WHAT DOES "200% LARGER" MEAN?
g weinstein
WHAT DOES "200% LARGER" MEAN?
As a math teacher I explain this as follows:
Assume John's salary is $1000 per month.
If Mary's salary (M) is 50% larger than John's (J), then Mary makes $1500 per month or M = J+(50/100)J = 1.5J
and
If Mary's salary (M) is 100% larger than John's (J), then Mary makes $2000 per month or M = J+(100/100)J = 2J
and
If Mary's salary (M) is 200% larger than John's (J), then Mary makes $3000 per month or M = J+(200/100)J = 3J
Unfortunately, television commercials and newspaper advertisements clearly imply that if some item costs 200%
more, it costs TWICE AS MUCH.
I have yet to see the media make the distinction between:
200% larger
200% as large as
I need advice in making this clear to my students.
Gerald Weinstein
g...@the.link.ca
Kin Chung
This is one of my pet peeves too. Don't forget to add the examples
where someone advertises that something costs "ten times less".
By my understanding, that would mean the price was negative.
However, I seem to recall having read somewhere that these comparisons
are always made relative to the smaller quantity. I guess that means
"less" and "more" are used for the direction of the inequality rather
than the as absolute differences. Thus, "ten times less" means
one tenth of the other quantity, and "200% more" means twice the
other quantity. This convention would allow one make claims that
sound much better than reality.
Personally, I don't think we should use "less" or "more" at all.
Instead, I prefer to say, for example, "10% of" or "200% of".
Any other thoughts?
--Kin Yan Chung
Neil Rickert
>WHAT DOES "200% LARGER" MEAN?
Whatever the person saying it wants it to mean.
>As a math teacher I explain this as follows:
>Assume John's salary is $1000 per month.
>If Mary's salary (M) is 50% larger than John's (J), then Mary makes $1500 per month or M = J+(50/100)J = 1.5J
>and
>If Mary's salary (M) is 100% larger than John's (J), then Mary makes $2000 per month or M = J+(100/100)J = 2J
>and
>If Mary's salary (M) is 200% larger than John's (J), then Mary makes $3000 per month or M = J+(200/100)J = 3J
The third one appears to be wrong. Common usage requires that the '%
larger' function have a large discontinuity at 100.
>Unfortunately, television commercials and newspaper advertisements clearly imply that if some item costs 200%
>more, it costs TWICE AS MUCH.
I take this as comparable to a team winning the World Series, then
playing Japan and being beaten. It appears to be part of the
American psychology, or at least the American media mogul psychology,
to be desire to be biggest, best, etc. Thus a discontinuity is
slipped into the '% greater' function, allowing one to give a bigger
number than would otherwise have been possible.
>I have yet to see the media make the distinction between:
> 200% larger
> 200% as large as
>I need advice in making this clear to my students.
Just tell them that what is common practice makes no mathematical
sense, but is too thoroughly entrenched for them to have any chance
of changing it.
Brian M. Scott
On 7 Dec 1997 06:43:20 GMT, g...@the.link.ca (g weinstein) wrote:
[snip]
>I have yet to see the media make the distinction between:
> 200% larger
> 200% as large as
I fear that it's a lost cause.
>I need advice in making this clear to my students.
I never use the formulations '200% larger' and 'ten times more' and
recommend that my students also eschew them. I offer explanations
similar to the one that you described. Finally, and perhaps most
important, I warn them that common usage is ambiguous and that the
*most* common usage is the illogical one.
Brian M. Scott
DNesselle
On Dec. 7, Gerald Weinstein asked how to explain to his students the difference
between "200% larger" and "200% larger than", when these phrases are used
interchangeably by the media.
It seems that Mr. Weinstein has already given an excellent explanation of the
difference and I am sure that his students understand the difference. I
believe that he should use this example to emphasize that:
1) His students should listen very carefully to all statements made by the
media because reporters and advertisements are either imprecise, inaccurate or
both, and
2) That they should always ask whether there is sufficient information in the
news item to enable them to evaluate the statement.
Unfortunately, I have had the same experience in interpreting the news so it is
certainly not unique to Mr. Weinstein's experience. A book by John Allen
Poulos, "A Mathemetician Reads the Newspapter", 1995, BasicBooks addresses
many of the issues involved in interpreting the news.
J. B. Rainsberger
In article <66ee4m$5...@ux.cs.niu.edu>,
ric...@cs.niu.edu (Neil Rickert) wrote:
>In <66dgi8$j...@snews2.zippo.com> g...@the.link.ca (g weinstein) writes:
>
>>WHAT DOES "200% LARGER" MEAN?
>
>Whatever the person saying it wants it to mean.
I don't know about that.
>I take this as comparable to a team winning the World Series, then
>playing Japan and being beaten.
The difference here is that of terminology. The World Series has nothing to
do with "the world". It's from the name of the original sponsoring newspaper.
It ought to be called its full name, "The World Series Championship." It's the
unfortunates who call the winners "World's Champions" who make it difficult.
The "World" in "World's Champions," again, is the original sponsoring
newspaper.
>Just tell them that what is common practice makes no mathematical
>sense, but is too thoroughly entrenched for them to have any chance
>of changing it.
Yep. Social and media inertia. Ain't it grand?
J. B. Rainsberger
Department of Computer Science, University of Toronto
http://www.cs.toronto.edu/~jbrains
"You've certainly been a model of restraint to this point."
- Hobbes the Tiger
Douglas P. McNutt
In Article <66dgi8$j...@snews2.zippo.com>, g...@the.link.ca (g weinstein) wrote:
>WHAT DOES "200% LARGER" MEAN?
WHENEVER I hear the word "percent" I ask the speaker for the values in the
numerator and the denominator.
If he/she doesn't know what I am talkng about I politely tell him that I
shall ignore his comment.
On TV, in print media, or at political rallys I ignore all percentages on
principle.
When dealing with a bank even the US government mandated "APR" is often a lie!
I'm sorry - I have to cut your salary by 50% this week. But I'll make it up
next week with a 50% increase.
-> From the USA. The only socialist country that refuses to admit it. <-
William L. Bahn
I think you are doing about as well as can be expected. The news media (to
name just one) is notoriously sloppy with math-related terminology. Every
time I see something where a reporter uses the phrase, "200% more" to mean
twice as much I cringe. When possible, I call up the reporter and ask them
if they really believe that if I have 100 dollars and they have 200% more
money than I do that they have 200 dollars. They almost always say yes. I
then ask them how much money they would have if they had 300% more than I
did, and they say 300 dollars. I then ask how much they would have if they
have 100% more than I did and they usually start going. "Uhm, uhm ...
well." I've had quite a few of them that respond with $100 to which I reply
"So, if you have 100% more than me, you actually have the same amount as
me? Does this mean that if you have 50% more than me that you actually have
less than I do?" To which a few have said yes.
The other big area where they get hopelessly confused is when dealing with
percentage changes. They can't distinguish between a 10 percent change in
the rate of something and a 10 percentage point change in that same rate.
g weinstein <g...@the.link.ca> wrote in article
<66dgi8$j...@snews2.zippo.com>...
> WHAT DOES "200% LARGER" MEAN?
>
>
> As a math teacher I explain this as follows:
>
> Assume John's salary is $1000 per month.
>
>
> If Mary's salary (M) is 50% larger than John's (J), then Mary makes $1500
per month or M = J+(50/100)J = 1.5J
>
> and
>
> If Mary's salary (M) is 100% larger than John's (J), then Mary makes
$2000 per month or M = J+(100/100)J = 2J
>
> and
>
> If Mary's salary (M) is 200% larger than John's (J), then Mary makes
$3000 per month or M = J+(200/100)J = 3J
>
> Unfortunately, television commercials and newspaper advertisements
clearly imply that if some item costs 200%
> more, it costs TWICE AS MUCH.
>
> I have yet to see the media make the distinction between:
> 200% larger
> 200% as large as
>
> I need advice in making this clear to my students.
>
>
> Gerald Weinstein
> g...@the.link.ca
>
>
>
>
>
Dr Michael Ecker
Unfortunately, although I agree with the sentiments about the need to be
careful, you missed the real issue.
"200% larger" and "200% larger than" mean the same thing. The former is
elliptic (short) for the latter, which in turn is elliptic for "200%
larger than (whatever original item is)".
The real issue is "200% larger" vs. "200% times as large". The first
means the difference is two times more than the original item - and
therefore actually three times as big. The second means the difference
is two times as big.
A good example of this about a decade ago was when Pete Rose became
manager (?) of the Cincinnati Red Sox for a salary of $1,000,000
compared to the $250,000 he had made earlier. CNN stated that he was
making 400% more.
In fact, he was making "only" 300% more, or 400% as much (as before).
Hope that helps!
DNesselle wrote:
-
Dr. Michael W. Ecker, Editor
Recreational & Educational Computing
Clarks Summit, PA 18411
& Math Professor, PSU
(Standard disclaimer: Affiliation for
ID only. Views expressed are my own.)
===============================
"Excellence is its own reward."
===============================
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but I do check it and you can reach me. You can
reach me as well at MWE1 at-sign psu dot edu
(Replace "at-sign" by "@" and dot by "."
- with no spaces. KILL THE SPAMMERS!)
Anonymous
A similar unclear construction is: "three times less"
nob...@nowhere.on.ca
On 7 Dec 1997 06:43:20 GMT, g...@the.link.ca (g weinstein) wrote:
>WHAT DOES "200% LARGER" MEAN?
>
>
>As a math teacher I explain this as follows:
>
>Assume John's salary is $1000 per month.
>
>
>If Mary's salary (M) is 50% larger than John's (J), then Mary makes $1500 per month or M = J+(50/100)J = 1.5J
>
[snip]
>I have yet to see the media make the distinction between:
> 200% larger
> 200% as large as
>
>I need advice in making this clear to my students.
>
>
As a former teacher, that's the way I would interpret it (in agreement
with you.)
"200% larger" is the same as "increased by 200%."
I would ask, "What does 100% larger mean?" There is no problem here
that I can see in the interpretation.
Douglas P. McNutt
In Article <348bc936...@news.igs.net>, nob...@nowhere.on.ca wrote:
>On 7 Dec 1997 06:43:20 GMT, g...@the.link.ca (g weinstein) wrote:
>
>>WHAT DOES "200% LARGER" MEAN?
>>As a math teacher I explain this as follows:
>>Assume John's salary is $1000 per month.
>>If Mary's salary (M) is 50% larger than John's (J), then Mary makes $1500 per
month or M = J+(50/100)J = 1.5J
>[snip]
>
>>I have yet to see the media make the distinction between:
>> 200% larger
>> 200% as large as
>>
>>I need advice in making this clear to my students.
A concurrent thread in alt.usage.english is comming to just the opposite
conclusions from this group!
Lynn Killingbeck
g weinstein wrote:
>
> WHAT DOES "200% LARGER" MEAN?
>
> As a math teacher I explain this as follows:
>
> Assume John's salary is $1000 per month.
>
> If Mary's salary (M) is 50% larger than John's (J), then Mary makes $1500 per month or M = J+(50/100)J = 1.5J
>
>
> If Mary's salary (M) is 100% larger than John's (J), then Mary makes $2000 per month or M = J+(100/100)J = 2J
>
> and
>
> If Mary's salary (M) is 200% larger than John's (J), then Mary makes $3000 per month or M = J+(200/100)J = 3J
>
> Unfortunately, television commercials and newspaper advertisements clearly imply that if some item costs 200%
> more, it costs TWICE AS MUCH.
>
> 200% larger
> 200% as large as
>
> I need advice in making this clear to my students.
>
> g...@the.link.ca
You might enjoy the classic 'How to Lie With Statistics' by Darrell
Huff, or '200% of Nothing' by A.K.Dewdney. Try such blatant nonsense
as '... an amazing savings of "200 percent on energy."'
Lynn Killingbeck
Terry Moore
In article <01bd033e$4f770de0$0400a8c0@BAHN>, "William L. Bahn"
<ba...@pcisys.net> wrote:
> The other big area where they get hopelessly confused is when dealing with
> percentage changes. They can't distinguish between a 10 percent change in
> the rate of something and a 10 percentage point change in that same rate.
Nor can I. I thought a "point change" had something to do with the railways.
But then I prefer to speak English rather than Jargon.
--
Terry Moore, Statistics Department, Massey University, New Zealand.
Theorems! I need theorems. Give me the theorems and I shall find the
proofs easily enough. Bernard Riemann
Anonymous
In article <T.Moore-0912...@130.123.97.36>, T.M...@massey.ac.nz
(Terry Moore) wrote:
> In article <01bd033e$4f770de0$0400a8c0@BAHN>, "William L. Bahn"
> <ba...@pcisys.net> wrote:
>
> > The other big area where they get hopelessly confused is when dealing with
> > percentage changes. They can't distinguish between a 10 percent change in
> > the rate of something and a 10 percentage point change in that same rate.
>
> Nor can I. I thought a "point change" had something to do with the railways.
> But then I prefer to speak English rather than Jargon.
>
> --
>
> Terry Moore, Statistics Department, Massey University, New Zealand.
Maybe they don't say it this way in New Zealand. Say the unemployment
rate was 10 percent, and then increased to 12 percent. That is an increase
of 2 percentage points, but an increase of 20 percent. At least here
in the US we say it that way.
But don't try to get public figures to use numbers correctly. Last year
we had a debate about "cuts" in tax support for health care (Medicare). The
amount of tax support was still to increase, but the RATE of that increase
was to be less. News headlines called it a "cut in Medicare" and
it therefore never had a chance.
PTWahl
On 9 Dec 1997 16:24:12 +0100, nob...@REPLAY.COM
(Anonymous) wrote, in part:
>But don't try to get public figures to use numbers correctly. Last year
>we had a debate about "cuts" in tax support for health care (Medicare). The
>amount of tax support was still to increase, but the RATE of that increase
>was to be less. News headlines called it a "cut in Medicare" and
>it therefore never had a chance.
Granted that this was widely debated, and that the truth
was obscured by political rhetoric. But the headlines were
not necessarily wrong.
If I budget 5% more for gasoline, and the price rises 10%,
my increased budget will still purchase less gasoline, and my
car won't go as far. It comes down to a question of which
item you choose to measure.
Most relevant here is not the US government's dollar
outlay, but the quantity of service provided.
It is entirely possible that an increased outlay of dollars
can occur in combination with a cut in the quantity of
service provided. Also, the total quantity of service may
increase while the average quantity decreases, since the
client population is growing rapidly.
Three major variables are all increasing: The population
receiving aid, the average unit cost of services they
consume, and the government outlay in dollars. If the
first two grow faster than the third, the citizen in the
street may well experience a "cut."
Patrick T. Wahl
nob...@nowhere.on.ca
>
>A concurrent thread in alt.usage.english is comming to just the opposite
>conclusions from this group!
>
Tell them to come here for the correct version. :-)
Padraig Breathnach
Douglas P. McNutt wrote:
>
> A concurrent thread in alt.usage.english is comming to just the opposite
> conclusions from this group!
>
I'm here, might I suggest that Douglas has effected a 100% increase in the
number of "m"s in "coming", and should now reduce it by 50%.
PB
Matthew A Halverson
In article <66dgi8$j...@snews2.zippo.com>, g...@the.link.ca says...
>
>WHAT DOES "200% LARGER" MEAN?
>
>
>As a math teacher I explain this as follows:
>
>Assume John's salary is $1000 per month.
>
>
>If Mary's salary (M) is 50% larger than John's (J), then Mary makes $1500 per
month or M = J+(50/100)J = 1.5J
>
>and
>
>If Mary's salary (M) is 100% larger than John's (J), then Mary makes $2000 per
month or M = J+(100/100)J = 2J
>
>and
>
>If Mary's salary (M) is 200% larger than John's (J), then Mary makes $3000 per
month or M = J+(200/100)J = 3J
>
>Unfortunately, television commercials and newspaper advertisements clearly
imply that if some item costs 200%
>more, it costs TWICE AS MUCH.
>
>I have yet to see the media make the distinction between:
> 200% larger
> 200% as large as
>
>I need advice in making this clear to my students.
>
>
>Gerald Weinstein
>g...@the.link.ca
>
>
>
>
This has annowed me for many years. x% larger should be (1+x%)y not x%*y. We
are expressing how much GREATER something is, not the ratio between sizes.
200% larger than 10 should be 30 not 20. Although, fellow mathematicians, we
all know the media makes many mistakes.
Terry Moore
> In article <T.Moore-0912...@130.123.97.36>, T.M...@massey.ac.nz
> (Terry Moore) wrote:
>
> > In article <01bd033e$4f770de0$0400a8c0@BAHN>, "William L. Bahn"
> > <ba...@pcisys.net> wrote:
> >
> > > The other big area where they get hopelessly confused is when dealing with
> > > percentage changes. They can't distinguish between a 10 percent change in
> > > the rate of something and a 10 percentage point change in that same rate.
> >
> > Nor can I. I thought a "point change" had something to do with the railways.
> > But then I prefer to speak English rather than Jargon.
> Maybe they don't say it this way in New Zealand. Say the unemployment
> rate was 10 percent, and then increased to 12 percent. That is an increase
> of 2 percentage points, but an increase of 20 percent. At least here
> in the US we say it that way.
I have heard the expression. But it doesn't really solve the problem.
The word "point" usually refers to the digits after a decimal point,
so "an increase of 2 percentage points" could mean an increase of
0.2%. I know it isn't used that way, but logically it could be.
I have no objection to jargon between consenting adults, but
it shouldn't be taken as proof of mathematical incompetance not
to know the jargon.
There is a difficulty that needs to be solved. If a Saturn V rocket
is upgraded from 10^6 kg thrust (I don't know what it really is)
by 1000kg that's an increase of 1000kg (obviously). By exactly
the same model of English usage, if an interest rate is increased
from 10% to 11% that's a 1% increase. That's an absolute increase
of 1%, but, of course, a relative increase of 10%. There would be
no ambiguity in saying that the Saturn V thrust had been increased
by 0.1% (the context implies a relative change), but there is clear
ambiguity in the case of units that are already expressed as
percentages.
The jargon (percent vs percentage point) is OK for people who
know it, but one must recognise the ambiguity. The proper
solution is to add the words "proportion", "relative",
"amount" or "absolute" (or some equivalent words) in the
appropriate places, in other words, to say what you mean.
On the original question, the mathematician in me says
that I should stick with the logical approach and not worry
about the more naive interpretation. It just offends my
aesthetic sensibilities too much to accept that a 1% (relative)
increase means the same as a 101% (relative) increase.
--
Terry Moore, Statistics Department, Massey University, New Zealand.
Theorems! I need theorems. Give me the theorems and I shall find the
Paul Kunkel
Since someone went to the trouble of opening this thread for letting
off steam, let me add another. What about the people who say percentage
when they mean average? Baseball announcers are the worst offenders of
all. A shortstop with a .980 fielding percentage is supposed to be a
rare talent. If I take that figure literally, it means that he is
fielding less than 1% of the balls that come his way. I guess that would
still make him a rare talent.
Kunkel
Daniel Giaimo
Terry Moore wrote:
>
> In article <01bd033e$4f770de0$0400a8c0@BAHN>, "William L. Bahn"
> <ba...@pcisys.net> wrote:
>
> > The other big area where they get hopelessly confused is when dealing with
> > percentage changes. They can't distinguish between a 10 percent change in
> > the rate of something and a 10 percentage point change in that same rate.
>
> Nor can I. I thought a "point change" had something to do with the railways.
> But then I prefer to speak English rather than Jargon.
>
Suppose that I have a 70% off sale on something that normally costs
10 dollars. It would now cost 3 dollars. Now if I take an additional
10% off it cost $2.70; however many advertisers call this a 70 + 10%
sale, confusing the public into believing that they are getting 80% off
rather than just 73% off.
--
"Do you know what a mathematician is? A mathematician is one to whom
(*) is as obvious as twice two makes four is to you."
--Lord Kelvin, to a class of physics students
_
/ inf
| / 2\ __
(*)| | -x |dx = \/pi
| \ e /
_/ -inf
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unless stated otherwise, everything in the above message is personal opinion
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