Weighted Average (I think!)

frankninja

New Member
Joined
Mar 28, 2013
Messages
2
Help!

I am trying to compile a return on investment (ROI) workbook for my business, which contains four subsequent departments. When I calculate my ROI for the whole organization I get one number, then when I break it down by each of the four departments and then compile those four ROI numbers together, I get a different number. Again, help!

Widget, Inc total annual investment is $1,088,881 and our organization return is 10218626 clams (just imagine with me, it's not real financial investing). So when I calculate that it is roughly 1 clam produced for every $0.11. And the point that I am trying to make is "for every $1, X amount of clams are produced (in this case it rounds to 9)".

Then, when I break it down by departments (A,B,C,D) which each had a different amount of investments put into them, and get that same measure, it starts to get funny:

Department A:
Investment: $209,830
Total Return: 287 Clams
Clams per $1: 0.001

Department B:
Investment: $519,550
Total Return: 10216344
Clams per $1: 19.664

Department C:

Investment: $237,114
Total Return: 1958
Clams per $1: 0.008

Department D:
Investment: $122,837
Total Return: 37
Clams per $1: 0.000 (after this decimal it's not important to me)


Am I to assume that I should use a weighted average formula to combine the "Clams per $1" number in order to get back to that cumulative 9 for the entire organization? Another formula? It doesn't seem like I should because it's not like I'm taking the average of another group...I don't think?

Repeat again...Help!
 

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FrankNinja,
First, I love your user name. :biggrin: If you are trying to proof your math by adding your claims per $ and getting the overall claims per overall dollar you will have a problem. The math doesnt work that way. You will have to do a claims per department / Overall Investment to get it to add up. Its like taking an average of averages and expecting them to equal out.

DeptInvestmentClaimsClaims Per Individual $Claims / Overall $
A $ 209,830.00 2870.0010.000
B $ 519,550.00 10,216,34419.6649.379
C $ 237,114.00 1,9580.0080.002
D $ 122,837.00 370.0000.000
Total $ 1,089,331.00 10,218,6269.3819.381

<tbody>
</tbody>


In the table above, I put Dept in Column A, investment in Column B, Claims in C, Claims / Individual $ in D, and Overall in E...

The formulas are:
D2-5: =C2/B2
E2-5: =C2/$B$6
Total row (row 6): =SUM(B2:B5)
D6 is = C6/B6

Hope that helps...
 
Last edited:
Upvote 0
I don't understand why (theoretically) why this is how the math works. Is it because this proportionately takes into consideration the clams (yes, clams) vs. the overall investment?

Yes, this is SUPER helpful, but it's still a little cloudy in my head!

Parrish



FrankNinja,
First, I love your user name. :biggrin: If you are trying to proof your math by adding your claims per $ and getting the overall claims per overall dollar you will have a problem. The math doesnt work that way. You will have to do a claims per department / Overall Investment to get it to add up. Its like taking an average of averages and expecting them to equal out.

DeptInvestmentClaimsClaims Per Individual $Claims / Overall $
A $ 209,830.00 2870.0010.000
B $ 519,550.00 10,216,34419.6649.379
C $ 237,114.00 1,9580.0080.002
D $ 122,837.00 370.0000.000
Total $ 1,089,331.00 10,218,6269.3819.381

<tbody>
</tbody>


In the table above, I put Dept in Column A, investment in Column B, Claims in C, Claims / Individual $ in D, and Overall in E...

The formulas are:
D2-5: =C2/B2
E2-5: =C2/$B$6
Total row (row 6): =SUM(B2:B5)
D6 is = C6/B6

Hope that helps...
 
Upvote 0
So in mathematical terms,
(X+Y)/Z = X/Z + Y/Z. If we split Z up into two numbers ... say A + B = Z then...
(X+Y)/(A+B) = X/(A+B) + Y/(A+B).

(X+Y)/(A+B) <> X/A + Y/B

That is what you are trying to do...

So in real numbers lets make X = 8 and Y = 7. Then Z = 5...
(8+7)/5 = 15/5 or 3... That is proofed by 8/5 + 7/5 = 1&3/5 + 1&2/5 = 3

If we split 5 up into 2 + 3...(A + B)

(8+7)/(2+3) = 3 but.... 8/2 + 7/3 <> 3... it = 4 + 2&1/3...

You are trying to split up your numerators and you cant mathematically get it to work. Math doesn't work that way.

Hope that explains it... I don't think I can explain it better... maybe someone else can.
 
Upvote 0
Heh, to make it more complicated or clear... you could use a weight... the weight would be the investment for department / total investment....

DeptInvestmentClaimsClaims Per Individual $Claims / Overall $WeightWeighted percent
A $ 209,830.00 2870.0010.0000.19262280.000
B $ 519,550.00 10,216,34419.6649.3790.47694419.379
C $ 237,114.00 1,9580.0080.0020.21766940.002
D $ 122,837.00 370.0000.0000.11276370.000
Total $ 1,089,331.00 10,218,6269.3819.381

<colgroup><col><col><col><col><col><col><col></colgroup><tbody>
</tbody>


Column F = =B2/$B$6 (copied down)
Column G = F2 * D2 (Copeid down)
G6 = sum(G2:G5)
 
Upvote 0

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