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IQ Basics

IQ normal curve
Graph drawn in Excel using the NORMDIST function.
What is intelligence? The definition I like is that intelligence is "the ability to learn or understand or to deal with new or trying situations ... also : the skilled use of reason" (7). I have heard some people misuse the word smart to mean knowledgeable. That is like confusing velocity with distance. That one can lead to the other does not mean that they are the same thing, especially in societies where education is not universal.
I.Q. = Intelligence Quotient
Originally, "IQ" tests were created to be able to identify children who might need special education (1). Binet's test included varied questions and tasks. The tasks even included unwrapping a piece of candy and comparing the weights of different objects (4)! 
To relate the mental development of a child to the child's chronological age the IQ was invented.  IQ =  (MA/CA) * 100. The intelligence quotient was equal to 100 times the Mental Age divided by the Chronological Age.  For example, if a certain child started reading, etc., at the age of 3 (CA) and average children start reading, etc., at the age of 6 (MA), the child would get an IQ score of 200. (Such a score is very, very rare). Since people wanted to also use IQs for adults, that formula was not very useful since raw scores start to level off around the age of 16 (2).
Thus the deviation IQ replaced the ratio IQ. It compares people of the same age or age category and assumes that IQ is normally distributed, that the average (mean) is 100 and that the standard deviation is something like 15. (IQ tests sometimes differ in their standard deviations). 
What is a standard deviation (SD)? Simply put, the standard deviation is a measure of the spread of the sample from the mean. As a rule of thumb, about 2/3 of a sample is within 1 standard deviation from the mean. About 95% of the sample will be within 2 standard deviations from the mean (3).
With the standard deviation and a mean, you can calculate percentiles. Percentiles tell you the percent of people that have a score equal to or lower than a certain score.

High IQ societies ask for certain percentile scores on IQ tests for you to be eligible to join them. Mensa asks for scores at the 98th percentile or higher. For a list of the selection criteria of other societies, click here.

There have been various classification systems for IQ.
Terman's classification was (6):
IQ Range


140 and over Genius or near genius
120-140 Very superior intelligence
110-120 Superior intelligence
90-110 Normal or average intelligence
80-90 Dullness
70-80 Borderline deficiency
Below 70 Definite feeble-mindedness
(Terman wrote the Stanford-Binet test (1), which has a SD of 16.)
Later, Wechsler thought that it would be much more legitimate to base his classifications on the Probable Error (PE) so his classification was (6):
Classification IQ Limits Percent Included
Very Superior 128 and over 2.2
Superior 120-127 6.7
Bright Normal 111-119 16.1
Average 91-110 50
Dull Normal 80-90 16.1
Borderline 66-79 6.7
Defective 65 and below 2.2

Mental deficiency used to be more finely classified using the following technical terms that later began to be abused by the rest of society (5):

IQ Range Classification
70-80 Borderline deficiency
50-69 Moron
20-49 Imbecile
below 20 Idiot

These are now obsolete. The terms 'mentally retarded' and 'mental retardation' were officially replaced by 'intellectual disabled' and 'intellectual disability' by Rosa's Law in 2010. Before the fifth edition of the Diagnostic and Statistical Manual (DSM 5), which now uses the terms 'intellectual disability (intellectual developmental disorder)', the following was the classification of retardation in the USA (5):

IQ Range Classification
50-69 Mild
35-49 Moderate
20-34 Severe
below 20 Profound

While IQ is still part of the assessment (the threshold is 70 ± the measurement error of the particular test), the DSM 5 has replaced those IQ ranges with assessments of functioning, with conceptual, social, and practical criteria (8). IQ is not enough. Maybe the same sort of thing should be done for labeling somebody a genius.



(1) Berk, L.E. (1997). Child Development, 4th ed. Toronto: Allyn and Bacon.

(2) Eysenck, H. (1994). Test Your IQ. Toronto: Penguin Books.

(3) Iman, R.L. (1994). A Data Based Approach to Statistics. Belmont: Duxbury Press.

(4) Nietzel, M.T., Berstein, D.A., Milich R. (1998). Introduction to Clinical Psychology. Upper Saddle River: Prentice Hall.

(5) Reber, A.S. (1995).  The Penguin Dictionary of Psychology, 2nd ed.  Toronto: Penguin Books.

(6) Wechsler, D. (1944).  The Measurement of Adult Intelligence.  Baltimore:  The Williams & Wilkins Company.

(7) The Merriam-Webster Dictionary Online:

(8) Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition. Arlington, VA, American Psychiatric Association, 2013.


Written by Rodrigo de la Jara. Updated December 17, 2018.


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