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June 12th, 2018, 11:58 AM  #1 
Newbie Joined: Jun 2018 From: USA Posts: 3 Thanks: 0  BoneHead in Search of Direction
Hello out there! I'm trying to calculate true growth year over year, and I'm thinking myself in circles. I don't know whether I'm using the right terms. I understand basic growth% YoY which would be (TYLY)/LY. That being said, I am trying to capture growth factoring in the change in "members" in the data set between TY and LY. For example: I have a store that sold 1000 units TY and 700 LY over the same time period. Using a Basic Growth calc (1000700)/700 I would get an approximate 42.85% increase over LY for that time period. However, I am carrying 30% more items in my store TY than over the same period LY. How do I "even out" the TY/LY sales increase using the growth of Items offered TY/LY? Or in other words, how do I put TY and LY on equal footing? I'm stumped!!! Last edited by skipjack; July 30th, 2018 at 04:22 AM. 
June 12th, 2018, 12:38 PM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,210 Thanks: 498 
There is no perfect way to do this. It depends in part on what exactly is most important for you to know. It also depends in part on what numbers are available to you. If you know that a was last year's sales of what was in stock both years and b was this year's sales of those items and c was this year's sales of new items. So the percentage increase in total sales is $100 * \dfrac{b + c}{a}.$ The percentage increase due to "old" stock is $100 * \dfrac{b}{a}.$ The percentage increase due to "new" stock is $100 * \dfrac{c}{a}.$ That is sort of intuitive, but things get stranger if you do not have b and c separately. 
June 12th, 2018, 02:49 PM  #3 
Newbie Joined: Jun 2018 From: USA Posts: 3 Thanks: 0 
Thanks for the reply!. Yes...things are about to get stranger as I do not have b and c separate. I know the Sales TY and Sales LY, and the # of items TY and the # of items LY...but I do not know if there were any items overlapping between TY and LY. Do I have any options? 
June 12th, 2018, 03:58 PM  #4  
Senior Member Joined: May 2016 From: USA Posts: 1,210 Thanks: 498  Quote:
You said in your first post that you stocked 30% more kinds of items this year. Now in the absence of any information, I'd guess that you added some early in the year and some late in the year, meaning that, on average, your sales of new items were for half a year, not a full year. So let's say as a crude estimate that new items represented 8%, 15%, or 22% of sales. Let a be last year's sales and b be this year's sales. Then sales growth overall is obviously $100 * \dfrac{b  a}{a}\%.$ $\text {Estimated sales of new items } = 8\% \implies$ $\text {Estimated percentage increase in sales of old items } = 100 * \dfrac{0.92b  a}{a}\%.$ The 0.92 = 1  0.08. Follow the logic? Notice I was clear that it was an estimate; otherwise you begin believing that guesses are truth. But we made different guesses. So work those out too. $\text {Estimated sales of new items } = 15\% \implies$ $\text {Estimated percentage increase in sales of old items } = 100 * \dfrac{0.85b  a}{a}\%.$ $\text {Estimated sales of new items } = 22% \implies$ $\text {Estimated percentage increase in sales of old items } = 100 * \dfrac{0.78b  a}{a}\%.$ If the three answers are not that different, you can have a fair amount of confidence that the numbers are reasonable. If the numbers are quite different, the best you can say is that it is probably better than x but worse than y. The other thing that this analysis shows is that you want to know, by type, the number of items sold and sales revenue. Your POS system should be able to track that for you. Last edited by skipjack; June 14th, 2018 at 12:02 PM.  
June 14th, 2018, 08:10 AM  #5 
Newbie Joined: Jun 2018 From: USA Posts: 3 Thanks: 0 
Thank you! I can work with this

July 29th, 2018, 08:49 PM  #6 
Banned Camp Joined: Jul 2018 From: beverly hills Posts: 15 Thanks: 0  Forget the problem itself, I'm curious Where all of a sudden out of nowhere the letters TY and LY came from? Why not UG and PG? I've never understood where people get letters and random numbers out of nowhere that have no relation to anything, but yet somehow get used to kind of do a math problem. Humans have math so screwed up because of all their rules, that they cannot even keep their own system straight and working 1 way. So far every basic rule math uses is absent from almost every advanced math problem I've seen, and some lame excuse was given and then people just make up their own methods and call it an exception or some random rule...but that all falls apart because basic math rules would prevent anyone from even be able to be doing the math the way they're doing it. Last edited by skipjack; July 30th, 2018 at 04:34 AM. 
July 30th, 2018, 04:33 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,003 Thanks: 1862 
A person's working notes may use abbreviations such as "TY" for "this year" and "LY" for "last year".

July 30th, 2018, 07:01 AM  #8 
Senior Member Joined: Sep 2016 From: USA Posts: 522 Thanks: 297 Math Focus: Dynamical systems, analytic function theory, numerics  Exactly! Is it this year or last year? Which is it? I'm sick of mathematicians trying to have it both ways. Unless time travel is possible, this is clear evidence of the corruption spread by "Big Arithmetic". Wake up sheeple.

July 30th, 2018, 07:06 AM  #9  
Senior Member Joined: May 2016 From: USA Posts: 1,210 Thanks: 498  Quote:
When I teach kids how to do word problems in beginning algebra, I tell them to start by writing down brief definitions of what their symbols mean. Which letters are used is completely arbitrary so explaining the meaning of each letter is essential to clear communication. This has nothing to do with the formal rules of math, but rather is a fundamental aspect of human speech: definitions are needed for communication to exist. I admit that people may start using symbols without explicitly defining them; part of the skill that humans have in communicating is to figure out how symbols are being used without formal definitions. I figured out from context that TY meant "this year's." That is not math; that is experience in interpreting sloppy, or in this case unskilled, language. I also try to teach kids not to use acronyms like "TY" because one of the conventions of modern algebraic notation is that a letter stands for one unknown and that multiplication of unknowns is shown by stringing letters together. These are conventions for communicating math efficiently. Math would not change if the conventions for displaying it were changed. Now it is a slightly annoying inconvenience that different branches of math have different notational conventions, and that some symbols (the minus sign is a blatant example) are used to mean different things even in the same branch of mathematics. These are deficiencies in the human ability to create unambiguous language. The language of mathematics has far fewer such ambiguities than natural language: why is the plural of "house" "houses" when the plural of "mouse" is "mice." The confusions that may arise from imprecision in the language of math do not represent confusions in underlying logic but in human communication, an area replete with confusion as anyone married can tell you. Could the conventions of mathematical notation be improved? For an example, it is a nuisance that people use minuscule roman letters to stand for unknowns and for functions: f(  x) is not the clearest of notations because it may mean f times the additive inverse of x or may mean the result of applying rule f to the additive inverse of x. It would be clearer if we used majuscule roman letters to represent functions and minuscule roman letters to represent variables and minuscule greek letters to represent constants. But these are issues of notation, not logic. Finally, it is unfortunately true that you will learn something only later to be taught that what you originally learned was not correct. This may be the result of bad teaching or the result of bad learning. When I introduce the idea of functions to students, I try always to start by saying that a function is a very general kind of relationship between the elements of one set and the elements of another set but that we are going to work initially with the very simplest types of function that relate a set of numbers to another set of numbers. But I may forget and start right in with very simple functions. Or, more likely, the student struggling to understand even very simple functions forgets that I explained that there are more complex types of function and then, when that same student learns that functions are far broader than the introductory examples, feels that the new examples are exceptions. Last edited by skipjack; July 30th, 2018 at 10:03 AM.  
July 30th, 2018, 11:28 AM  #10  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,927 Thanks: 775 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  

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