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On Wed, 21 Jul 2010 18:17:36 +0100, Orchid XP v8 wrote:
>>>> But look on the bright side; your score of 121 is still quite a bit
>>>> higher than the mean of 100.
>>> Unfortunately, the "average" person is really, really stupid...
>>
>> By definition, you know that's not true. "Average" is *average*, not
>> *below average*.
>
> How do you work that out?
Mathematically.
> Depending on precisely which "average" you mean and what kind of
> distribution the population follows, if *most* people are stupid, then
> the "average" person is also... stupid.
Mathematically, if most people are stupid, the average goes down, and
"stupid" becomes "below average" for the new average.
A score in the 120's is not "stupid" by any stretch. Sheesh.
Jim
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On 21/07/2010 6:35 PM, Jim Henderson wrote:
> A score in the 120's is not "stupid" by any stretch. Sheesh.
There is a terrible stench of snobbery about. o_O
--
Best Regards,
Stephen
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On Wed, 21 Jul 2010 18:51:30 +0100, Stephen wrote:
> On 21/07/2010 6:35 PM, Jim Henderson wrote:
>> A score in the 120's is not "stupid" by any stretch. Sheesh.
>
> There is a terrible stench of snobbery about. o_O
LOL
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Jim Henderson <nos### [at] nospam com> wrote:
> On Wed, 21 Jul 2010 18:17:36 +0100, Orchid XP v8 wrote:
> >>>> But look on the bright side; your score of 121 is still quite a bit
> >>>> higher than the mean of 100.
> >>> Unfortunately, the "average" person is really, really stupid...
> >>
> >> By definition, you know that's not true. "Average" is *average*, not
> >> *below average*.
> >
> > How do you work that out?
> Mathematically.
If the curve of people's intelligence is not linear, it can mean that
the majority of people are actually below average than above it (or the
other way around, of course, depending on the sign of the derivative of
the curve).
As a simple example, if we have 4 people with IQs 90, 90, 90 and 130,
the average will be 100, but the majority of these people is below average.
In other words, three quarters of the people are "stupid" and one quarter
is "smart".
If you enter this group and score 100, it means that you will be smarter
than the majority (three people are "stupider" than you, while only one
is "smarter"), yet the average is still 100.
Thus scoring 100 does not automatically mean that you fall exactly in
the middle, with half the population being "stupider" and the other half
"smarter" than you. There may still be more of one than the other.
--
- Warp
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On Wed, 21 Jul 2010 13:58:06 -0400, Warp wrote:
> If the curve of people's intelligence is not linear, it can mean that
> the majority of people are actually below average than above it (or the
> other way around, of course, depending on the sign of the derivative of
> the curve).
For a large statistical sample, IIRC, it's basically a bell curve.
> As a simple example, if we have 4 people with IQs 90, 90, 90 and 130,
> the average will be 100, but the majority of these people is below
> average. In other words, three quarters of the people are "stupid" and
> one quarter is "smart".
Except that when measuring "average" intelligence, your sample size is a
population, not a small discrete number.
Jim
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Am 20.07.2010 20:03, schrieb Tim Cook:
> http://www.cerebrals.org/wp/?page_id=209
>
> Had to randomly guess for a few I couldn't figure out. Got 130.
144. Despite having not the slightest clue how those puzzles that looked
like "twist'n'mix" were supposed to be solved, and just doing more or
less "solid guessing" on them - I suspect you have to have seen this
type of puzzles before. (Then again, you actually do during the test, so
I did make use of the "back" button.)
At any rate, the IQ test I did at age ~10 was a lot more straightforward :-P
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Jim Henderson wrote:
> On Wed, 21 Jul 2010 13:58:06 -0400, Warp wrote:
>
>
>> If the curve of people's intelligence is not linear, it can mean that
>> the majority of people are actually below average than above it (or the
>> other way around, of course, depending on the sign of the derivative of
>> the curve).
>
> For a large statistical sample, IIRC, it's basically a bell curve.
It depends on what it's a statistical sample of. It only comes out a
bell curve under certain assumptions about how what you're sampling
behaves, and these will not hold in many circumstances.
That said, I think IQ tests do tend to come out more or less a symmetric
distribution (and close to a bell curve) so pretty close to half of the
population will indeed be below average, so the theoretical point Warp's
making doesn't really apply in this case.
>
>> As a simple example, if we have 4 people with IQs 90, 90, 90 and 130,
>> the average will be 100, but the majority of these people is below
>> average. In other words, three quarters of the people are "stupid" and
>> one quarter is "smart".
>
> Except that when measuring "average" intelligence, your sample size is a
> population, not a small discrete number.
>
It turns out that Warp's overall point is correct in this case, and you
can also generate examples for continuous probability distributions.
This occurs in cases where the distribution is asymmetric (see
http://en.wikipedia.org/wiki/Skewness). I'm not sure what he meant by
"the sign of the derivative", but maybe this was what he was thinking about.
I don't totally see how it applies to the conversation since "stupid"
and "smart" in this context haven't been given rigorous definitions, but
if you are to define them by which side of the IQ median you lie on,
then he would be correct if the IQ distribution were asymmetric (which
it mostly doesn't seem to be).
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On Wed, 21 Jul 2010 11:50:45 -0700, Kevin Wampler wrote:
> Jim Henderson wrote:
>> On Wed, 21 Jul 2010 13:58:06 -0400, Warp wrote:
>>
>>
>>> If the curve of people's intelligence is not linear, it can mean
>>> that
>>> the majority of people are actually below average than above it (or
>>> the other way around, of course, depending on the sign of the
>>> derivative of the curve).
>>
>> For a large statistical sample, IIRC, it's basically a bell curve.
>
> It depends on what it's a statistical sample of. It only comes out a
> bell curve under certain assumptions about how what you're sampling
> behaves, and these will not hold in many circumstances.
>
> That said, I think IQ tests do tend to come out more or less a symmetric
> distribution (and close to a bell curve) so pretty close to half of the
> population will indeed be below average, so the theoretical point Warp's
> making doesn't really apply in this case.
They do tend to come out to be pretty symmetric - though it seems recent
study suggests that this may not be accurate; but it has been the
'standard' for some time.
>>> As a simple example, if we have 4 people with IQs 90, 90, 90 and
>>> 130,
>>> the average will be 100, but the majority of these people is below
>>> average. In other words, three quarters of the people are "stupid" and
>>> one quarter is "smart".
>>
>> Except that when measuring "average" intelligence, your sample size is
>> a population, not a small discrete number.
>>
>>
> It turns out that Warp's overall point is correct in this case, and you
> can also generate examples for continuous probability distributions.
> This occurs in cases where the distribution is asymmetric (see
> http://en.wikipedia.org/wiki/Skewness). I'm not sure what he meant by
> "the sign of the derivative", but maybe this was what he was thinking
> about.
Well, yes, his point is correct in this case because he's crafted a small
sample size that actually does bear out his assertion. That's kind like
a friend of mine saying that the red telephone boxes in England are
extremely rare, only to have one show up pretty much everywhere we went -
his sample size was his local neighbourhood, where there weren't any -
ie, his assertion was based on a sample size that wasn't representative
of anything other than what he was asserting.
Warp's done the same thing here as well - and in a small sample, sure, I
can prove that over 50% of people are of above average intelligence as
well by picking numbers that prove that. That doesn't prove anything
with regards to a large population distribution, though.
> I don't totally see how it applies to the conversation since "stupid"
> and "smart" in this context haven't been given rigorous definitions, but
> if you are to define them by which side of the IQ median you lie on,
> then he would be correct if the IQ distribution were asymmetric (which
> it mostly doesn't seem to be).
Well, true, neither of those terms really has a rigorous definition; it
seems that when talking about IQ, those terms tend not to be applied
along the curve.
Jim
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Jim Henderson wrote:
>
> Warp's done the same thing here as well - and in a small sample, sure, I
> can prove that over 50% of people are of above average intelligence as
> well by picking numbers that prove that. That doesn't prove anything
> with regards to a large population distribution, though.
>
Perhaps the difference is that Warp's making a theoretical point while
you're making a practical one? It's certainly true in a theoretical
sense that there can be distributions where the mean is different than
the median even with many samples (which is what Warp is saying), but
for the particular case of IQ this doesn't seem to be the case (which is
what I think you're saying).
Did I understand correctly?
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Jim Henderson <nos### [at] nospamcom> wrote:
> Well, yes, his point is correct in this case because he's crafted a small
> sample size that actually does bear out his assertion.
My point was that people tend to think that "the average IQ is 100"
automatically implies that half of the people will be below that and the
other half above it. That's obviously not the case. It depends on the
actual distribution of the samples (iow. if the distribution is asymmetric
around the average, then less than half of people will be on one side and
the rest on the other).
It just sounded like this misconception was being touted in this thread.
--
- Warp
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