A person’s IQ (intelligence quotient) is a score derived from standardized tests designed to measure human intelligence and intellectual potential. IQ tests include questions that measure reasoning and problem-solving skills. The discovery that average IQs differ worldwide has been a focus of inquiry and controversy.
Yeah, the 1 in 4 billion seemed exaggerated on the low end when I read it. I went ahead with it anyway since, even if there are 1000 people with an IQ at or above 200, that by itself would not pull the curve upwards much (because it’s 1000 out of 8 billion people) and hence your original claim that the mean is not the same as the median “because the distribution is skewed as IQs can be higher than 200 but not negative” was bollocks.
My point stands untouched that the justification you originally gave backing your claim that the IQ mean not being the same as the median was mathematically unsupported or, as you so colourfully put it: “opinion dressed as fact”.
As for this paper you linked, it curiously doesn’t back your claim either. From the abstract, we get that whilst the mean is 100 and the mode is indeed 105, the statistical distribution of IQs is NOT a Normal Distribution but rather the sum of TWO Normal Distributions. This means that you can’t in fact make claims about the median from the mode (as you would be able to for a normal distribution, were mean = median = mode) because a sum of two normal distributions has TWO peaks so you can perfectly have one at 105 and another one below that which can yield a median which is equal to or even below the mean.
Again from the abstract those two distributions are “one reflecting normal variation in general intelligence and one refecting normal variation in effects of genetic and environmental conditions involving mental retardation”, which seems to imply that the second has a peak at an IQ value below the first.
That said, I don’t even disagree that your claim that the median is above the mean might be right. What I have yet to see from you so far is something other than “opinion dressed as fact” or quoting of papers which don’t mathematically back your point.
Your source was calculated using the NORMDIST function in Excel. Not from empirical data.
Here’s an actual list containing more than 2 people above 200
Opinion dressed up as fact. To give a counter example this study showed that there were substantial departures from normality in the distribution.
Yeah, the 1 in 4 billion seemed exaggerated on the low end when I read it. I went ahead with it anyway since, even if there are 1000 people with an IQ at or above 200, that by itself would not pull the curve upwards much (because it’s 1000 out of 8 billion people) and hence your original claim that the mean is not the same as the median “because the distribution is skewed as IQs can be higher than 200 but not negative” was bollocks.
My point stands untouched that the justification you originally gave backing your claim that the IQ mean not being the same as the median was mathematically unsupported or, as you so colourfully put it: “opinion dressed as fact”.
As for this paper you linked, it curiously doesn’t back your claim either. From the abstract, we get that whilst the mean is 100 and the mode is indeed 105, the statistical distribution of IQs is NOT a Normal Distribution but rather the sum of TWO Normal Distributions. This means that you can’t in fact make claims about the median from the mode (as you would be able to for a normal distribution, were mean = median = mode) because a sum of two normal distributions has TWO peaks so you can perfectly have one at 105 and another one below that which can yield a median which is equal to or even below the mean.
Again from the abstract those two distributions are “one reflecting normal variation in general intelligence and one refecting normal variation in effects of genetic and environmental conditions involving mental retardation”, which seems to imply that the second has a peak at an IQ value below the first.
That said, I don’t even disagree that your claim that the median is above the mean might be right. What I have yet to see from you so far is something other than “opinion dressed as fact” or quoting of papers which don’t mathematically back your point.