Question

Everything you know about both companies is identical except for the salary and neither firm will tell you your starting salary until AFTER you agree to work for them so you have no idea what you could get. The only thing each firm is willing to tell you is that "The average starting salary for the last 7 new hires was $50,000".

1) Considering that both have the same AVERAGE starting salary, and everything else is identical, is there any reason to investigate this further? Why or why not?

2) In the context of descriptive statistics (chapter 3) what might be another useful salary statistic, aside from the average salary, to help you make your decision ?

Now suppose you've said no to both of the previous companies and you ended up with an offer from two others, Firm C and Firm D. Again everything about them is the same, only this time they give you the salary data for the last 7 new hires. The data for Firm C has been ordered so you have no idea what order the starting salaries occurred.

Firm C: $20,000, $30,000, $40,000, $50,000, $60,000, $70,000, $80,000

Firm D: $50,000, $50,000, $50,000, $50,000, $50,000, $50,000, $50,000

3) Now that you've seen the data, which company do you choose to work for? Explain your reasoning.

Answer 1

So in the company A and company B both are having the same average salary so we could not judge the salary that they will offer to us unless we are not having any idea about the distribution of the salary.

So distribution of the salary is equally likey so that we can have the range for which we can expect the minimum and maximum salary that will be offered to us or in other words the risk that we want to have.

As average salary might ahve a outlier so we are not sure how the oulier is spreaded so let us say if any of the above company might have given 1000 $ and other one might have been offered with 99000 $ then we will ahve the same average but the distribuiton is spread a lot in other word variance or standard deviation gets increased significantly.

1)Yes, we need to investigate the other parameter apart form the average salary

2) The other statistic would be the distriubtion of the salary of the last 7 employeed that the company has hired.

3)

The answer of the quesiton varies signifcantly based on the approach that you want to adopt depends on the risk that particular person willing to take.

In company C if we calcualte the standar deviation $ 21602 so if we want to have the salary more than $50,000 we will have only 50 % chance and based on that we can determine the probability that we want to have the salary.

While in the case of Company D, standard deviation of salary is 0 so if we got hired, we would expect to have the $50,000.

So based on that , if person is risk averse, one should go with Company D and if person is risk taking one, he/she shoudl join the Company C by following the distribuion and its probability to having higher salary than particular more than $50,000 (for example if person wants to have more than 71602 (1 standard deviation higher salary), eqvivalent to Z = 1 (ideally we should use t distribution as n=7 but for example we have taken Z score for easy understanding), it would have 16 % chance).