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