Tuesday, October 15, 2013

IQ and common sense and standard deviation.

You have probably heard of IQ.  Personally I think IQ is over rated and mostly crap, but, I like the fact that I am in the top 2%.  Anyone with an IQ of over 150 is.  So lets think about that.  I am going to use some basic ballparks here, but, you are welcome to check out my data.

Every normal distribution is going to have a mean, modality and a median and they are all going to be the same number, or about the same number.

If an IQ of over 150 is in the top 2% that means the standard deviation (std dev) is about 25.  Huh?

This is statistics hocus pocus and you can check it out on wikipedia or some other more reasonable source.  There is a chart that will show you the idea how a standard deviation works in a normal distribution.

There is a problem with that concept.  If the standard deviation in IQ is 25 then about 15% of people have an IQ of below 75.  About 68% of people have an IQ of between 75 and 125, about 13% have an IQ of between 125 and 150 and 2% have an IQ of over 150.

An IQ of below 75 is special needs.  That means out of 100 kids 15 should be special needs.  I don't see that in my experience.  Maybe, but, I don't think there are that many special needs people.  I think the standard deviation is probably lower or the mean is higher or both.

I went looking for more input and found this quote:

"If a person scores below 70 on a properly administered and scored I.Q. test, he or she is in the bottom 2 percent of the American population10 and meets the first condition necessary to be defined as having mental retardation."

at this website:

http://www.hrw.org/reports/2001/ustat/ustat0301-01.htm

Okay, WTF, below 70 is in the bottom 2% and above 150 is in the top 2%.  That doesn't make sense if the average IQ is 100.  The standard deviation changes to 15 on the low side.

So the range between 70 and 150 is 80 and this range is covered by 4 standard deviations so the std dev should be 20.  70 plus 40 (2 std dev)  is 110.  150 minus 40 is 110.

Okay, so the IQ data only makes sense if the mean is 110.  In a Gausian or normal distribution, a Bell Curve, the mean, the median, the middle and the mode are all about the same.

Okay, so the middle is 110 and the average or mean is 100.  This suggests that the majority of people have an I.Q. of under 100.

Suppose we have two people with an IQ of 90 and one person with an IQ of 120.  We have three people with a mean IQ of 100, but, the modality is 90.  More people with an IQ below the mean than above the mean.

We can suggest that this is probable based on the distribution, 4 sigma between 70 and 150 with a middle of 110 and a mean of 100.  These number suggest a skewed distribution with a modality of about 90.

I found a study once that documented the IQ of teachers and the std dev was really small, around 2 and the average was 112.  This means 68% of teachers have an IQ of between 110 and 114.  13% had an IQ of 114 to 116 and 2% had an IQ of 116 to 118.

How good was the study?  No clue.  From the teachers I had in school I would say it is pretty accurate, but, from teachers I have met socially I would say it is low.  Thinking about it though, I like hanging with smarter people so ...

In my experience the smartest group of people I ever worked with are skilled trades.  Good money, less formal education, lot of smarts.

Computer geeks usually don't rate high in my estimation, although, I have met some really smart guys into computers.  I think computer geeks might rate as well as skilled trades, but, a lot of geeks are way too closed minded and focused on propaganda for me to draw a straight line between them.  Some of the self styled "hackers" I have met actually think Europeans thought the Earth was flat before Columbus and that the Church tried to squash science.  To much crap, not enough brains.

Edit: By the way, this seems incredibly obvious to me, but, it might not be obvious to others.  If the median is 110, and the mean is 100, the modality should actually be 90, which would mean that more than half of everyone you meet is below average IQ.