IQ scores are expressed as a number normalized so that the average IQ in an age group is 100 — in other words an individual scoring 115 is above-average when compared to similarly aged people. It is common, but not invariable, practice to standardize so that the standard deviation (s) of scores is 15 or 16 ( 24 is used occasionally as well ). Tests are designed so that the distribution of IQ scores is Gaussian, that is to say that it follows a bell curve.

(The following numbers apply to IQ scales standard deviation s = 15.) Roughly 68% of the population has an IQ between 85 and 115. The "normal" range, or range between -2 and +2 standard deviations from the mean, is between 70 and 130, and contains about 95% of the population. A score below 70 may indicate mental retardation, and a score above 130 may indicate intellectual giftedness. Retardation may result from normal variation or from a genetic or developmental malady; analogously, some otherwise normal people are very short, and others have dwarfism. Giftedness appears to be normal variation; autistic savants have often astonishing cognitive powers but below-average IQs.

It has been observed that scores outside the range 55 to 145 must be cautiously interpreted because there are smaller numbers of respondents with which to make comparisons in those ranges. Moreover, at such extreme values, the normal distribution is a less accurate estimate of the true IQ distribution.

In actuality there is a higher percentage of the population measured at 3sd+ levels on the test than the probabilities of the normal distribution would predict. Some IQ scoring procedures may attempt to integrate such clusters of statistical outliers into the curve by adjusting the scores so that they better represent actual probabilities (according to Silverman) and in these cases, scores around 145 and above may actually have been notably higher, were they not so adjusted.

Children's test scores are based on a simple ratio of a child's "mental age" (representing the age at which the subject's test performance would normally be expected) divided by the child's chronological age, times 100. (MA/CA) x 100 = IQ By age 14 and above, youth and adults are typically tested using adult-normed measures that no longer use simple ratios for IQ determination.

IQ and G:

Modern IQ tests produce scores for different areas (e.g., language fluency, three-dimensional thinking, etc.), with the summary score calculated from subtest scores. Individual subtest scores tend to correlate with one another, even when seemingly disparate in content. Analyses of an individual's scores on a wide variety of tests (Stanford-Binet, WISC-R, Raven's Progressive Matrices and others) will reveal that they all measure a single common factor and various factors that are specific to each test. This kind of factor analysis has led to the theory that underlying these disparate cognitive tasks is a single factor, termed the General_intelligence_factor, that represents the common-sense concept of intelligence. In the normal population, g and IQ are roughly 90% correlated and are often used interchangeably.

Genetics vs Environment:

The role of genes and environment in determining IQ is reviewed in Plomin et al. (2001, 2003). The degree to which genetic variation contributes to observed variation in a trait is measured by a statistic called heritability. Heritability scores range from 0 to 1, and can be interpreted as the percentage of variation (e.g. in IQ) that is due to variation in genes. Twins studies and adoption studies are commonly used to determine the heritability of a trait. Until recently heritability was mostly studied in children. These studies yield an estimate of heritability of 0.5; that is, half of the variation in IQ among the children studied was due to variation in their genes. The remaining half was thus due to environmental variation and measurement error. A heritability of 0.5 implies that IQ is "substantially" heritable.

Considerable research has focused on biological correlates of g; see General_intelligence_factor and the section on brain size below. For example, general intelligence and MRI brain volume measurements are correlated, and the effect is primarily determined by genetic factors.

Environment:

Nearly all personality traits show that, contrary to expectations, environmental effects actually cause adoptive siblings raised in the same family to be as different as children raised in different families (Harris, 1998; Plomin & Daniels, 1987). Put another way, shared environmental variation for personality is zero, and all environmental effects are nonshared. Intelligence is actually an exception to this rule, at least among children. The IQs of adoptive siblings, who share no genetic relation but do share a common family environment, are correlated at .32. Despite attempts to isolate them, the factors that cause adoptive siblings to be similar have not been identified. However, as explained below, shared family effects on IQ disappear after adolescence.

Active genotype-environment correlation, also called the "nature of nurture", is observed for IQ. This phenomenon is measured similarly to heritability; but instead of measuring variation in IQ due to genes, variation in environment due to genes is determined. One study found that 40% of variation in measures of home environment are accounted for by genetic variation. This suggests that the way human beings craft their environment is due in part to genetic influences.

Environmental factors may play a larger role in determining IQ in situations where environmental conditions are more variable. Proper childhood nutrition appears critical for cognitive development; malnutrition can lower IQ. Other research indicates environmental factors such as prenatal exposure to toxins, duration of breastfeeding, and micronutrient deficiency can affect IQ.