Does the following make sense to you:

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Discussion Overview

The discussion revolves around the concept of expressing reductions as percentages of a total amount. Participants explore the clarity and implications of such expressions in mathematical contexts, including potential misunderstandings and the effectiveness of communication in mathematical language.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants affirm that expressing a reduction as a percentage of the total amount makes sense, citing examples with numerical values.
  • Others argue that the phrasing can lead to confusion, particularly regarding whether the reduction refers to the original total or the remaining items.
  • Concerns are raised about the clarity of language in mathematical statements, with references to common pitfalls in wording that can lead to misinterpretation.
  • Some participants mention the concept of percentage points (pp) as an alternative way to express reductions, although this is also questioned in terms of clarity.
  • There is a discussion about the implications of using percentages multiple times in calculations, emphasizing the need for careful treatment of such expressions.
  • Several participants express uncertainty about the term "reduction percentage" and its meaning, indicating a lack of consensus on terminology.
  • Some participants reflect on the broader implications of how percentages are presented in everyday contexts, suggesting that many people may not fully understand them.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the clarity and effectiveness of expressing reductions as percentages. While some find it understandable, others highlight significant ambiguities and potential for misunderstanding.

Contextual Notes

Limitations include varying interpretations of what constitutes a reduction and the potential for confusion when percentages are used in multiple contexts. The discussion also highlights the importance of precise language in mathematical communication.

Who May Find This Useful

This discussion may be of interest to individuals engaged in mathematical communication, educators, and those exploring the nuances of percentage calculations in various contexts.

  • #31
There isn't an understandable way if you chuck away too much information. You HAVE to do more than giving a single figure if you want your statement to make sense. Which would you rather have - air or water? You need both of them.
You ask too much, I think.
 
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  • #32
I could point out how little use the value of the Mean of a distribution is, without some indication of the range, too. Your example is along exactly the same lines.
 
  • #33
sophiecentaur said:
There isn't an understandable way if you chuck away too much information. You HAVE to do more than giving a single figure if you want your statement to make sense. Which would you rather have - air or water? You need both of them.
You ask too much, I think.

How would the specific size of the work force (i.e. the total) be relevant to the question...

"does expressing the reduction, as a percent of the total"
 
  • #34
sophiecentaur said:
I could point out how little use the value of the Mean of a distribution is, without some indication of the range, too. Your example is along exactly the same lines.

Hardly.

My example would revolve around the relation of the means of distribution, to the range, and would be completely independent on the value of the range.

Again, you're over complicating the issue.
 
  • #35
If you want to give a single figure then, in most contexts, you may as well give them your shoe size. (That is, if they don't already have a load of side information that you're not telling us about)
Are you paying '£100 per character' for publishing this information? Do you want to make sense or 'get away' with giving minimal information?
Have you ever studied statistics in any form or had to present data in practice? Look at the way data is presented in scientific journals and elsewhere. If you read just a single figure then someone may be trying to hide something.
Is a 10% change in your body temperature more or less significant than a 10% change in your salary? Of course range is vital for many statistics.

I don't think anyone is likely to give you a 'one of three' answer, which is what you seem to want. Certainly not me.

PS "Means of distribution" is not the same as "Mean of a distribution". Karl Marx would turn in his grave.
 
  • #36
sophiecentaur said:
If you want to give a single figure then, in most contexts, you may as well give them your shoe size. (That is, if they don't already have a load of side information that you're not telling us about)
Are you paying '£100 per character' for publishing this information? Do you want to make sense or 'get away' with giving minimal information?
Have you ever studied statistics in any form or had to present data in practice? Look at the way data is presented in scientific journals and elsewhere. If you read just a single figure then someone may be trying to hide something.
Is a 10% change in your body temperature more or less significant than a 10% change in your salary? Of course range is vital for many statistics.

I don't think anyone is likely to give you a 'one of three' answer, which is what you seem to want. Certainly not me.

PS "Means of distribution" is not the same as "Mean of a distribution". Karl Marx would turn in his grave.
I think it is safe to say that this question is simply too simple for you to understand.

Again, values are completely irrelevant. This is a general question about expressing the relationship in an understandable way.
 
  • #37
Okay how about this.

If I were to say..

6.9%-6.1% = a decline of 0.8%


Would you have a problem with that??

Again, it could be a decline of 0.8% of the total
It could be 0.8pp
or it could be an 11.6% reduction.



How do you guys see it?
 
  • #38
Not sure how you could calculate a decline of .8%
 
  • #39
I understand that you want something that isn't possible. Otherwise, why haven't you received an answer from someone else of the form that you want?

When they want to talk about changes in percentages in the context of money - interest etc. the use of pp is fairly common BUT is is a snare and delusion because it's not fully appreciated. When the mortgage interest rate goes up from 2% to 4% they try to say the interest has only gone up by 2%. Oh yes - tell that to someone who is paying £400 per month and it goes up to £800. That's an increase of 100% in any other world than banking.
 
  • #40
sophiecentaur said:
I understand that you want something that isn't possible. Otherwise, why haven't you received an answer from someone else of the form that you want?

Um, did you miss the very first response in the thread??

A simple yes, or no is all you need to say. Asking a bunch of irrelevant questions such as what are the specific values, in a question where they don't matter is well, irrelevant.

When they want to talk about changes in percentages in the context of money - interest etc. the use of pp is fairly common BUT is is a snare and delusion because it's not fully appreciated. When the mortgage interest rate goes up from 2% to 4% they try to say the interest has only gone up by 2%. Oh yes - tell that to someone who is paying £400 per month and it goes up to £800. That's an increase of 100% in any other world than banking.
Youre getting there, c'mon.

Now say there was an example with a finite total amount.

Would it be acceptable, and would you understand it if someone expressed the increase/decrease as a percentage of the total amount?
 
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  • #41
The statement in the OP certainly makes sense if you give the extra information. If you just give the single value "increase by 25%", then it is ambiguous in this case. It's all a matter of cleanly presenting data. Nobody in a scientific paper is going to say "increase by 25%" without adding more context.

I really don't see the problem here.
 
  • #42
markymark69 said:
Not sure how you could calculate a decline of .8%

"a decline" is not a technical term for anything specifically, and would be dependent on what you wanted to relate it to.. Such as, a decline relative to the total, or a decline relative to the amount you already have. Hell, you could measure the decline relative to the number moons on Saturn if you wanted to.

Point being that saying "= a decline of 0.8%" does not really lock you into any specific relation. There would need to be more information for you to claim that you could not calculate it.
 
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  • #43
micromass said:
I really don't see the problem here.

The problem, and the reason for this thread, is that I've had someone tell me that "expressing a reduction, as a percentage of a total amount" does not make sense to them.

Not only do I think it makes sense, but I think anyone with a basic understanding of percentages should be able to pick up on what that means. Therefore, I was just trying to get a general feel as to whether or not people knew what I was talking about when I said it.

Thanks for your answer tho.
 
  • #44
NotAnEngineer said:
The problem, and the reason for this thread, is that I've had someone tell me that "expressing a reduction, as a percentage of a total amount" does not make sense to them.

Not only do I think it makes sense, but I think anyone with a basic understanding of percentages should be able to pick up on what that means. Therefore, I was just trying to get a general feel as to whether or not people knew what I was talking about when I said it.

Thanks for your answer tho.

OK, I think you have enough answers now to get a general feel. This thread has gone on for long enough now. Locked.
 

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