(i) Draw a histogram to represent this data and clearly identify the shape of the distribution and any implications that this may infer.

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Question 1 – [50 marks].

 

Comfort Care is the parent company of a number of themed hotels. You are employed at the Rock ‘n’ Roll hotel and have been given the task by your manager, Mr. Bolan, of analysing the salary distributions of employees for the current year. The hotel employs staff on a full-time, part-time and seasonal basis.

 

The following data was collated for Rock ‘n’ Roll:

 

Salary (£ per week)

Number of employees

250 but under 300

15

300 but under 350

13

350 but under 400

12

400 but under 450

8

450 but under 500

4

500 but under 550

2

550 but under 600

2

 

(i)                   Draw a histogram to represent this data and clearly identify the shape of the distribution and any implications that this may infer.

      (5 Marks)

(ii)                  

Determine by using a spreadsheet model and drawing an Ogive, a variety of averages and measures of dispersion (Mean, Standard Deviation, Median, Q1, Q3, SIR).  Calculate the total average weekly salary.  Place a copy of your Ogive in your report.

(10 marks)

       b)     The data for The Oriental Hotel was not provided but the following summary statistics were:

                                                Mean salary per week                        £380

                                                Median salary per week                     £350

                                                Lower quartile                                      £310      

                                                Upper quartile                                      £420

                                                Standard deviation                              £110

                                                Number of employees                        160

 

Determine the following additional summary statistics for this data: the semi-interquartile range and the average weekly total salary.  Identify the shape of the distribution, fully explaining your reasoning.

                                                                                                                                                                (5 marks)

c)

(i)                   Draw up a table of your results for each company easily allowing your manager to compare results for both hotels.

(ii)                 What is generally the difference between the mean and the median, and when should you use which one (use your own words)?  Compare and contrast the mean and median for the two hotels.

(iii)                Using raw data – a colleague has calculated the mean for Rock ‘n’ Roll as £360.  Explain why this is different to your calculated value.  Use a fully calculated example to help with your explanation.

(iv)                Recommend any additional data (information) that would be useful to improve the analysis, and briefly explain why this would be useful.

(v)                 Compare the standard deviation for Rock ‘n’ Roll and Oriental and briefly explain what this says about the distribution of salaries in the two hotels.  Relate this back to your answer for (ii).

(vi)                Explain why 3D graphs are not generally considered to be useful in formal reports.

 (25 marks)

 

All calculations (no matter how simple) should be done on and by the spreadsheet.  All diagrams must be drawn using Excel.  Formulae must be used where appropriate.                                                           (5 marks)

Question 2 – [50 marks].

 

You have been promoted and are now employed by Comfort Care at Stargazer Hotel. A new Chief Executive for the chain has made it clear that hotels not performing well, face the threat of closure. Your manager Mr. Cox is worried about this because he thinks Stargazer Hotel has declining occupancy levels, based on his observations of the last three quarters (see below).

He has given you the task of analysing some data with the hope that his impressions are incorrect. He has provided you with the following quarterly data of occupancy levels (%) for the past few years:

 

Year

Quarter

Occupancy %

2013

2

60

 

3

78

 

4

70

2014

1

58

 

2

62

 

3

82

 

4

72

2015

1

60

 

2

65

 

3

85

 

4

72

2016

1

61

 

2

67

 

3

87

 

4

76

2017

1

68

 

2

 
 

3

 
 

4

 

 

A graph of this data has been produced – see below:

 

 

 

 

All of this data is in your provided spreadsheet

 

 

 

(a)      

  1. Using this graph, determine the model to use and explain your choice.  You need to copy in the graph to show how you arrived at this answer.
  2. Using the provided spreadsheet, you will see that the trend has already been calculated.  Use this and your model choice to calculate the seasonal variation, then the average seasonal variation.  Briefly explain to Mr. Sweaty what each of the average seasonal variation values represents.

[12 marks]

(b)                    

  1. Draw and label 3 projected trend lines on your graph and put a copy of this graph into your report.
  2. Use the values that you have read from these lines to produce 3 different forecasts for the remainder of 2017.  Put these results (forecasts ONLY) in a suitable table in your report.

[8 marks]

(c)      

  1. Write an assessment of the accuracy of your forecasts including an identification of at least 4 random factors that may affect cover levels. 
  2. Write an overall conclusion of your analysis that addresses Mr. Cox’s opinion that the occupancy levels are declining.  Clearly explain why you either agree or disagree with him.

[15 marks]

 

(d)     The following data has been collected re the different types of customers staying at Stargazer Hotel.  Construct a suitable graph to show this data, and explain your choice of graph.  Also construct a graph(s) that is (are) unsuitable and clearly explain why.  All graphs to be copied into your report.

 

 

 

2016

Families

Groups

Other

Q1

250

65

52

Q2

405

130

95

Q3

575

145

106

Q4

290

105

80

 

[10 marks]

 

 

Spelling, grammar and general presentation including the spreadsheet model with appropriate use of formulae.

[5 marks]

 

 

 

 

 

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