A correct way, would be to suggest that for instance - 44 out of 45 people asked said.... Percentages only work well, with much larger quantities.
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- Thread starter Harry Bloomfield
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A correct way, would be to suggest that for instance - 44 out of 45 people asked said.... Percentages only work well, with much larger quantities.
As I've written to Harry, I think that most people 'understand' percentages, in the sense that the find them more easily conceptualised and thought about than fractions. I suppose that makes sense, in as much as one is essentially converting fractions to ones that all had a common denominator, enabling one to compare chalk with chalk, rather than with cheese.
For example, I suspect that many, even very 'numerate', people could not tell you, at a glance (i.e. with at least doing some mental arithmetic), whether, say, 7/17 was more or less than 5/16. However, if one converted that to (approximately, rounded), 41.2% and 31.3% the answer would be obvious to almost anyone. Even more dramatic if the fractions were, say, 59/171 and 76/211
What a lot of people understand far less is how to 'apply' percentages - in particular, as you go on to illustrate, getting the numerator and denominator 'the right way around'.
That's actually quite a subtle one, and a very common sort of error. In fact, I suspect that an appreciable proportion of even fairly 'numerate' people would come up with the incorrect answer 'intuitively', even if they would produce the correct answer if they 'stopped and thought about it'.
Consumers can sometimes be exploited when two or more 'percentage discounts' are applicable to a purchase, since the order in which the discounts are applied will affect the total amount of discount they agree - so guess what order the sellers usually use
.Very often, to the extent that if they say "200% increase", one really can't be even remotely sure as to whether they actually mean a 'doubling' opr 'trebling'. However ......
That's a more complicated one, and one which I personally often have to deal with quite often, and where standard terminology/language does not necessarily result in clarity!
There are plenty of quantities which are normally expressed in 'units' of "%" - things like relative humidity, inflation, interest rates etc. etc. and, in the medical field, things like HbA1c, many respiratory function tests, some 'blood counts', % surviving at X months etc. etc.
If a quantity increases from 200 Volts to 220 Volts, we would describe that as an increase of 20 Volts - and similarly if the increase was from 200 metres to 220 metres, 200 degrees to 220 degrees or whatever. However, if the 'unit' of the quantity is "%", then a statement such as "an increase of 10%", this is quite likely to be taken to mean (as per your thinking above) as meaning a 10% increase in the percentage. In many cases, that is not the 'change'/'difference' of interest, actual interest being in the 'absolute change in percentage'. When I'm dealing with this, I have little choice but to explicitly talk about "absolute change/difference in percentage", but that's rather long-winded and 'messy'!
Another problem with 'percentage changes/differences' is that they are not infrequently talked about without the necessary consideration of the absolute magnitudes of the changes/differences concerned. We've seen that with various "Pill scares" and "Vaccine scares". The revelation that something results in, say, a 50% (or even 100%) increase in the risk of death, or something else nasty, sounds pretty dramatic, and worrying. However, if (as has sometimes been the case) the "50% increase" has been an increase from "1 in 5 million" to "1.5 in 5 million", it is very questionable as to whether anyone should lose much sleep over it
If that suits you better, then fair enough - but, as I've said, most people prefer percentages - which, as I've said, makes comparisons much simpler, since percentages are really only fractions with the denominator always being the same (100).
It's also the case that percent figures are what really 'matters'. For example, in terms of estimation of the figure for the entire population, 44,000 out of 45,000 has exactly the same significance as 44 out of 45, since both can be expressed as the same percentage.
What on earth does that mean? Do you not think t useful to being able to say, for example, what percentage of people with lung cancer survive for 10 years from diagnosis, or what is considered to be the maximum safe percentage of arsenic in tap water (both of those answers being extremely small) ?
I will certainly ditto that.I'm not sure what that has got to do with this discussion, but I totally agree. I may well have previously told this story stemming from my days in the 6th form at school, some 60 years ago ....
... there had traditionally been Saturday Night School Dances, but interest/attendance had been waning to the extent that we were contemplating stopping them. A series of people had tried all sorts of ploys and gimmicks to try to attract attendees, but with very little effect, and the buck was eventually passed to me!
Like those before me, all of the changes/gimmicks I tried had very little effect. As a last resort, when I was also about to 'give up', I dramatically increased the price of tickets, to a level which ought to have been 'unaffordable' for most school kids. Everyone started coming, presumably on the basis that "it's so expensive that it must be good" - and these (very expensive) weekly events thereafter remained a great success for the rest of my time at school- and I, of course, became a "hero"
It seems that there are a lot of 'gullible' people in this world
I have known it at secondhand markets etc, if it doesn’t sell then out the price up and it sells.
One chap I knew on Preston Market used to sell second hand tea makers, he expressed a view that if a particular teasmaid was not sell for £12 he would rather it doesn’t sell at £14 so he puts the price up to £14 and it sells immediately, he said he had done this kind of thing many times and it most often works and very quickly in comparison with trying to sell at the lower price for a few weeks.
I tried a similar thing myself once and yes it did work! .
I visited a second hand market many years back and a relative had a stall there and she showed me two wooden skulls she’d just bought for 10p each and thought she might get as much as a pound each, I advised her to sell them for £12 for the two, she tried it and sold them straight away.
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When I worked in sales, it was accepted practice that you never gave services away for free, as people don't value something which is free. Put chargeable ones in the bid, and discount the total, leaving the customer with the same net price, but nominally paying for services.
Another thing about percentages is that you are changing the baseline.
an increase from 100 to 120 is a 20% increase,
A decrease from 100 to 80 is a 29% decrease.
Wait for it —- ——- An increase from 80 to 100 is a 25% increase.
So 80 and 100 two numbers from one to the other is 20 percent one way but is 25% the other way .
Therefore if you start from 100 then keep adding 10% at every step then you get to the end of your series of steps then decrease by 10% for the same number of steps you get two confusingly different answers.
I did once mention a story on here from my apprentice days about two blokes arguing percentages they’d done on their Sinclair Cambridge calculators.
The difference between them being 20% or 25% and asked me to settle the argument?
I told them they were both wrong ……… but they were both correct, depends where you start and where you finish.
Happy days , the penny did drop eventually.
I did the same more recently with the Brexit Vote, couple of blokes arguing by how far the votes were won/lost.
Millions more/lost votes against percentages.
I liked it to two rooms each containing 50 voters.
Two voters from one room moved into the other room, not a big change is it?
Add on the differences in rooms if it was only older voters against only younger voters or rich v poor or north v south or by other categories too numerous to mention and the differences could be quite startling one way or the other .
Personally I thought that for something as important as a change like that then a 50/50 vote was not a deciding line to go after .
I think that any very important change then a clearer majority should be the deadline for such a monumental change, 60/40 or 70/30 perhaps in my humble opinion but in any case well outside the 55/45 range if results for a monumental change to the whole country or the whole nation
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an increase from 100 to 120 is a 20% increase,
A decrease from 100 to 80 is a 29% decrease.
Wait for it —- ——- An increase from 80 to 100 is a 25% increase.
So 80 and 100 two numbers from one to the other is 20 percent one way but is 25% the other way .
Therefore if you start from 100 then keep adding 10% at every step then you get to the end of your series of steps then decrease by 10% for the same number of steps you get two confusingly different answers.
I did once mention a story on here from my apprentice days about two blokes arguing percentages they’d done on their Sinclair Cambridge calculators.
The difference between them being 20% or 25% and asked me to settle the argument?
I told them they were both wrong ……… but they were both correct, depends where you start and where you finish.
Happy days , the penny did drop eventually.
I did the same more recently with the Brexit Vote, couple of blokes arguing by how far the votes were won/lost.
Millions more/lost votes against percentages.
I liked it to two rooms each containing 50 voters.
Two voters from one room moved into the other room, not a big change is it?
Add on the differences in rooms if it was only older voters against only younger voters or rich v poor or north v south or by other categories too numerous to mention and the differences could be quite startling one way or the other .
Personally I thought that for something as important as a change like that then a 50/50 vote was not a deciding line to go after .
I think that any very important change then a clearer majority should be the deadline for such a monumental change, 60/40 or 70/30 perhaps in my humble opinion but in any case well outside the 55/45 range if results for a monumental change to the whole country or the whole nation
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Remember that time Farage said 52-48 votes should lead to a second referendum?
Guess he didn't see what was coming...
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Typo.
Indeed. I have in my time quite often quoted for work at a rate well above 'the going rate', but then included in the quote a 'discount' to get it back down to something like that 'going rate'.
A good few clients seem to be naive enough to believe that this means that they would be getting a service which was 'better' (because it was more expensive) than 'normal', but at a normal rate, and therefore were attracted by such a quote - and I never complained if that';s how they thought
Quite so [assuming that your "29%" wss a typo for "20" !], as I wrote (and morqthana had already illustrated) ....
I'm very inclined to agree (in relation to the Brexit voting). In many walks of life (including, I think, some political/parliamentary ones) votes on 'very important' (let alone 'monumental') issues require appreciably more than 50% of the votes to 'win' - and, like you, I'm bit surprised that was not the case with the Brexit vote.
Of course, it depends on exactly what is being voted for. If, as with Brexit, it a vote for a change from a long-established 'status quo', then what I've just written seems reasonable (at least to me!). However, if one were voting for, say, the choice between two new things (or even two parties in a General Election) one could not really get away from the 'winner' being the choice with the greater number of votes, no matter how small the margin.
Typo yes sorry
In my opinion not even a 100% vote in favour should permit membership of a supranational body such as the so-called "EU" which seeks to usurp national sovereignty. Obviously the irony is that the so-called "UK" is a similar supranational body.
So a 100% vote you would still block membership? Maybe you are a dictator then???
That wouldn't be 100%, would it?
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