Statistics Assignment
You must answer all parts of this assignment
This assignment is marked out of a total of 100.
Semester 2 (b) 2017 / 2018
IMPORTANT INFORMATION
Your answers should be produced in a single word processed document, with any charts produced being copied into this document, and a summary of the results of any calculations that you have made being put into a suitable table. Your spreadsheet should also be submitted, as evidence your use of formulae.
For each part, your answers are being presented to your manager, and whilst a formal report format is not required, you must take care with the presentation, spelling and grammar, as in each section there are marks for this â€“ are the results presented in a format that is suitable for your manager to read and fully understand?
Word counts have been included in some parts to give you an idea of the amount that you should be writing â€“ they are NOT marked to and you do not need to state the number of words that you have used.
A spreadsheet is provided (see Blackboard) which contains some of the basic information. Please save this spreadsheet with your student id as the file name, and add the remaining calculations.
Question 1 â€“ [50 marks].
Comfort Care is the parent company of a number of themed hotels. You are employed at the Rock â€˜nâ€™ Roll hotel and have been given the task by your manager, Mr. Bolan, of analysing the salary distributions of employees for the cu
ent year. The hotel employs staff on a full-time, part-time and seasonal basis.
The following data was collated for Rock â€˜nâ€™ Roll:
Salary (Â£ 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.
XXXXXXXXXXMarks)
(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 Â£380
Median salary per week Â£350
Lower quartile Â£310
Upper quartile Â£420
Standard deviation Â£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 â€“ a colleague has calculated the mean for Rock â€˜nâ€™ Roll as Â£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
iefly explain why this would be useful.
(v) Compare the standard deviation for Rock â€˜nâ€™ Roll and Oriental and
iefly 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. XXXXXXXXXXmarks)
Question 2 â€“ [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 wo
ied 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 inco
ect. He has provided you with the following quarterly data of occupancy levels (%) for the past few years:
Yea
Quarte
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 â€“ see below:
All of this data is in your provided spreadsheet
Using this graph, determine the model to use and explain your choice. You need to copy in the graph to show how you a
ived at this answer.
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]
Draw and label 3 projected trend lines on your graph and put a copy of this graph into your report.
Use the values that you have read from these lines to produce 3 different forecasts for the remainder of XXXXXXXXXXPut these results (forecasts ONLY) in a suitable table in your report.
[8 marks]
Write an assessment of the accuracy of your forecasts including an identification of at least 4 random factors that may affect cover levels.
Write an overall conclusion of your analysis that addresses Mr. Coxâ€™s opinion that the occupancy levels are declining. Clearly explain why you either agree or disagree with him.
[15 marks]
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
Othe
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]
Occupancy percentage for Stargazer Hotel
Data 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 2013 2014 2015 2016 2017 60.0 78.0 70.0 58.0 62.0 82.0 72.0 60.0 65.0 85.0 72.0 61.0 67.0 87.0 76.0 68.0 Trend 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 2013 2014 2015 2016 2017 66.75 67.5 68.25 68.75 XXXXXXXXXX XXXXXXXXXX 70.5 XXXXXXXXXX 71.0 71.5 72.25 XXXXXXXXXX Year / Quarte
Percentage
1
[Type text]