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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...

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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 – 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 – 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 – [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 cu
ent 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.
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 – 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
iefly explain why this would be useful.
(v) Compare the standard deviation for Rock ‘n’ 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 – [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 – 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. Cox’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]
Answered Same Day May 02, 2020

Solution

Shakeel answered on May 06 2020
126 Votes
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 – 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 – 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–[50 marks].
Comfort Care is the parent company of a number of themed hotels. You are employed at the Rock ‘n’ Rollhotel 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 ‘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)
The frequency distribution graph (histogram) is negatively skewed. Most of the employees have salary of lower range.
(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.
(10marks)
    Mean salary (A)
    Number of employees (B)
    (A)*(B)
    275
    15
    4125
    325
    13
    4225
    375
    12
    4500
    425
    8
    3400
    475
    4
    1900
    525
    2
    1050
    575
    2
    1150
    Sum
    56
    20350
    
    
    
    Mean
    20350/56
    363.39
    Mean salary (x)
    (x - mean)^2
    Number of employees (f)
    f*(x - mean)^2
    275
    7812.7921
    15
    117,191.88
    325
    1473.7921
    13
    19,159.30
    375
    134.7921
    12
    1,617.51
    425
    3795.7921
    8
    30,366.34
    475
    12456.7921
    4
    49,827.17
    525
    26117.7921
    2
    52,235.58
    575
    44778.7921
    2
    89,557.58
    Mean =363.39
    Sum
    56
    359,955.36
    
    
    
    
    Standard Deviation
    359,955.36/56
    80.17
    
    
    
    
    
    Salary (£ per week)
    Number of employees
    First Quartile, Q1
    
    
    250 but under 300
    15
    
    
    300 but under 350
    13
    
    Median Group
    
    350 but under 400
    12
    3rd Quartile, Q3
    
    
    400 but under 450
    8
    
    
    450 but under 500
    4
    
    
    500 but under 550
    2
    
    
    550 but under 600
    2
    
    
    
    
    Median
    =350.5+(((56/2)-28)/12)*50
    350.5
    Q1
    =250.5+(((56/4)-0)/15)*50
    297.17
    Q2
    =400.5+(((3*56/4)-40)/8)*50
    413
The summarize form of descriptive statistics is as follows:
    Mean
    363.39
    Standard Deviation
    80.17
    Median
    350.50
    Q1
    297.17
    Q3
    413.00
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)
Semi-interquartile range    =    (420 - 310) / 2
                =    55
Average weekly total salary    =    380*160
                =    Â£60,800
The distribution of weekly salary is left skewed as mean salary is greater than median salary.
c)
(i) Draw up a table of your results for each company easily allowing your manager to compare results for both hotels.
    
    Roll hotel
    Oriental hotel
    Mean salary per week
    Â£363.39
    Â£380.00
    Median salary per week
    Â£350.50
    Â£350.00
    Lower quartile
    Â£297.17
    Â£310.00
    Upper quartile
    Â£413.00
    Â£420.00
    Standard Deviation
    Â£80.17
    Â£110.00
    Number of employees
    56.00
    160.00
(ii)...
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