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Business Decision Making: Age Analysis and Fleet Maintenance

View Solution # 27141

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Assessment Title: Age Analysis and Fleet Maintenance

Learning Outcomes:
1 Use a variety of sources for collection of data
2 Apply a range of techniques to analyse data

Assessment Criteria:
1a Prepare a plan for the collection of primary and secondary data
1b describe survey methodology
2a Create information by summarising data using representative values
2b Analyse data using measures of dispersion
Calculate correlation coefficient and use to draw conclusions

PART ONE
A firm is comparing the structure of its workforce in the current year with that of five years ago, as shown in the table below.

Age Group (years) 5 years ago current year
Number in group number in group
25<30 2 5
30<35 6 10
35<40 8 13
40<45 13 28
45<50 15 21
50<55 35 12
55<60 12 8
60<65 9 3

The mean age and standard deviation of ages five years ago were
as follows :
Mean age 49.05 years
Standard deviation 8.45 years

Tasks
1. Calculate the mean age and the associated standard deviation for the current year.
2. Write a brief explanation of what the mean and the standard deviation values represent.
3. Compare your results from task 1 with the calculations for five years ago; saying why you think the means and standard deviations may have changed.
4. Draw an appropriate chart that will illustrate the changes in the age structure of the workforce over the five year period.

PART TWO
A company has a fleet of vehicles and is trying to predict the annual maintenance costs per vehicle. The following data have been supplied for a sample of vehicles.

Vehicle number Age in years (x) Maintenance cost (£) per annum (y)
1 2 600
2 8 1,320
3 6 1,000
4 8 1,200
5 10 1,500
6 4 840
7 4 900
8 2 680
9 6 1,040
10 10 1,400

Tasks
1.Produce a statistical measure to indicate the strength of the relationship between age and maintenance cost and comment on its meaning and significance.

2.Using the least squares technique, calculate the values of a and b in the equation y = a + bx, to allow managers to predict the likely maintenance cost, knowing the age of the vehicle.

3.Prepare a table of maintenance costs covering vehicles from 1 to 10 years of age, based on your calculations in task 2.

4.Estimate the maintenance costs of a 12 year old vehicle and comment on the validity of making such an estimate.

Solution

The attached file has all the answers to the questions presented in Part 1 and Part 2. An excel sheet is also attached which shows the calculations done to arrive at the results. Detailed analysis along with all the formulae are included in the solution.

No. of Words: 959 words Help

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Business Decision Making: Age Analysis and Fleet Maintenance

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