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Let's discuss Mathematics

Discussion in 'Science & Technology' started by ParadigmShifter, Mar 16, 2009.

  1. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    Don't ask me advice on dusting. I'm not bad at probability and statistics (if rather rusty).
     
  2. Ultraworld

    Ultraworld Emperor

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    For a company the following data is given.
    Code:
    Quarter|Employees|Total costs 
    ----------------------------------
      1        342     $  4540
    2,3,4      721     $ 37221
    
    (so for the months april - december you have 721 people who work for you and you have costs of $ 37221)

    How do you find the 'Average Cost per Employee per Year'?

    My answer: 1/(1/4) * 1/342 * 4540 + 1/(3/4) * 1/721 * 37221 = 121.9
     
  3. Mise

    Mise isle of lucy

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  4. Gabryel Karolin

    Gabryel Karolin Gammelgädda

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    Data is not clear, does "2,3,4" mean those three combined or that the three have equal values in terms of employees and total costs.
     
  5. Mise

    Mise isle of lucy

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    Yeah, it's a terrible table. To me the answer is (1/4 * 4540/342 + 3/4 * 37221/721)*4 = $168
     
  6. Gabryel Karolin

    Gabryel Karolin Gammelgädda

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    yepp, I got the same. Either that or 65, if you count it the other way I mentioned.
     
  7. Ultraworld

    Ultraworld Emperor

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    combined
     
  8. El_Machinae

    El_Machinae Colour vision since 2018 Retired Moderator

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    Moderator Action: Merged threads
     
  9. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    Hmm I think the original method is correct, you divide the 3 quarterly total by 3 to get it per quarter, then multiply it by 4 to get yearly.

    Mise is just multiplying the 3 quarterly total by 3 (effectively).

    That's not multidimensional data anyway. A multidimensional mean is a vector.
     
  10. Ultraworld

    Ultraworld Emperor

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    You can visualise it by thinking about 2 cuboids right next to each other
     
  11. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    Yeah it's a good way to visualise statistics as areas of a histogram.

    I wonder why this thread has been moved to OT?

    I'll report this post to see if it will get moved back ;)
     
  12. Ultraworld

    Ultraworld Emperor

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    Personally I am uncertain about my own answer, despite having a good background in quantitative reasoning. I am hoping people at CFC could help me.
     
  13. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    I'm not totally sure either, but I prefer your answer to Mise's since you have a divide by 3 rather than a multiply for the 3 quarter table entry.

    You are effectively normalising each entry to cost/employee/quarter, then multiplying the sum by 4 to get yearly.
     
  14. oagersnap

    oagersnap Emperor

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    You are overcomplicating it. It's

    (4540/342)+(37221/721) = 64.9
     
  15. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    That depends whether there are 721 employees for each quarter in the 3 quarterly total, or 721 in total for the 3 quarters.

    The table is unclear about which is the case though. Now I think you may be right!
     
  16. Ultraworld

    Ultraworld Emperor

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    please my own thread for this one!!!!!!!!!!!!!!
     
  17. Gabryel Karolin

    Gabryel Karolin Gammelgädda

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    I have a cold and haven't done much college math but I'm curious why the answer isn't simply 4580/342 + 37221/721. Or 4580/342 + (37221/721)*3.

    You already have the total cost per year, its 4580+37221, why are you even dividing with 1/4, 3/4, it shouldn't be neccesary.
     
  18. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    Calm down!

    I take it the example is from a book - are there not similar examples showing what the usual method is?

    EDIT: I'm in the oagersnap/Gabryel camp now.
     
  19. oagersnap

    oagersnap Emperor

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    Yes, that's right. I just naturally assumed that there would be 721 employees for each quarter.. But the table is quite unclear.


    Exactly my point. The second solution you suggest would be correct if the 721 employees are a combined total for the last 3 quarters.
     
  20. Mise

    Mise isle of lucy

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    Right, so now you have two "Cost Per Year" figures, one that is based on 1 quarter and has 342 employees and one that is based on 3 quarters and has 721 employees. So you divide Cost Per Year by employees to get 2 different "Avg Cost per Year per Employee" figures. Then you take a weighted average: the company spends 1 quarter using one avg cost, and 3 quarters using the other avg cost, so you weight one by 1 and the other by 3. The number you get will be the same as the number I have :p
     

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