Statistics & IQ

A long comment in response to Carlotta’s post:

In North America most (excluding military which have their own scale) IQ measurement is done with a mean (average) of 100 and a standard deviation of 20 which arbitrarily define a standard bell curve. A standard bell curve is a nice smooth symmetrical hump (a graph) that conforms to the following statistical observations:

  1. The highest point on the curve is the mean
  2. 68% of a normal distribution fall within 1 standard deviation of the mean (34% below and 34% above). So, irrespective of who takes IQ tests (with a std dev of 20) there will always be 34% whose IQ is identified as 80-100 and 34% whose IQ is identified as 100-120.
  3. 14% fall in each second standard deviation from the mean: 14% will be identified as 60-80 and 14% as 120-140
  4. That leave 2% above and below: 2% less than 60 and 2% more than 140
  5. On this scale 140+ is considered genius.
  6. Less than 40 and greater than 160 is pegged at about .1% each

The standard bell curve is a substantial degree just a mathematical theory that is used to box things in. I don’t put much stock in IQ. To an extent it might be representative of the combination of how familiar the test takers are with the way the questions are posed, mentally how fast they are and how prone they are to mistake. Someone could perform consistently on a series of these tests and get varying numerical results because of where their score falls against that average of those who have taken that particular formula of test.

About Ron

Homeschooling dad of 4 (ages 27 - 14), grampy to 3, WordPress core contributor, former farmboy & software developer by profession.


  1. Thanks Ron. It is beginning to become clearer to me, and I agree with your overall conclusion.

  2. Yikes. Good timing for me as I happen to be taking a statistics class right now. So I understand quite intimately what a standard deviation is. I agree with your assessment of IQ test value. I think there are many types of IQ which cannot be measured by these tests also.

  3. Hi. I’m reading a fabulous book called Cracking Creativity in which a psychologist analyses the thinking patterns of “geniuses” and finds a number of useful applications for all of us interested in the mind, the child, the human potential.

    One of my intellectural heroes is Richard Feynman, the Nobel Prize winning physicist. Reading Feynman’s biography is a fun trip sitting next to a truly bright man.

    The author says Feynman’s IQ was “only 120,” but he just had unique ways to dealing with things. Feynman’s book, Surely You’re Joking, Mr. Feynman, relates in great detail how he arrived at a number of ideas that eventually were recognized by the Nobel committee. True, his discovery was sinultaneous with others’, but it was done in his “graphic” way, while the other winners dit everything with numbers.

    Your comments about the bell curve and so forth are very astute. When I first taught (1959)in a boarding school in New Mexico, a local student tested out at about 105. His mother was a lovely lady, and asked me if I thought he could make college. I assured her, having taught her son, that he would certainly “make it” in college. Four or five years later I was back in Santa Fe and I met the lady. “I have to tell you, Juan is in Law school at the University of New Mexico, and is doing very well!” she said.

    At best, even the brightest people get along on about ten, may q5 percent of their potential. Only challenges, “mind popping” events (see Cracking Creativity) and often dumb luck account for all that is done.

    You know well the story of Harry Potter’s creator. So many “illuminations” come like a bold from the blue (actually welling up from the constant work going on in the subconscious) that distinguishing between a “genius” and a really inspired regular person become quite difficult.

    I admire you and your work.
    James P. Louviere
    Editor (Apologies – I have no spell checker in this system.)

  4. Carlotta – You’re welcome. The info may be useful in following stories on the Child database.

    Kim – Kim depending on the hours of the course you may get to the one way anova secret formula which gallop has been using for decades.

    Dr. JPL – Thanks for leaving the note. I’d like to say the absence of the spell checker is deliberate on my part. TBH, I haven’t encountered a spell checker for comments on any blog. I always enjoy stories like the one of Juan. I read an article a long time ago where a researcher’s hypothysis was that genius was often a result of a higher percentage use of potential. Whether that true or not, I don’t know.