http://groups.google.ca/groups?hl=en&lr=&ie=UTF-8&th=3585703d5142e2f9&rnum=12
1a)
The wealth of nations depends more on the variance of IQ than the mean (average) of IQ. That is why there are so many more per capita geniuses in USA than in any other place, and why the USA has achieved technological, economic, and political breakthroughs unprecedented in all of human history.
2a)
Don't quite understand what you mean. Please elaborate.
1b)
IQs fall in a statistical distribution, and merely quoting an average does not capture all the information on IQs, and in fact does not capture the most important information concerning "wealth of nations." A bell curve is a (Gaussian) distribution and is described by two numbers: 1. the center (average) and 2. the width (variation or standard deviation). Country A can have a lower average IQ than Country B but still have a larger fraction of its population as geniuses (IQ>150) if its IQ variation is larger. And it is more important (for economic development) how many Bill Gates's, Thomas Edison's, and Henry Ford's there are than whether your average truck driver, garbage collector, or secretary can go home and program his or her VCR.
2b)
A bell curve is standard normal distribution. A bell curve is a distibution function symmetrical about its mean value and has the shape of a bell. About 68% of the curve is within one standard deviation, 99.5% within two standard deviation, 99.7% within three standard deviations. What you described would not be true for bell curves. Of course, the IQ distribution of Americans needs not follow the normal distribution, they may be bimodal or with non-zero kurtosis. Are these what you are hinting at?
3a)
IQs fall in a statistical distribution, and merely quoting an average does not capture all the information on IQs, and in fact does not capture the most important information concerning "wealth of nations." A bell curve is a (Gaussian) distribution and is described by two numbers: 1. the center (average) and 2. the width (variation or standard deviation). Country A can have a lower average IQ than Country B but still have a larger fraction of its population as geniuses (IQ>150) if its IQ variation is larger. And it is more important (for economic development) how many Bill Gates's, Thomas Edison's, and Henry Ford's there are than whether your average truck driver, garbage collector, or secretary can go home and program his or her VCR.
3b)
A bell curve is standard normal distribution. A bell curve is a distibution function symmetrical about its mean value and has the shape of a bell. About 68% of the curve is within one standard deviation, 99.5% within two standard deviation, 99.7% within three standard deviations. What you described would not be true for bell curves. Of course, the IQ distribution of Americans needs not follow the normal distribution, they may be bimodal or with non-zero kurtosis. Are these what you are hinting at?
4a)
First of all, it is 95% within two standard deviations (not 99.5%). A Gaussian distribution is the same thing as a normal distribution. Typically a standard normal distribution is one with a mean of zero, so strictly speaking the IQ distibution is not standard. I believe the IQ distribution has non-zero kurtosis but probably not bimodal, but I do not need to appeal to kurtosis to make my point. Consider the following scenario using normal distributions only: Country A: mean IQ = 100, one standard deviation = 25 Country B: mean IQ = 105, one standard deviation = 15 What percentage of each country has IQ > 150 (genius)? Country A has 95% within two standard deviations (50 < IQ < 150), and half of the remaining have IQ > 150. So 2.5% of Country A are geniuses. Country B has 99.7% within three standard deviations (60 < IQ < 150), and half of the remaining have IQ > 150. So only 0.15% of Country B are geniuses. Understand now?
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Oui, M'sieur. Ch'commence à comprendre.
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Voir aussi :
Évariste
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