Graph drawn in Excel using the NORMDIST function.
This is a quick explanation of IQ, put up
due to popular demand. There are many books
on psychology or
intelligence that would provide a more rigorous explanation of IQ.
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.
I.Q. = Intelligence Quotient
Originally, "IQ" tests were created to be able to identify children
who might need special education due to their retarded mental development (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 =
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
There have been various classification systems for IQ.
Terman's classification was (6):
|140 and over
||Genius or near genius
||Very superior intelligence
||Normal or average intelligence
(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
||128 and over
||65 and below
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):
These are now largely obsolete and mental deficiency
is now generally called mental retardation. The following is the
currently used classification of retardation in the USA (5):
Moreover, "educable mentally retarded" is
roughly equivalent to mild mental retardation, and "trainable" mentally retarded
is roughly equivalent to moderate (5). The DSM now requires an assessment of a
person's adaptive functioning as an additional criterion for labeling
someone retarded. 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
(2) Eysenck, H. (1994). Test Your IQ. Toronto:
(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:
* Originally, my definition simply said "the ability to learn", but
I found that the expanded dictionary definition is better even if it is not
Written by Rodrigo de la Jara
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