Answer To: Statistics Assignment You must answer all parts of this assignment This assignment is marked out of...
Shakeel answered on May 06 2020
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 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)
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 £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)
Semi-interquartile range = (420 - 310) / 2
= 55
Average weekly total salary = 380*160
= £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
£363.39
£380.00
Median salary per week
£350.50
£350.00
Lower quartile
£297.17
£310.00
Upper quartile
£413.00
£420.00
Standard Deviation
£80.17
£110.00
Number of employees
56.00
160.00
(ii)...