Originally, IQ, or Intelligence Quotient, was used to
detect persons of lower intelligence, and to detect
children of lower intelligence in order to place them in
special education programs. The first IQ tests were
designed to compare a child's intelligence to what his
or her intelligence "should be" as compared to the
child's age. If the child was significantly "smarter"
than a "normal" child of his or her age, the child was
given a higher score, and if the child scored lower than
expected for a child of his or her age, the child was
given a lower IQ score.
Today IQ testing is used not primarily for children,
but for adults. Today we attempt to write tests than
will determine an adult's true mental potential,
unbiased by culture, and compare scores to the scores of
other adults who have taken the same test. So
today we compare an adult's objective results to the
objective results of other adults, and determine how
intelligent each test taker is compared to all other
test takers, instead of comparing test takers to an
arbitrary age related standard.
The first step to understanding IQ testing is to
understand standard deviation.
Standard deviation is kind of the "avg of the avg,"
and often can help you find the story behind the data.
To understand this concept, it can help to learn about
what statisticians call normal distribution of data.
A normal distribution of data means that most of the
examples in a set of data are close to the "average,"
while relatively few examples tend to one extreme or the
Let's say you are writing a story about nutrition.
You need to look at people's typical daily calorie
consumption. Like most data, the numbers for people's
typical consumption probably will turn out to be
normally distributed. That is, for most people, their
consumption will be close to the mean, while fewer
people eat a lot more or a lot less than the mean.
When you think about it, that's just common sense.
Not that many people are getting by on a single serving
of kelp and rice. Or on eight meals of steak and
milkshakes. Most people lie somewhere in between.
If you looked at normally distributed data on a
graph, it would look something like this:
The x-axis (the horizontal one) is the value in
question... calories consumed, dollars earned or crimes
committed, for example. And the y-axis (the vertical
one) is the number of datapoints for each value on the
x-axis... in other words, the number of people who eat x
calories, the number of households that earn x dollars,
or the number of cities with x crimes committed.
Now, not all sets of data will have graphs that look
this perfect. Some will have relatively flat curves,
others will be pretty steep. Sometimes the mean will
lean a little bit to one side or the other. But all
normally distributed data will have something like this
same "bell curve" shape.
The standard deviation is a statistic that tells you
how tightly all the various examples are clustered
around the mean in a set of data. When the examples are
pretty tightly bunched together and the bell-shaped
curve is steep, the standard deviation is small. When
the examples are spread apart and the bell curve is
relatively flat, that tells you you have a relatively
large standard deviation.
Computing the value of a standard deviation is
complicated. But let me show you graphically what a
standard deviation represents...
One standard deviation away from the mean in either
direction on the horizontal axis (the red area on the
above graph) accounts for somewhere around 68 percent of
the people in this group. Two standard deviations away
from the mean (the red and green areas) account for
roughly 95 percent of the people. And three standard
deviations (the red, green and blue areas) account for
about 99 percent of the people.
If this curve were flatter and more spread out, the
standard deviation would have to be larger in order to
account for those 68 percent or so of the people. So
that's why the standard deviation can tell you how
spread out the examples in a set are from the mean.
Why is this useful? Here's an example: If you are
comparing test scores for different schools, the
standard deviation will tell you how diverse the test
scores are for each school.
Let's say Springfield Elementary has a higher mean
test score than Shelbyville Elementary. Your first
reaction might be to say that the kids at Springfield
But a bigger standard deviation for one school tells
you that there are relatively more kids at that school
scoring toward one extreme or the other. By asking a few
follow-up questions you might find that, say,
Springfield's mean was skewed up because the school
district sends all of the gifted kids to Springfield. Or
that Shelbyville's scores were dragged down because
students who recently have been "mainstreamed" from
special education classes have all been sent to
In this way, looking at the standard deviation can
help point you in the right direction when asking why
data is the way it is.
The standard deviation can also help you evaluate the
worth of all those so-called "studies" that seem to be
released to the press everyday. A large standard
deviation in a study that claims to show a relationship
between eating Twinkies and killing politicians, for
example, might tip you off that the study's claims
aren't all that trustworthy.
Here is one formula for computing the standard
deviation. A warning, this is for math geeks only!
Writers and others seeking only a basic understanding of
stats don't need to read any further. Remember, a decent
calculator and stats program will calculate this for
Terms you'll need to know x =
one value in your set of data (x) = the mean
(average) of all values x in your set of
data n = the number of values x in your set of
For each value x, subtract (x)
from x, then multiply that value by itself
(otherwise known as determining the square of that
value). Sum up all those squared values. Then multiply
that value by this value... 1/(n-1). Then take the
square root of the resulting value. That's the standard
deviation of your set of data.
Most people have an intuitive notion of what
intelligence is, and many words in the English language
distinguish between different levels of intellectual
skill: bright, dull, smart, stupid, clever, slow, and so
on. Yet no universally accepted definition of
intelligence exists, and people continue to debate what,
exactly, it is. Fundamental questions remain: Is
intelligence one general ability or several independent
systems of abilities? Is intelligence a property of the
brain, a characteristic of behavior, or a set of
knowledge and skills?
The simplest definition proposed is that intelligence
is whatever intelligence tests measure. But this
definition does not characterize the ability well, and
it has several problems. First, it is circular: The
tests are assumed to verify the existence of
intelligence, which in turn is measurable by the tests.
Second, many different intelligence tests exist, and
they do not all measure the same thing. In fact, the
makers of the first intelligence tests did not begin
with a precise idea of what they wanted to measure.
Finally, the definition says very little about the
specific nature of intelligence.
Whenever scientists are asked to define intelligence
in terms of what causes it or what it actually is,
almost every scientist comes up with a different
definition. For example, in 1921 an academic journal
asked 14 prominent psychologists and educators to define
intelligence. The journal received 14 different
definitions, although many experts emphasized the
ability to learn from experience and the ability to
adapt to one's environment. In 1986 researchers repeated
the experiment by asking 25 experts for their definition
of intelligence. The researchers received many different
definitions: general adaptability to new problems in
life; ability to engage in abstract thinking; adjustment
to the environment; capacity for knowledge and knowledge
possessed; general capacity for independence,
originality, and productiveness in thinking; capacity to
acquire capacity; apprehension of relevant
relationships; ability to judge, to understand, and to
reason; deduction of relationships; and innate, general
People in the general population have somewhat
different conceptions of intelligence than do most
experts. Laypersons and the popular press tend to
emphasize cleverness, common sense, practical problem
solving ability, verbal ability, and interest in
learning. In addition, many people think social
competence is an important component of
Most intelligence researchers define intelligence as
what is measured by intelligence tests, but some
scholars argue that this definition is inadequate and
that intelligence is whatever abilities are valued by
one's culture. According to this perspective,
conceptions of intelligence vary from culture to
culture. For example, North Americans often associate
verbal and mathematical skills with intelligence, but
some seafaring cultures in the islands of the South
Pacific view spatial memory and navigational skills as
markers of intelligence. Those who believe intelligence
is culturally relative dispute the idea that any one
test could fairly measure intelligence across different
cultures. Others, however, view intelligence as a basic
cognitive ability independent of culture.
In recent years, a number of theorists have argued
that standard intelligence tests measure only a portion
of the human abilities that could be considered aspects
of intelligence. Other scholars believe that such tests
accurately measure intelligence and that the lack of
agreement on a definition of intelligence does not
invalidate its measurement. In their view, intelligence
is much like many scientific concepts that are
accurately measured well before scientists understand
what the measurement actually means. Gravity,
temperature, and radiation are all examples of concepts
that were measured before they were understood.