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Francis Galton's Ox
Topic Started: Jan 5 2011, 07:43 PM (694 Views)
CJ
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A very minor case of serious brain damage

Francis Galton was a British scientist who, in 1906, visited a country fair. He found that there was a contest, where people attending the fair were invited to guess the weight of an ox. The winning guess was 1,208lb (the actual weight of the ox was 1,198lb, so the winner was 10lb off), but when he analysed the guesses, he found two very interesting things:

1) The winning guess was the median: just as many people guessed above it as below, and;
2) Even more interestingly, when he found the mean of the guesses (added all of the guesses up and divided by the number of people guessing), he found that it came to 1,197lb: just 1lb away from the actual weight of the ox!

So, the average of all the guesses was much closer to the correct answer than any guess. It was as if all the people, as a collective, had a much greater knowledge than even the best individuals. People with experience of animals like this, such as butchers and large animal vets, were all at the fair and making their guesses, but even they couldn't get their guesses as close as the average! Even when Galton excluded the experts from his calculations, the average of all the 'normal' people was still very close.

This has been verified repeatedly (for example, with jelly bean experiments, where the average of all the guesses ends up very close to the correct answer), and it does have widespread applications. An obvious one would be democracy, where individual voters, with their varying knowledge of politics, are as well-equipped to judge the candidates' policies as the people at the fair were to judge the weight of the ox.

And I thought statistics was boring :P !
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Michelle
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Err don't really understand but, but cool.
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Candyguitar
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I've always found this bizarre. How on earth could this work :blink: ?? It would be helpful if everyone knew the approximate weight of the ox, but that doesn't explain how they were so accurate collectively.

I'd also think it only works for numerical matters, since in politics we've had anti-scientific nonsense being implemented (e.g. creationism in schools (mainly US) and homeopathy in the NHS), not to mention that the United States had GWB as president for 2 terms.
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CJ
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A very minor case of serious brain damage

Yeah, it is bizarre. If it had happened just once (i.e. in the original experiment), I would probably have put it down to coincidence, but since it's been verified repeatedly, I can't really do that.

As for the other things, it might be that it only works for numerical matters, but there is another important thing about this as well. There are ways to throw it off: one is that you need a wide variety of people from different backgrounds, so if you have too many people from the same culture (e.g. fundamentalist Christians in the USA), this isn't going to work. It also won't work if the subject is too emotional, and people are unable to make a reasoned decision. With the numerical matters, the guesses also need to be independent, so it won't work if people can see all of the previous guesses, because they'll be biased by those.

I'm not sure about Dubya, but then, we don't know whether either of his opponents would have been any better. I blame the two-party system :P .
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Michelle
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*struggling to understand* Umm I don't get it. Someone actually teach me?

(No one replied to my above post....)

(Sorry if I sound pushy..., just hate it when people ignore me when I don't understand something...)
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CJ
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A very minor case of serious brain damage

Sorry....I wasn't sure how to reply.

Basically, there was this country fair where you had to guess the weight of an ox. The actual weight was 1198lb, and the winning guess was 10lb off (at 1208lb). However, the average of all the guesses was 1197lb (only 1lb off the correct answer!).

It's not just a coincidence either: it works for all sorts of things. If you do a 'Guess the number of jelly beans in a jar' experiment, and get hundreds of guesses, you should find that the average of all the guesses is VERY close to the correct answer. It'll probably be much closer than the winning guess.
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Michelle
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Kinda doesn't make any sense... but okay.
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