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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

February 26th, 2014, 01:32 AM   #1
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Weighted Ratios Question

Hi,

I have ratios for a number of different components that add up to a total ratio. I'm then comparing those ratios across two time periods and working out the movement in percentage points across the periods at both component and total level.

I'd like to know how to work out how each component contributes to the total percentage point movement.

Example:
Area 1 goes from 5/10 = 50% to 8/10 = 80% giving a 30 percentage points increase.
Area 2 goes from 20/60 = 33.3% to 15/60 = 25% giving an 8.3 percentage points decrease.
The total therefore goes from 25/70 = 35.7% to 23/70 = 32.9% giving a 2.9 percentage points decrease.

How do I calculate the absolute percentage points increase or decrease that Area 1 and Area 2 respectively contribute to the overall 2.9 percentage points decrease - taking into account their relative weightings. The answers to Area 1 and Area 2 should add up to -2.9 percentage points.

I have posted an Excel sheet in case that helps.

thanks
Mark
Attached Files Book2.xlsx (9.1 KB, 0 views) February 26th, 2014, 04:47 AM   #2
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Re: Weighted Ratios Question

Quote:
 Originally Posted by mrt423 Area 1 goes from 5/10 = 50% to 8/10 = 80% giving a 30 percentage points increase. Area 2 goes from 20/60 = 33.3% to 15/60 = 25% giving an 8.3 percentage points decrease. The total therefore goes from 25/70 = 35.7% to 23/70 = 32.9% giving a 2.9 percentage points decrease.
5/10 + 20/60 is NOT = 25/70
8/10 + 15/60 is NOT = 23/70

Make sure you understand that before going on to something more advanced... February 26th, 2014, 06:45 AM   #3
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Re: Weighted Ratios Question

Quote:
Originally Posted by Denis
Quote:
 Originally Posted by mrt423 Area 1 goes from 5/10 = 50% to 8/10 = 80% giving a 30 percentage points increase. Area 2 goes from 20/60 = 33.3% to 15/60 = 25% giving an 8.3 percentage points decrease. The total therefore goes from 25/70 = 35.7% to 23/70 = 32.9% giving a 2.9 percentage points decrease.
5/10 + 20/60 is NOT = 25/70
8/10 + 15/60 is NOT = 23/70

Make sure you understand that before going on to something more advanced...
Thanks for your response Denis. It might be helpful to look at the Excel sheet I included in the post as I was finding it tricky to put into words.

I'm not trying to add fractions together. I am aggregating market share ratios. In November Area 1 sold 5 units out of a market size of 10 units and Area 2 sold 20 units out of a market size of 60 units. In December Area 1 sold 8 units out of a market size of 10 units and Area 2 sold 15 units out of a market size of 60 units.

If you aggregate that up to the company as a whole then total November sales were 25 units out of a market size of 70 units and December is 23 units out of a market size of 70 units.

Original question stands: what are area 1 and area 2's respective contributions to the 2.9 percentage points reduction across Nov to Dec. Answers will sum to -2.9

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