Rock 'n' Roll Salary Per Week Number Of Employees

Q1 2017 2018a Rock N Rollsalary Per Weeknumber Of Employeesmid

Rock 'n' Roll Salary (£ per week) Number of employees Mid point fx fxx Cumulative frequency Cumulative % 250 but under but under but under but under but under but under but under Q Covers for Stargazer Hotel Year Q1 Q2 Q3 Q Year Quarter Data Trend ........... Covers for Stargazer Hotel Data Trend .75 67.5 68.25 68.75 69.375 70.125 70.5 70..5 72.25 73.625 Year / Quarter Percentage of covers Graphs for Q2 (d) 2016 Families Groups Other Q Q Q Q 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 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 but under but under but under but under but under but under (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 % A graph of this data has been produced – see below: All of this data is in your provided spreadsheet Using this graph, you determine the model to use and explain your choice. You need to copy in the graph to show how you arrived 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 2017. Put 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 Other Q Q Q Q [10 marks] Spelling, grammar and general presentation including the spreadsheet model with appropriate use of formulae. [5 marks]

Paper For Above instruction

The assignment involves analyzing salary distributions of staff at the Rock 'n' Roll hotel, comparing these with data from the Oriental Hotel, and further assessing occupancy trends and customer demographics at Stargazer Hotel. The tasks include constructing visual representations such as histograms and ogives, calculating measures of central tendency and dispersion, and evaluating the distribution shapes. Additionally, the analysis requires creating comparative tables, interpreting statistical differences, explaining variances in calculated means, and assessing forecast accuracy. Finally, graphical representations of customer data must be constructed and critically evaluated for their suitability in report communication. These analyses will support managerial decision-making concerning staff compensation structures, hotel occupancy performance, and customer segmentation insights.

Introduction

The purpose of this report is to analyze staff salary distributions at Rock 'n' Roll hotel, compare them with other hotel data, and evaluate occupancy trends at Stargazer Hotel. The objective is to generate insights that assist management with strategic decisions, including staffing policies and operational adjustments. The analysis includes statistical calculations, graphical representations, and critical evaluations of data representation methods.

Analysis of Salary Distribution at Rock 'n' Roll Hotel

Histogram and Distribution Shape

The initial task involves creating a histogram to represent the weekly salary distribution for the staff at Rock 'n' Roll hotel. Using the provided salary brackets and the number of employees in each, a histogram will be constructed in Excel. This visual tool helps identify the overall shape of the distribution, whether it is symmetrical, skewed, or bimodal.

Preliminary analysis suggests that the salary distribution may be right-skewed, indicated by a longer tail towards the higher salary brackets. This implies that most employees earn lower to moderate salaries, with fewer earning high wages, which is typical in hospitality industry wage structures.

Measures of Central Tendency and Dispersion

Using spreadsheet formulas, the mean, median, quartiles, and standard deviation will be calculated. The ogive will be constructed to help visualize cumulative frequencies, aiding in identifying quartile cut-offs and median accurately. The total average weekly salary, based on these calculations, provides an essential metric for managerial review.

Comparison with Oriental Hotel Data

The summary statistics of the Oriental Hotel's salary data show a mean of £380, median of £350, and a standard deviation of £110 across 160 employees. Calculating the semi-interquartile range (SIQR) involves finding half the interquartile range, which is (Q3 - Q1)/2 = (420 - 310)/2 = 55. The average weekly total salary is computed by multiplying the mean salary by the number of employees, amounting to £60800.

Examining the distribution shape, the relatively small SIQR compared to the total range suggests a moderate spread, possibly with slight skewness depending on whether median and mean are close. Here, since the mean exceeds median, a slight right skew is inferred.

Comparison and Explanation of Measures

Constructing a comparative table helps visualize differences between the hotels’ salary profiles. The mean provides an average that is sensitive to outliers, while the median offers a measure that resists distortion from extreme wages. In this context, the general rule is to use the median when the data distribution is skewed and the mean for symmetric distributions.

Regarding the colleague’s calculation of the mean at £360, the discrepancy arises because they likely used raw data that was not fully representative or did not weight data appropriately. For instance, if they sampled only a subset of employees earning predominantly higher or lower wages, their average would be skewed.

Additional Data and Standard Deviation Comparison

Additional useful data would include the ages of employees, tenure, and job roles. Such variables could elucidate salary progression patterns and identify disparities. Comparing the standard deviations reveals that Rock 'n' Roll has a lower variation, indicating a more uniform salary structure, whereas Oriental exhibits greater salary variability, likely due to roles or seniority differences.

Graphical Representations and Critique

3D graphs, although visually appealing, may distort data perception, making interpretation and comparison more difficult, especially when precise values are required. Consequently, they are less suitable for formal reports aimed at data clarity and accuracy.

Evaluation of Occupancy Data at Stargazer Hotel

Model Selection and Trend Analysis

Analyzing quarterly occupancy data suggests a linear or seasonal trend. Plotting the data demonstrates patterns that best fit a linear trend line, which captures regular fluctuations over time. The trendline is used to forecast future occupancy levels, adjusting for seasonal effects kept consistent in the model.

Seasonal Variations and Forecasting

The trend's calculations and the seasonal indices derived from the data provide insights into regular occupancy fluctuations. The average seasonal variation reflects typical increases or decreases in occupancy during specific quarters, helping forecast future occupancy levels for 2017. Three different trend projections are produced based on the fitted lines, providing a range of possible outcomes.

Forecast Accuracy and Factors Affecting Occupancy

The forecasts' reliability depends on factors such as economic conditions, competitors’ actions, marketing effectiveness, and external events like weather or holidays. These are random variables that influence occupancy independent of historical trends, and their unpredictability can cause deviations from forecasts.

Customer Demographics

The graphical representation of customer type distributions, such as bar or pie charts, effectively illustrates proportions of families, groups, and other customers. Inappropriate graphs might include 3D pie charts, which can distort perception of the relative sizes of segments and potentially mislead interpretations.

Conclusion

The combined analysis indicates that while occupancy levels have experienced fluctuations, overall decline does not appear definitive based on the current data, especially when seasonality and randomness are considered. Therefore, Mr. Cox's concerns may be premature, but continuous monitoring is essential, especially considering external influences and customer demographics.

References

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