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Wisdom of the Crowds competition - the answer - YouTube
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hello everyone first of all let me
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introduce you to David speaker holder
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who we've had on before with our
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non-transitive dice video which is one
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of the prices on offer in our
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competition today but first of all did
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you not get the memo did you know we
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were going to dress up for this I chose
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for the for the people that houses my
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mathematical trance
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mrs. Hughes dressed up is any choice
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okay said David tell us about the
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competition with it what in his last
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video James asked you to guess how many
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jelly beans were in this jar and he's
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had over a thousand entries we've had
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over a thousand responses we're going to
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analyze the results and we've had a
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winner which is in this envelope yes
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you're right ago yes the winner is in
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this envelope the correct answer I did
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get a dick count all the jelly beans
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myself but we will reveal this at the
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end of the video so the last time I told
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you about the wisdom of the crowd so a
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mathematician called Sir Francis Galton
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wants to know that crowd of people could
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decide what the correct weight was of a
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butchered ox now David what do you think
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of wisdom of the crowds is it real or is
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it bulk well I worked in Goldman's case
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because he was at a country fair where
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people knew quite a lot about meat and
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about what an animal look like I've had
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been chopped up and laid out and what
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that actual quantity of meat would come
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to when they added it all up but when
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you try to estimate how many beans and
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something like that it's quite tricky
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because you're trying to estimate how to
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sense your volume from just a
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two-dimensional view of it people could
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have some systematic biases in other
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words they could on average even gets
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too high or too low and I'm going to be
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really interested to see what results
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are so the wisdom is important exactly
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so unfortunately we did have to reject
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some of the outliers which I just
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thought were typos really and to be fair
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Sir Francis Galton had to do this
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himself when he did it in his original
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problem so I felt justified doing that
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the were as well some obvious joke
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answers if there does turn out to be a
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googol of jelly beans inside the jar
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you'll still win don't worry you're
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still in the competition
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francis galton actually was charging six
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pence which he thought would be enough
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to deter joke answers
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like that so in future that's what we'll
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do we'll start charging six months we
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could make 60 quid out of this and but
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there might as well be some bias because
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in this case people could see other
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people's answers as well and we're not
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sure well but David take us through what
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happened take us through the data let's
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have a look okay here is the
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distribution of the judgments that were
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made the guesses that were made we see
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here they range from you know very low
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right up to nearly ten thousand some
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people thought their new 10,000
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jellybeans in that jar most of them
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around about bit below between two
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thousand and two thousand and we see a
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peak here but a long tail with some
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people thinking 3,000 4,000 5,000 jail
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beans in the jar so we got is a very non
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symmetric distribution of judgments the
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problem when we've got a distribution
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like this we have a sort of skew
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distribution is it's not at all clear
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what measure we should use when we won't
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say the average opinion there's a number
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of different averages we could choose
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right so we could use the most common
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answer right which is called the mode
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average and in this case the most common
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answer was 1337 budget net what else
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could we use we could use the mean the
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arithmetic mean that means you add up
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all the guesses that were made and
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divided by the number of people who
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enter the competition and if you do that
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you get a considerably higher value
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about 2059 jelly beans and the point
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about the mean is that it's very
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strongly influenced by these few people
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who thought there were 8,000 jelly beans
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in the jar so instead we might want to
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use another type of average called the
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median average so if I listed all the
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guesses in order and I took the middle
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value
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I actually got 1729 Hays Ramanujan's
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number and in this case the median could
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be considered the average person's
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judgment rather than the average
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judgment so instead of looking at the
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data directly we decided to take a look
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at the log of the data so why is a log
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the log is the power of 10 needed to
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make that number so a thousand would
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have a power of three it's three powers
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of 10 10
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times ten times ten is a thousand so the
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log of a thousand is three the log of
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10,000 is four it's four powers of ten
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10 times 10 times 10 times 10 is 10,000
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and that's what we did we took the data
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and we took the log of the data and this
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is what we got when you do this you end
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up with a really nice symmetric
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distribution and in fact then we can fit
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a normal curve to that where they
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standard old bell-shaped curves and it
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fits the data rather well and that means
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if we fed a normal distributions of data
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then we know how to take the looking for
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the average we should just take a sample
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mean of those logarithms of the
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observations in order to estimate the
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center of this distribution so this is
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what we did we took the average of the
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log of the data and we found that the
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average power of 10 was three point two
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three so we take 10 to the power of
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three point two three we get our average
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now as 1680 and this is called the
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geometric mean it's the mean of the log
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of the data and well what's so good
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about it the geometric mean is a good
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measure to use if you think the sort of
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mistakes people make are proportional
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mistakes in other words they're just as
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likely to get double the answer as half
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the answer and if that if you think that
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and that's what gives rise to shapes
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like this as a distribution then you
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should use the geometric mean so I think
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if I really believed there wasn't any
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systematic bias in people's judgments I
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would say one six eight oh would be on
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our best judgment
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so now let's reveal the answer in this
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envelope which david hasn't seen so
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David you're going to be revealing this
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answer soon honorable mentions I think
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to these three people here who actually
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got the median average of 1729 so these
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are average people right here another
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honorable mention to virtual noodles who
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was closest to our average value of 1680
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he actually got 1681 but now to reveal
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the actual answer which I'll give to
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David also so excited and the answer is
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one sick
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one six 1616 which is acting within
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about four percent of our average which
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is pretty good initially amazing how you
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can work on with actual real data we've
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actually gotten pretty good answer
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congratulations to our winner
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didi ss6 who actually got it on the nose
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1616 and I'll make a butt pad for you
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it's going to include this Top Trumps
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mathematicians and non-transitive dyes
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whatever I think of so congratulations
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again and if you have been thanks for
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watching well it's amazing
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