Let's discuss Mathematics

[ParadigmShifter]

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

 

[Ultraworld]

For a company the following data is given.

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

 

[Mise]

That's per quarter. EDIT: ninja edit, n/m.

Anyway I suggest that this thread be moved here: http://forums.civfanatics.com/showthread.php?t=314282

 

[Gabryel Karolin]

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.

 

[Mise]

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

 

[Gabryel Karolin]

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

 

[Ultraworld]

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.

combined

 

[El_Machinae]

Moderator Action: Merged threads

 

[ParadigmShifter]

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.

 

[Ultraworld]

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

 

[ParadigmShifter]

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

 

[Ultraworld]

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.

 

[ParadigmShifter]

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.

 

[oagersnap]

You are overcomplicating it. It's

(4540/342)+(37221/721) = 64.9

 

[ParadigmShifter]

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!

 

[Ultraworld]

please my own thread for this one!!!!!!!!!!!!!!

 

[Gabryel Karolin]

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.

 

[ParadigmShifter]

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.

 

[oagersnap]

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

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

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.

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

 

[Mise]

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.

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