Any statistics guru's, need help with a question

Flash of power

Club Legend
Aug 19, 2013
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AFL Club
Port Adelaide
Question

Company A and Company B have the same average starting salary, which is $80,000 pa. However, the value of standard deviation (SD) for starting salaries at Company A is $20,000, while at Company B it is $5,000

  • Assuming that the data is normally distributed, and following the Empirical Rule,
  • 68.2% of starting salaries fall between what ranges for the two companies?
  • (3 marks)

  • Given the difference in SD, which of the two companies would you rather work for? Explain why in a few sentences. (3 marks)

Just wondering if I am missing something in this question? First part of the question seems fairly straight forward, eg Company A has a variation of $20k which means 68% of salary fall between $60k and $100k with company be it 68% fall between $75k and $85k. Correct?

The second part of the question doesn't seem to be straight forward as you can't definitively answer which company would pay you more. eg: could earn more eg $100k, but you could also earn less than company B and only get $60k - is it just that company B is more of a sure thing, could negotiate higher for company a or is there something I am missing here?


Any help appreciated
 

Sydney Kicker

Club Legend
Jan 18, 2015
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As a statistician I think the second part of the question is a bit too open. I guess the examiner is expecting a range of answers that demonstrate some understanding of what greater SD/variance means in real life.

eg I'd rather work for B because I'm risk adverse and I'd like to avoid the chance of earning below 60k which in the case of company A is 16% and in company B is zero. But at the same time I'm giving up the 16% chance that if I choose company A I could get a salary of over 100k.

Of course it's a pretty unnatural example - In the real world answers are more like - I'd take the one that first offered me the job, the one with the shorter commute, better working conditions, best ethics, best coffee shop next door, most young and single co workers etc etc.
 

Flash of power

Club Legend
Aug 19, 2013
1,296
1,313
AFL Club
Port Adelaide
As a statistician I think the second part of the question is a bit too open. I guess the examiner is expecting a range of answers that demonstrate some understanding of what greater SD/variance means in real life.

eg I'd rather work for B because I'm risk adverse and I'd like to avoid the chance of earning below 60k which in the case of company A is 16% and in company B is zero. But at the same time I'm giving up the 16% chance that if I choose company A I could get a salary of over 100k.

Of course it's a pretty unnatural example - In the real world answers are more like - I'd take the one that first offered me the job, the one with the shorter commute, better working conditions, best ethics, best coffee shop next door, most young and single co workers etc etc.

Thanks so much that was exactly my thinking, but I kept thinking I was missing something. Cheers :)
 

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