This might not be in any book, but it is quite intuitive
and has to be true.
At least sometimes we need to fix the books.
Ratio has to do with proportions and fraction has to do with parts of a
whole.
If we go for etymology, ratio is associated with reckoning (http://www.etymonline.com/index.php?term=ratio)
and fraction is associated with breaking and part (http://www.etymonline.com/index.php?allowed_in_frame=0&search=fraction&searchmode=none),
so that everything is compatible with what we are saying.
There is then a huge difference between one item and another.
We use ratio, and represent it by a:b, when we mean proportion and we use
fraction, and represent it by a/b, when we mean parts of a whole.
The media frequently changes normal figures of entrance exams into proportions, what may cause a lot of misconception and
misunderstanding even in our experienced scientific minds.
http://blogs.abc.net.au/antonygreen/2013/11/average-candidates-per-vacancy-at-federal-elections-1949-2013.html talks about an average of 13.2 candidates per vacancy when they
had 529 candidates contesting 40 Senate seats.
It then looks like they have simply divided 529 by 40, is it not?
If we put 529/40 in our calculators, we certainly get 13.225.
What is wrong with this? – you will ask.
We also initially saw nothing wrong with that sort of
assertion.
This assertion is not only untrue; it is also absurd.
We cannot make the three-point rule with this sort of matter because it is
not true that there is a proportion involved there.
See: 529 candidates per 40 vacancies does not imply that if we have fewer vacancies (say 30), we will have fewer candidates or that if we have fewer vacancies, we will have more candidates, or that if we have more vacancies (say 50), we will have fewer candidates or that if we have more vacancies, we will have more candidates.
See: 529 candidates per 40 vacancies does not imply that if we have fewer vacancies (say 30), we will have fewer candidates or that if we have fewer vacancies, we will have more candidates, or that if we have more vacancies (say 50), we will have fewer candidates or that if we have more vacancies, we will have more candidates.
Even if there were a projection in this direction, say that the number of
vacancies could influence the candidate’s decisions, we would need to know how
exactly that happens to be able to tell whether we have a proportion or not.
It is not true that, if we double the number of seats, we have
twice as many candidates or half as many.
Yet, with true proportions, that is an acceptable inference.
Yet, with true proportions, that is an acceptable inference.
We will have the same number of candidates if the number of our vacancies changes
after everyone has entered the competition, so that the dispute
over one or 40 seats involves always the same 529 candidates and we then have
529 people disputing over the 40 vacancies all together, at the same time.
The upshot is that it is wrong making these divisions and telling
people that things are like that.
It is not because we have these figures (529 and 40) that we are disputing with at most
13 other people over one vacancy in the Senate.
No, we are still disputing them with everyone else, that is, with the other 528 candidates.
No, we are still disputing them with everyone else, that is, with the other 528 candidates.
Notice that we could only do things the other way around: suppose that all vacancies have been assigned apart from one. We then have 490 candidates for one vacancy.
All that we say and write has got a certain level of social impact (Psycholinguistics) and it is really not pleasant feeling lured, so that we should not make these outrule divisions anymore (we recently saw a fellow using the term illegal in this situation and we felt tempted to do that, but we then thought twice and decided for inventing outrule (copying outlaw), since what we mean is that it is against the rules of Science/Mathematics).
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