Let's discuss Mathematics

modified table so it is more clear
Code:
time period|Employees|Total costs 
----------------------------------
 jan-mar       342     $  4540
 apr-dec       721     $ 37221
 

because it states 'per year'. If I sell 10 apples in the months jan + feb. Then how many apples do I sell on average per year? 10 / (2/12) = 60.

I got this question from an nameracy practice test. In that question the 'Average Cost per Employee per Year' was given and you had the find the # of employees in Q1. But without a good definition of 'Average Cost per Employee per Year' I am clueless.
 
That would be correct only if you didn't sell any apples for the rest of the year though.
 
Imagine this... For 1 quarter, you have 1 employee with an annual salary of $100. Then you employ another employee at the same rate, $100 per year, for the rest of the year. I'm sure you'll agree that the Average Cost per Year per Employee is $100. How could it be anything else?

Well, lets draw up that table and see...

Quarter .................. Employees .................. Total Cost
1 ................................. 1 ............................. $25
2,3,4 ............................ 2 .............................$150

So, lets use Oagersnap/Gabryel's method: 25/1 + 150/2 = 100
Now Ultraworld: 4/1 * 25/1 + 4/3 * 150/2 = 200
Mise: (1/4 * 25/1 + 3/4 * 150/2)*4 = 250
 
That would be correct only if you didn't sell any apples for the rest of the year though.

No, it would only be correct if the year had only two months.

EDIT: I wonder how I came up with that... I stand by what i said regarding the actual problem though :D
 
Am confusing myself now.

I'm glad I'm not an accountant ;)

EDIT: Looks like Mise is in the oagersnap/Gabs camp now too along with myself.
 
Anyone know how to approach this?

p is a prime number, n is any natural number

Prove (1 + n)^p - n^p - 1 is divisible by p.
 
So you have, for each employee, to scale UP the costs. After that devide by the number of employees.

Code:
time period|Employees|Total costs 
----------------------------------
 jan-mar       342     $  4540
 apr-dec       721     $ 37221

scaling up

Code:
time period|Employees|Total costs 
----------------------------------
 jan-dec       342     $ 18160
 jan-dec       721     $ 49628

summation


Code:
time period|Employees|Total costs 
----------------------------------
 jan-dec      1063     $ 67788

gives

'average cost per employee per year' of 63.8
 
Spoiler :
So you have, for each employee, to scale UP the costs. After that devide by the number of employees.

Code:
time period|Employees|Total costs 
----------------------------------
 jan-mar       342     $  4540
 apr-dec       721     $ 37221

scaling up

Code:
time period|Employees|Total costs 
----------------------------------
 jan-dec       342     $ 18160
 jan-dec       721     $ 49628

summation


Code:
time period|Employees|Total costs 
----------------------------------
 jan-dec      1063     $ 67788

gives

'average cost per employee per year' of 63.8

The problem with your method is that you essentially make a yearly average of the first quarter, a yearly average of the three last quarters, and then simply average the two. This is wrong, because that makes the average of the first quarter become just as important as the average of the three last quarters when calculating the overall average.
 
Back home in Sci/Tech!

I suppose the move to OT was good for thread publicity.

On topic: you shouldn't really use "average" as a term in the maths thread - the wikipedia page lists 14 different types of averages ;)
 
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