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Section2
25th April 2003, 01:54 AM
Alexander Sharp's comment first of all annoyed me, then I realised he isn't actually saying anything, merely abusing a statistic.

Even if the British population consisted of 60 million Einstein clones, just under 30 million of those Einstein clones would be considered to have below average intelligence.

To be exact less than 50% of the British population have an intelligence less than the British average intelligence, since there will be a finite number of people who have an intelligence exactly equal to the average intelligence (At a given instant, since a given person's intelligence is not generally constant, unless he is dead, or otherwise incapacitated in such a way that a measure of his intelligence has no meaning. In fact, measuring somebody's intelligence is surely subject to the quantum effect, that the act of measuring it will change it.)

§tu

(P.S. did you know that 49.9999... = 50.00000... = 50?)

Hellcat
25th April 2003, 02:03 AM
Is that the half who said "S*d that....... I am not doing these stupid intelligence tests? "

hgc
25th April 2003, 12:16 PM
Perhaps it should be "below median intelligence."

CurtC
25th April 2003, 08:39 PM
Section2 wrote:
To be exact less than 50% of the British population have an intelligence less than the British average intelligence, since there will be a finite number of people who have an intelligence exactly equal to the average intelligence.If you're going to be nitpicky, you should make sure that you're right. Depending on how intelligence in the population is distributed, it doesn't even have to be anywhere near 50% that are below the average intelligence. For example, the vast majority of people have more than the average number of legs.

Section2
26th April 2003, 12:03 PM
I suppose that it is safe to assume that a fair test of intelligence is, by definition, evenly distributed and, to continue with arguments that support my view, "continous" and symmetrically distributed about the mean.

Secondly, when /casually/ throwing around the word "average" I would assume "mean" is implied, and so is a normal distribution.

Fair point about the legs though, but irrelevant since it is clearly a completely different kind of distribution. Comparing your legs with my Einstein clones.

Obviously I didn't make my point clear enough - that Sharp's comment was misleading - I wasn't nitpicking, merely pointing out that Sharp's comment had no value (aside from how it misleads the reader towards his view). And I thought it was worth mentioning because this is exactly the kind of behaviour you would expect from the groups that JRef seeks to expose.

§tu

K-W
27th April 2003, 02:35 PM
Is intelligence normally distibuted?

CurtC
27th April 2003, 09:24 PM
Well, Section2, I understood Sharp's comment to be talking in approximations, so it was perfectly valid, and he knew the point he was trying to make. I can't see how it was misleading at all.

Then you come along and argue that he was wrong based on some ideas of yours that are themselves misunderstandings. There's an old rule in usenet that if you're going to pick on someone's grammar, then you better be sure that your grammar is perfect while you do it. We can extend that to say that if you're accusing someone of misunderstanding numbers, then you should understand what you're saying.

Here's the errors I see in your last post:

* It's not safe to assume that intelligence is symmetric about the mean. I would be highly surprised to find that it's so.

* It's not clearly a continuous distribution - maybe it is continuous, but I can't see why it's safe to assume so.

* Although you're right that "average" implies "mean," that does not imply a normal distribution. You can take an average for *any* distribution.

By the way, welcome to the JREF Forum. I think you must have read some meaning into Sharp's comments which I missed.

Dub
28th April 2003, 01:36 AM
I agree with Section. While the statistic is mathematically acurate, i think it may be mis-leading. Most people take average as the mean, so they may misunderstand the statistic. I remember I was at a party once and jokingly said 'half the people here are below the average intelligence' [meaning the average of the group of peple at the party] It didnt go down too well :D

CurtC: I think you're mis-understanding what Section is saying.

CurtC
28th April 2003, 06:41 AM
Most people take average as the mean, so they may misunderstand the statistic.I'm sorry if I misunderstood what you were saying. *I* take average as the mean - does that mean I misunderstand the statistic? Because I think I understand what's going on with the numbers.

It's an old trick to say something like "fully half of the children in Davis Elementary School are below average!" That's what Mr. Sharp was alluding to. I wouldn't, however, feel so confident stating that in a small private setting such as a party, since I think the people I hang out with are above the average in intelligence. The ones with really low intelligence don't have the same kinds of jobs, typically don't live in the same neighborhoods, and don't enjoy the same things as me, so it's a biased sample.

Section2
28th April 2003, 10:34 AM
I tried to put as many caveats into my comments as I thought were necessary, and leave it to the reader to figure out all the others... I could keep trying until the reader is finally boxed in and forced to agree with me...

"Intelligence" is unquantifiable, as far as I am aware. IQ is "a measure" of intelligence but it is not necessarily a fair test. Let's say that the measure of intelligence that I have in mind:I define it to be normally distributed about the mean, and also that we can't say what the maximum intelligence is, nor what the minimum is. Also I would have to conclude that intelligence is not zero, but "undefined" for people who are no longer equipped with life (or claim to be able to converse with those who are no longer equipped with life).

1) I said that we could assume it is continuous - since if all 60 million Brits' intelligence was quantified it would likely approximate a continuous distribution

Thanks for welcoming me - I'll make sure I spend a couple of hours of my working day thinking through all the angles before making another comment...

I think you let slip the main issue, CurtC: "It's an old trick...". If this is such an "old trick" then one could conclude that Sharp was deliberately trying to mislead the reader, (or allude to this trick at the very least...) which was my main point in the first place.

§2

MRC_Hans
28th April 2003, 11:00 AM
Originally posted by K-W
Is intelligence normally distibuted? Assuming that those statistics are valid (not certain at all, still..), we can infer that intelligence is normally distributed. Otherwise the term average makes no sense. Of something is not conforming to normal distribution, you would use median instead (median being the value where an equal number of instances are below and above). The "number of legs" argument is OK, but in the way that it demonstrates abuse of stastitistics. The number of legs that humans have is not applicable to statistics; two legs are the norm, and only special cases have a different number, thus it makes no sense to compute an average number of legs.

And its an old joke that half a population is below average intelligence. Presumably some politician became upset with that, but obviously, thats the way statistics work.

Hans

Dub
30th April 2003, 08:15 AM
Originally posted by CurtC
I wouldn't, however, feel so confident stating that in a small private setting such as a party, since I think the people I hang out with are above the average in intelligence. The ones with really low intelligence don't have the same kinds of jobs, typically don't live in the same neighborhoods, and don't enjoy the same things as me, so it's a biased sample.

Well you've missed the point totally, which is why I agree with Section2 that Sharp's statment could be misleading. You have been mislead by my statment. All my friends at the party have good university degrees, so they would be classed as above average intelligence. But, my statment was 'half the people here are below the average intelligence'. Which, statistically is true for the room. By default, no matter how intelligent everyone in the room is, half will be below they average of the room. So now you can see how Sharps statement can be misleading. You fell for mine and started spouting how it wouldnt work with your friends because they are 'above the average intelligence'. Put them all in a room and half the people in their will be below the average (of that room). So sayin 50% of British people are below average' can be misleading. People reading that might assume 'average intelligence' include everyone, not just the British population. Now you can see how that type of statment can be misleading; even you fell for it. :)

JesFine
13th May 2003, 11:27 AM
Here's a point that everyone seems to be missing: Let's assume that there are 10 people in the room (or England or the world or whatever) and that intelligence is completely quantifiable. Also assume that intelligence is measured on a scale of 1-10 with 10 being the highest.

Everyone's IQ breaks down thusly:
Person IQ
1---------10
2---------- 9
3---------10
4---------- 9
5---------10
6---------- 9
7---------10
8---------- 9
9---------- 9
10---------1

OK then. Pretty smart party. The average intelligence at this party is (10*4+9*5+1)/10 = 8.6

The only person under the average is person #10. Thus, only 10% of this population is of below average intelligence.

I haven't read the Alexander Sharp article (and I didn't see any links to it?) so I can't comment on what he said. But of course I will anyway -- Maybe he was saying that in an ideal school system, everyone would be very smart except for a few stragglers who couldn't be helped anyway. This position would be incredibly naive for a number of reasons, but the arguments I read here wouldn't work against it.

Soapy Sam
13th May 2003, 02:40 PM
Good heavens.
There's a novelty.

Dub
13th May 2003, 04:57 PM
Originally posted by JesFine
Here's a point that everyone seems to be missing: Let's assume that there are 10 people in the room (or England or the world or whatever) and that intelligence is completely quantifiable. Also assume that intelligence is measured on a scale of 1-10 with 10 being the highest.

Everyone's IQ breaks down thusly:
Person IQ
1---------10
2---------- 9
3---------10
4---------- 9
5---------10
6---------- 9
7---------10
8---------- 9
9---------- 9
10---------1

OK then. Pretty smart party. The average intelligence at this party is (10*4+9*5+1)/10 = 8.6

The only person under the average is person #10. Thus, only 10% of this population is of below average intelligence.

I haven't read the Alexander Sharp article (and I didn't see any links to it?) so I can't comment on what he said. But of course I will anyway -- Maybe he was saying that in an ideal school system, everyone would be very smart except for a few stragglers who couldn't be helped anyway. This position would be incredibly naive for a number of reasons, but the arguments I read here wouldn't work against it.

Only #10 in that population is below average IF you use the mean as the average. No one has missed that point. The mode of that group is 9, so 4 people are above average; the rest are on or below it. Of course using single digits and giving many people exactly the same value makes calculations less accurate. Therefore, even if you have a group of super-intelligent people in a room (like CurtC's party :) ), as long as there are slight differences in everyone's intelligence level (even down to very small percentage differences), depending on which average you use, half the people there will be below the average.

Zep
15th May 2003, 08:45 PM
The supplied table of data is not particularly "normally distributed", so the "average" will be a fairly meaningless number. The "mode" and "mean" will be more significant here.

Incidentally, going back to the topic, I understood it to be that IQ scores were set such that the statistical average score of a population is "100" and all individual scores are measured against that. So even if you have a big bunch of Einsteins or a bunch of cavemen still all banging rocks together, their "average IQ" will be "100". The idea then was to have the same "test" for everyone, physicists and rock-bangers, to cover a bigger population.

It soon became apparent that the "testing" was the problem - it had social dependencies. Eg. As a "westerner" I may score highly in logic and numerics related stuff, but in complex bushcraft and survival skills the Australian aborigines would have me beat a long way (and would consider ME a dummy, IQ-wise!).

Result? I don't put much stock in IQ testing - it is less and less indicative of anything useful. Look at Bill Gates! :rolleyes:

Zep

allanb
25th May 2003, 01:27 AM
Not long ago there was an article in one of the more respectable British newspapers, presenting as a devastating condemnation of the National Health Service an investigation "revealing" that 48% of all hospitals in the country were still below the national average in quality of service. It was reported quite seriously (this was not the April 1 edition), with a suitably sensational headline.

Honestly, I think elementary statistics should be a compulsory part of the school curriculum.

Dymanic
25th May 2003, 07:34 AM
Originally posted by allanb

Honestly, I think elementary statistics should be a compulsory part of the school curriculum.
Here in California, schools recieve a lot of their funding from sales of lottery tickets.

davefoc
26th May 2003, 09:11 AM
MRC_Hans made what I thought was a very interesting point, if I understood him correctly.

I think he said that it only makes sense to take averages of things which are normally distributed. This might be elementary statistics but I had never heard that before.

This might explain something that I have been curious about for years. The median home price for an area is reported but the average home price never is. Is the basis of this that home prices are not normally distributed? I wonder if MRC_Hans could explain how one decides that a given goup of data is normally distributed?

andylen
16th March 2008, 07:20 AM
If intelligence is normally distributed, then aren't you guaranteed 50% above the mean? Seeing as the expected value is the peak of the bell curve?

How do you know it's normally distributed though? The mean still makes sense in other distrubtions, right? You still have expected values etc...

16th March 2008, 07:56 AM
Only #10 in that population is below average IF you use the mean as the average. No one has missed that point. The mode of that group is 9, so 4 people are above average; the rest are on or below it.

No. You cannot use the mode and say 4 people are below the average. Average is defined as the arithmetic mean. You can say 4 people are below the mode and nothing more.

Of course using single digits and giving many people exactly the same value makes calculations less accurate. Therefore, even if you have a group of super-intelligent people in a room (like CurtC's party :) ), as long as there are slight differences in everyone's intelligence level (even down to very small percentage differences), depending on which average you use, half the people there will be below the average.

Your argument is incorrect. We could give everyone different values and still construct a plausible set in which there was no mode and only one person was below the arithmetic mean of that set. We could also construct a realistic set in which 90% were below the mean of that set of people. Results that appear very strange can easily occur when small groups are not randomly selected from a very, very large normal distribution.

Big Les
16th March 2008, 08:02 AM

2003? Sweet lord. It must have been all fields round here then.

MRC_Hans
17th March 2008, 05:55 AM
MRC_Hans made what I thought was a very interesting point, if I understood him correctly.

I think he said that it only makes sense to take averages of things which are normally distributed. This might be elementary statistics but I had never heard that before.

This might explain something that I have been curious about for years. The median home price for an area is reported but the average home price never is. Is the basis of this that home prices are not normally distributed? I wonder if MRC_Hans could explain how one decides that a given group of data is normally distributed?

Well, well, sorry I took a little time to get around to replying to this one ;):blush:.

The average is the sum of all values divided with the number of values.

The median is the value where half the values are below and half the values are above.

If data has a so-called normal distribution (and a number of other symmetrical distributions) the average and the median have the same value.

Normal distribution (the well-know bell curve) can be established by a statistical test, which gives you the goodness of fit.

However, a number of data sets are notoriously not normal distributed, and for those the average is not very useful, so the median is usually used instead (but often called "average" especially by the media).

Examples are:

Age distribution in a population. Obviously, even in a stable population, there will always be more members, the younger age you choose (because all have started young, but not all get old).

Wages and riches. A very small part of the population have very high wages/fortunes. Actually, less than 10% of the people in the works have over 50% of the riches, so an average income would be absurdly high.

I would suspect that prices often work the same way (somewhat dependent on the type of goods). Certainly home prices. The average of most areas will be dominated by a small group of very expensive estates, so using the median is more useful.

Hans

SezMe
17th March 2008, 06:12 AM
2003? Sweet lord. It must have been all fields round here then.
Aren't you happy to discover that it is not only jesus that rises from the dead? :)

ronananderson
23rd March 2008, 03:21 PM
I must say this comes as no shock, as an Irish man who lived in the UK, i was appalled by the poor level of education.I will never forget the time i was talking to a colleague about WWII , when another colleague interjected with the choice line - 'Who's Hitler?.I don't put much stock into IQ tests even though mine is really quite impressive, but listen guys this is our planet, we really cannot afford to let it be overrun by idiots.Something drastic needs to be done if we are ever to become a type 1 civilization ( sorry, i'v just discovered Michio Kaku)

WildCat
23rd March 2008, 04:50 PM
http://home.mindspring.com/~chitaper/b-r_zombie.jpg

dann
24th March 2008, 11:02 AM
However, a number of data sets are notoriously not normal distributed, and for those the average is not very useful, so the median is usually used instead (but often called "average" especially by the media).

Examples are:
(...)
Wages and riches. A very small part of the population have very high wages/fortunes. Actually, less than 10% of the people in the works have over 50% of the riches, so an average income would be absurdly high.

High? Probably. Absurdly high? No, I think that we could live with that! :)

UnrepentantSinner
26th March 2008, 12:02 AM
Cool, there's even a Hellcat post in this thread.

Zep
26th March 2008, 12:56 AM
And one of my very first posts too!

Ian Osborne
28th March 2008, 06:00 AM
I've only just realised why people are calling this a 'zombie thread'. I guess I must be the guy that scored a '1' at JesFine's party. Now if you'll excuse me, I need to sit in the corner and dribble...

NeilC
28th March 2008, 06:12 AM
I must say this comes as no shock, as an Irish man who lived in the UK, i was appalled by the poor level of education.I will never forget the time i was talking to a colleague about WWII , when another colleague interjected with the choice line - 'Who's Hitler?.I don't put much stock into IQ tests even though mine is really quite impressive, but listen guys this is our planet, we really cannot afford to let it be overrun by idiots.Something drastic needs to be done if we are ever to become a type 1 civilization ( sorry, i'v just discovered Michio Kaku)

For someone with such an impressive IQ I'm surprised you don't know the difference between IQ and education

Luzz
28th March 2008, 03:58 PM
There is an impressive positive correlation between education and high IQ, so your observation is out of place.

tracer
9th April 2008, 05:46 PM
Let me just say that, when Ronald Reagan was president, there was a rumor circulating that he was "shocked" to learn that 50% of Americans were of below-average intelligence.

UnrepentantSinner
10th April 2008, 01:04 AM
Let me just say that, when Ronald Reagan was president, there was a rumor circulating that he was "shocked" to learn that 50% of Americans were of below-average intelligence.

This sounds like something a good skeptic would run through Snopes.