IND508 OPERATIONS RESEARCH I

Department of Management, UTSC

ECMB11H3Y Quantitative Methods in Economics I L01

Lecture 02 - In Class Exercise Summer 2012Problem 1The Co-op office at a department keeps track of the number of students placed with jobs each month. Below is a sample of 6 months data. Determine the sample mean, median, mode, range, standard deviation for the number of students placed in a month. Compute the first quartile. What is the number of hires in a month such that 2/3 of the months will have placements below this value?MonthJanFebMarAprMayJune

students hired324260

Problem 2(a) A marketing company requires that a student must have an average above 75% in their courses to get an interview. Below are grades for a student, would the student get an interview?

Coursemarketingfinancestats accountingO.B.

mark %6580709272

(b) Suppose the company views some courses as being more important than others and so assigns different weights to them as shown below. Would the student get an interview?

Coursemarketingfinancestats accountingO.B.

mark %6580709272

Weight98734

Problem 3 You are studying the salary of new business student graduates. The Alumni office provided you with the following summary for a sample of business students that graduated in 2011. What is the mean starting salary? Standard deviation?starting salary (in $1,000)22 2627 - 3132 - 3637 - 41

# of students3584

Problem 4

Five observations are taken for 2 variables.

x4611316

y5050406030

(a) Does there appear to be a relationship between x and y?

(b) Compute the sample covariance and sample correlation coefficient, what conclusions can you draw?

Problem 5 case (Lets talk about it)

Employees in a certain department are given $1250 each year for professional development. The fund is placed in each employees account and unused amount can be carried forward. The Director is worry that there is too much unused money piling up in the accounts and the Vice President may stop giving money to the department for professional development. The Director called a meeting with the 14 employees where he said the average amount of money in an account is $3750 and there are 4 employees with over $7500. He said the $3750 implies that employees have not done any professional development in 3 years so there is a problem. He did not want to provide the amounts in each account because of confidential reasons.

Employee Bruce Lee having taken ECMB11 said unless we know how much money is in each accounts, we dont really have enough info to determine if there is indeed a problem. Do you agree with Bruce? Explain. Bruce goes on to say that the way to fix the problem may be very different if we knew how much was in each account. Provide 2 different methods to fix this problem and explain how your method relates to the amounts in the accounts.

Assuming it is not possible to give the amounts in each individual accounts, what additional statistic would you suggest the Director give and why?

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