Solutions
There are 11 variables in the dataset.
What is the type of data (Quantitative or Qualitative) for each of the columns (variables) in the dataset? If quantitative, is the data discrete or continuous? Neatly summarize your response in a table for all the columns (variables) in your Word document.
The qualitative variables give the quality and the quantitative variables are measurable, Bruce, (2008).
Delegate your assignment to our experts and they will do the rest.
Table 1: Variables and their type
| Variable | Type of variable |
| Business School | Qualitative |
| Full-Time Enrolments | Quantitative |
| Students per Faculty | Quantitative |
| Local Tuition ($) | Quantitative |
| Foreign Tuition ($) | Quantitative |
| Age | Quantitative |
| %Foreign | Quantitative |
| GMAT | Qualitative |
| English Test | Qualitative |
| Work Experience | Qualitative |
| Starting Salary ($) | Quantitative |
Using Excel®, find the mean, median, standard deviation, minimum, maximum, and the three quartiles for each of the quantitative variables identified in part 1 above. Neatly summarize in a table in your Word document. Comment on what you observe.
| Variable | Mean | Median | Standard deviation | Minimum | Maximum | Lower Quartile | Median | Upper Quartile |
| Full-Time Enrolments | 165.16 | 126 | 140.84 | 12 | 463 | 44 | 112 | 234 |
| Students per Faculty | 8.48 | 7 | 5.06 | 2 | 19 | 5 | 6.5 | 11.5 |
| Local Tuition ($) | 12374.90 | 11513 | 7778.42 | 1000 | 33060 | 6146 | 11381.5 | 16799 |
| Foreign Tuition ($) | 16581.80 | 17765 | 9134.85 | 1000 | 33060 | 9000 | 17560 | 22062.5 |
| Age | 28.36 | 29 | 3.78 | 22 | 37 | 25 | 29 | 30 |
| %Foreign | 28.08 | 27 | 25.01 | 0 | 90 | 6 | 26.5 | 40 |
| Starting Salary ($) | 37292 | 41400 | 23459.30 | 7000 | 87000 | 16000 | 37700 | 51050 |
What are the minimum and maximum full-time enrolments? Which schools have the minimum and maximum full-time enrolments?
The minimum full-time enrolment is: 12
The maximum full-time enrolment is: 463
Macquarie Graduate School of Management (Sydney) school have the minimum full-time enrolment.
Indian Institute of Management (Calcutta) school have the maximum full-time enrolment.
What is the average number of students per faculty member? Is this low or high? What does this mean to prospective applicants who are interested in pursuing an MBA in one of the leading international business schools?
The average number of students per faculty member is 8.48. This is high. Given median as 7 for this variable of study, this means that majority of the students developed an interest in pursuing an MBA. Therefore, this encourages the prospective applicants to have an interest in pursuing an MBA in one of the leading international business schools
What is the mean, median, and modal ages? What does this mean to prospective applicants?
The mean age is: 28.36
The median age is: 29
The modal age is: 29
The modal age and the median are the same. This means that majority of the members are 29 years of age on average. More specifically, half of the people are above 28.36 and half are below 28.36 with reference to the median age of 29.
What is the mean percentage of foreign students? How many and which schools have 1% and 0% foreign students? Which schools have highest percentage of foreign students? Please state these percentages.
The mean percentage of foreign students is 28.08. The school which have 1 % is Indian Institute of Management (Bangalore) and there are 5 in number. The schools which have 0% foreign students are; Indian Institute of Management (Ahmedabad), Indian Institute of Management (Calcutta) and Jamnalal Bajaj Institute of Management Studies (Bombay) with numbers 5,8 and 9 respectively.
The school which have the highest percentage of foreign students are those schools which exceed the mean percentage foreign i.e.
:
| School |
% Foreign |
| Melbourne Business School |
47 |
| International University of Japan (Niigata) |
60 |
| Asian Institute of Management (Manila) |
50 |
| National University of Singapore |
51 |
| Australian National University (Canberra) |
80 |
| Hong Kong University of Science and Technology |
37 |
| Monash Mt. Eliza Business School (Melbourne) |
30 |
| Asian Institute of Management (Bangkok) |
90 |
| Massey University (Palmerston North, New Zealand) |
35 |
| Royal Melbourne Institute of Technology |
30 |
| Curtin Institute of Technology (Perth) |
43 |
What percentage of schools require the GMAT test?
The schools that require the GMAT test are 14 out of 25. This represents 56% of the total number of schools.
What percentage of schools require English tests such as Test of English as a Foreign Language (TOEFL)?
The count of schools that require English tests such as TOEFL are 8. This represents 32%.
What percentage of schools require work experience? From this percentage, does this appear to be a significant factor in gaining admissions?
The total number of schools is 25. The count of school that require work experience is 19 i.e.
|
Frequency |
|
| Yes |
19 |
| No |
6 |
This represents 76% of schools require work experience. This percentage is relatively high especially when we consider the sample size. Statistically, this is not significant factor in gaining admissions.
What are the mean and median starting salaries? Which schools have the minimum and maximum starting salaries? How much are these minimum and maximum salaries?
The mean and median starting salary are 37292 and 41400 respectively. The school that have maximum starting salary is International University of Japan (Niigata) and Jamnalal Bajaj Institute of Management Studies (Bombay) have the minimum starting salaries with their salaries as $87,000 and $7,000 respectively.
What are the mean tuition for foreign students and for local students? Does there appear to be a significant difference? What is the difference between the two means?
| School |
Mean |
| Foreign Tuition ($) |
16581.80 |
| Local Tuition ($) |
12374.90 |
From the two means, we can observe a significant difference between the mean tuition for foreign students and for local students by
How many schools require work experience and how many of them don't? What is the mean starting salary for schools requiring work experience? What is the mean starting salary for schools requiring no work experience?
The schools that require work experience and their mean starting salary includes:
| School | Starting Salary ($) |
| Melbourne Business School |
71,400 |
| University of New South Wales (Sydney) |
65,200 |
| Asian Institute of Management (Manila) |
22,800 |
| National University of Singapore |
43,300 |
| Australian National University (Canberra) |
46,600 |
| Nanyang Technological University (Singapore) |
49,300 |
| University of Queensland (Brisbane) |
49,600 |
| Hong Kong University of Science and Technology |
34,000 |
| Macquarie Graduate School of Management (Sydney) |
60,100 |
| Chulalongkorn University (Bangkok) |
17,600 |
| Monash Mt. Eliza Business School (Melbourne) |
52,500 |
| Asian Institute of Management (Bangkok) |
25,000 |
| University of Adelaide |
66,000 |
| Massey University (Palmerston North, New Zealand) |
41,400 |
| Royal Melbourne Institute of Technology |
48,900 |
| Jamnalal Bajaj Institute of Management Studies (Bombay) |
7,000 |
| Curtin Institute of Technology (Perth) |
55,000 |
| Universiti Sains Malaysia (Penang) |
16,000 |
| De La Salle University (Manila) |
13,100 |
Their mean starting salary is $41,305.
The schools that require work experience and their mean starting salary includes:
| School | Starting Salary ($) |
| Indian Institute of Management (Ahmedabad) |
7,100 |
| Chinese University of Hong Kong |
31,000 |
| International University of Japan (Niigata) |
87,000 |
| Indian Institute of Management (Bangalore) |
7,500 |
| Indian Institute of Management (Calcutta) |
7,400 |
| Lahore University of Management Sciences |
7,500 |
Their mean starting salary is $24,583.
How many schools require English tests and how many don't? What is the mean starting salary for schools requiring English tests? What is the mean starting salary for schools requiring no English tests?
The schools that require English tests include:
| Business School |
English Test |
Starting Salary ($) |
| International University of Japan (Niigata) |
Yes |
87,000 |
| National University of Singapore |
Yes |
43,300 |
| Australian National University (Canberra) |
Yes |
46,600 |
| Monash Mt. Eliza Business School (Melbourne) |
Yes |
52,500 |
| Asian Institute of Management (Bangkok) |
Yes |
25,000 |
| Massey University (Palmerston North, New Zealand) |
Yes |
41,400 |
| Royal Melbourne Institute of Technology |
Yes |
48,900 |
| Universiti Sains Malaysia (Penang) |
Yes |
16,000 |
The mean starting salary for these schools is $45,088
The schools that don’t require English tests include:
| Business School |
English Test |
Starting Salary ($) |
| Melbourne Business School |
No |
71,400 |
| University of New South Wales (Sydney) |
No |
65,200 |
| Indian Institute of Management (Ahmedabad) |
No |
7,100 |
| Chinese University of Hong Kong |
No |
31,000 |
| Asian Institute of Management (Manila) |
No |
22,800 |
| Indian Institute of Management (Bangalore) |
No |
7,500 |
| Indian Institute of Management (Calcutta) |
No |
7,400 |
| Nanyang Technological University (Singapore) |
No |
49,300 |
| University of Queensland (Brisbane) |
No |
49,600 |
| Hong Kong University of Science and Technology |
No |
34,000 |
| Macquarie Graduate School of Management (Sydney) |
No |
60,100 |
| Chulalongkorn University (Bangkok) |
No |
17,600 |
| University of Adelaide |
No |
66,000 |
| Jamnalal Bajaj Institute of Management Studies (Bombay) |
No |
7,000 |
| Curtin Institute of Technology (Perth) |
No |
55,000 |
| Lahore University of Management Sciences |
No |
7,500 |
| De La Salle University (Manila) |
No |
13,100 |
The mean starting salary for these schools is $33,624.
Comment on the skewness for the data on starting salaries:
Skewness is the measure of asymmetry or lack of symmetry. The skewness on the data on starting salaries is 0.2229 which means that the data is positively skewed, i.e. it has a long tail to the right. The mean is also to the right of the peak.
Plot a histogram and determine the skewness.
The histogram shows that the data is positively skewed as the normal curve is skewed to the right, Christopher J. Mecklin and Daniel (2004)
Find the mean, median, and mode for starting salaries and compare the three measures to determine skewness.
Mean = 37292
Median = 41400
Mode = 7500
The mean is greater than the mode and therefore, the distribution is positively skewed.
Finally, use Empirical Rule on the starting salaries and determine whether the salaries follow the Empirical Rule.
The empirical rule, also known as the 68-95-99.7 rule.
From the histogram drawn from part 16, shows that starting salaries is not normally distributed. Mathematically, the starting salaries does not follow the Empirical Rule.
References
Bruce, N., Pope, D. and Stanistreet, D. (2008). Quantitative methods for health research. Chichester, England: John Wiley & Sons.
Christopher J. Mecklin and Daniel J. Mundfrom International Statistical Review / Revue Internationale de Statistique Vol. 72, No. 1 (Apr., 2004), pp. 123-138
https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule
