What Does IQ Stand For?

What does IQ stand for? It was originally an abbreviation for intelligence quotient. Learn the history of the term and the math behind the name.

Dr. Russell T. WarneChief Scientist

IQ is the score produced by an intelligence test. “IQ” was originally an abbreviation for “intelligence quotient.” This name and abbreviation were chosen because the original formula for calculating the score on an intelligence test was:

(mental age ÷ chronological age) ✕ 100 = IQ

A “quotient” is the result of a division, and so the score on intelligence tests was called the “intelligent quotient” because the division of this equation (in parentheses) produces a quotient. That quotient is then multiplied by 100 to get rid of the decimal that appears in some quotients.

In this formula, “chronological age” is the examinee’s actual age. The “mental age” was the age of the typical person who performed just as well on the intelligence test as the examinee. For example, if an examinee is 12 years old, and he performs as well on the test as the average 9-year-old, his IQ would be:

(9 ÷ 12) ✕ 100 = 75

Likewise, a 12-year-old who tests as well as the average 16-year-old would have an IQ of:

(16 ÷ 12) ✕ 100 = 133

In this equation, 100 is the average IQ for every age. Numbers below 100 indicate that the examinee is less intelligent than the average person their age. People who score above 100 are smarter than average for their age.

The original IQ equation is convenient and easy to understand, but it has problems. First, the equation doesn’t make sense for adults. Unlike children, adults do not steadily increase in their mental abilities as they age. Second, the scores are difficult to compare across age groups. This is apparent when considering a child who is 5-years-old and scores as well as the average 7-year-old. That child’s IQ would be:

(7 ÷ 5) ✕ 100 = 140

If we retested that child three years later (at age 8), and he scored as well as the average 10-year-old, the child’s IQ would be:

(10 ÷ 8) ✕ 100 = 125

Comparing these scores shows the problem with the equation. Even though the child is still 2 years more advanced than his peers, his IQ went down. Clearly, we can’t say that “140” has the same meaning at both age groups. In fact, no IQ created with this equation can be compared across ages, except 100 (which is always average for any age group).

Current IQ Equation

To fix this problem with IQ, psychologists have moved to a new calculation procedure, which requires two steps. The first is to calculate a z-score for the examinee. This is calculated using the following formula:

(Score - Average) ÷ Standard deviation = z-score

The z-score equation requires knowing the average and the standard deviation for a group of test takers, which the IQ test creators call the “norm sample.” The average is a number signifying the typical performance of norm sample member, and the standard deviation is a measure of how spread out scores are. (You can learn more about the standard deviation and z-scores from an introductory statistics textbook.)

After calculating the z-score for the examinee, the second step is to convert it to an IQ with the following equation:

(z-score ✕ 15) + 100 = IQ

Like the old IQ equation, this new equation sets the average IQ for any age at 100. But it can also be used with adults, and it permits comparisons across age groups.

Because the new equation is not a simple quotient, the term “IQ” is not an abbreviation today. But IQ is a very useful piece of information to know about a person.

Watch “What Does an IQ Test Measure?” with Dr. Russell T. Warne on the Riot IQ YouTube channel to understand what IQ actually represents and what it does not.