My Math Forum Percent Change

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 July 30th, 2015, 08:17 PM #1 Member   Joined: May 2015 From: USA Posts: 33 Thanks: 1 Percent Change I'm looking at sales of appliances for 2 months. If I'm calculating percent change for the 2 months, it is appropriate to calculate percent change between the proportion of appliances sold, and, percent change between the total number of appliances sold?
 July 31st, 2015, 03:06 AM #2 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,084 Thanks: 699 Math Focus: Physics, mathematical modelling, numerical and computational solutions There are few mistakes here, but nothing too major: Firstly, the final column, should be renamed to "% change in proportion" to make it clear to the reader that that is what you are calculating. Most people would think of percentage change as "% change in number of units". I would add another column at the end to represent this new percentage so that you have both in your table. Secondly, the "% change in proportion" of the total appliances is actually 0% because it will always be 100% of the total. This figure isn't particularly useful! The 8% you have calculated is actually a "% change in number of units". Thirdly, percentage changes between different appliances won't add up, so you cannot total up "% change in proportion" to get a "total % change in proportion". When doing accounting, try to keep everything in terms of raw data (such as the number of appliances) and get totals straight from the raw data instead. Then, after that, percentages can be used to characterize that data and provide insight as to what the numbers represent.
July 31st, 2015, 05:01 AM   #3
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Quote:
 Originally Posted by Benit13 Thirdly, percentage changes between different appliances won't add up, so you cannot total up "% change in proportion" to get a "total % change in proportion".
Thanks Benit13!

There is no way to calculate "total % change in proportion"?

July 31st, 2015, 08:04 AM   #4
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 Originally Posted by Scully Thanks Benit13! There is no way to calculate "total % change in proportion"?
Let's think about it... a good way to start is to consider a simpler example.

Let's say we have two flavours of ice cream, Vanilla and Strawberry. We have 10 tubs in total and an initial proportion of 50% for each (so we have 5 tubs of each flavour).

Now we replace a Vanilla tub with a Strawberry one so that there are 4 Vanilla tubs and 6 Strawberry tubs.
The proportion is now 40% Vanilla and 60% Strawberry.
The change in proportion is -10% for Vanilla and 10% for Strawberry.
The "% change in proportion" is -20% for Vanilla and +20% for Strawberry.

So what is "total % change in proportion"? Well, we add up -20% and 20% to get 0%. If we are only allowed to replace tubs with different flavours, then this parameter is always going to be 0%. The only way to get it to change is to be able to change the total number of items.

Therefore, I would suggest that "total % change in proportion" is not a useful parameter at all.

If you want to get an idea for how much variety there is in your stock and how this changes with time, then I would recommend calculating a different parameter, such as the root-mean-square (rms for short). To do this,

1. take your "% change in proportion" results
2. square each number
3. calculate the average
4. square root the final result.

For example, If we square the -20% for Vanilla and +20% for Strawberry, we get 400% and 400%. The mean of those is (400%+400%)/2 = 400%. The square root of that is 20%. Therefore, the rms "% change in proportion" is 20%.

The advantage of rms measures is that they are simple to do and they work for any number of values. Try calculating it for your data sample

Last edited by Benit13; July 31st, 2015 at 08:07 AM.

 July 31st, 2015, 11:49 AM #5 Member   Joined: Jun 2015 From: Casablanca Posts: 47 Thanks: 3 If you aren't asked to use rms, then following your method: $\left(\dfrac{5-10}{100}\right)*100=-50 \%$ $\left(\dfrac{40-20}{20}\right)*100=100 \%$ $\left(\dfrac{20-30}{30}\right)*100=-33.33 \%$ $\left(\dfrac{65-60}{60}\right)*100=8.33 \%$

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