, especially concerning the ovens, and the variability in staff availability
necessitate a more nuanced approach to costing.
II. Problem Statement
The current flat rate of R130 for maintenance service per machine does not accurately reflect the
actual maintenance costs incurred by the department. This discrepancy may lead to budgeting
inaccuracies and potential underfunding of critical maintenance activities.
III. Descriptive Statistics
We'll provide a statistical summary of the data, which includes measures like mean, median,
standard deviation, and range for each column in the data.
Summarised statistics for the provided data:
Metric Output Nr employees Direct labour Total cost (R
hours
Count 12 12 12 12
Mean 525.83 35.00 5,510 70,800
Std Dev 222.73 4.805 1,231.10 21,191.68
Min 250 28 3,960 43,626.67
25% 315 31.50 4,645 53,213.33
Median 515 34 5,135 69,320
75% 757.5 39.50 6,600 91,860
Max 820 41 7,300 101,066.67
IV. Commentary on Descriptive Statistics
, 1. Output: On average, 525.83 machines are serviced each month, with a variation (standard
deviation) of about 222.73 machines.
2. Nr employees: The mean number of employees available for maintenance is 35, with a
variation of approximately 4.8 employees.
3. Direct labour hours: The average direct labour hours spent on maintenance monthly is 5,510
hours, with a standard deviation of 1,231.10 hours.
4. Total cost: The average monthly maintenance cost is R70,800, with a standard deviation of
R21,191.68, highlighting a significant fluctuation in monthly costs.
The widespread in data, especially in 'Output' and 'Total cost', signifies variability in the number of
machines serviced and the associated costs. It underscores Mr. Mashaba's assertion that a flat
maintenance fee does not truly represent the actual costs incurred.
V. Scatterplots
a. Relationship between Output and Total Cost
The scatterplot illustrates the relationship between the number of machines serviced (Output) and
the Total Cost. A positive trend is visible, indicating that as the number of machines serviced
increases, the total cost also rises. The coefficient of determination (\( R^2 \)) is 0.90, suggesting
that approximately 90% of the variance in the Total Cost can be explained by the number of
machines serviced.
*b. Relationship between Number of Employees and Total Cost
The scatterplot showcases the relationship between the number of employees and the Total Cost.
Again, a positive trend is observed, indicating that as the number of employees increases, the total
cost also goes up. The coefficient of determination (\( R^2 \)) for this relationship is 0.83, implying
that about 83% of the variance in the Total Cost can be attributed to the number of employees.
