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IQ, Intelligence Tests and Individual Differences

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Calculate IQ, interpret IQ ranges, compare types of intelligence tests from Binet to Raven, and understand individual differences in the classroom.

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IQ, Intelligence Tests and Individual Differences

Read at your own pace. Try the practice, then continue your course.

How do psychologists measure intelligence, and what does an IQ score really mean? This lesson explains how intelligence quotient (IQ) is calculated, how scores are interpreted, the main types of intelligence tests and the history behind them, and what individual differences mean for teachers. Expect at least one numerical IQ question in practice papers, so learn the formula well.

Calculating IQ

Mental age (MA) is the level of intellectual performance typical of a certain age. Chronological age (CA) is a person’s actual age.

IQ = (Mental age ÷ Chronological age) × 100

The idea of a mental quotient was proposed by William Stern (1912); Lewis Terman multiplied it by 100 and popularised the term IQ in the Stanford-Binet test (1916).

Worked examples

Child	Mental age	Chronological age	IQ
Ravi	10 years	8 years	(10 ÷ 8) × 100 = 125
Sita	8 years	8 years	(8 ÷ 8) × 100 = 100
Arun	6 years	8 years	(6 ÷ 8) × 100 = 75

An IQ of 100 means mental age equals chronological age. Above 100 means mental age is ahead of actual age.

Finding a missing value

If a child aged 10 has an IQ of 120, their mental age = (120 × 10) ÷ 100 = 12 years.

Deviation IQ

The MA ÷ CA formula does not work well for adults, because mental age stops increasing. Modern tests use a deviation IQ: a score compared with others of the same age, on a scale with an average of 100 and a standard deviation of 15 in most modern tests. About two-thirds of people score between 85 and 115.

Interpreting IQ

IQ range (approximate)	Common description
130 and above	very superior / gifted
120–129	superior
110–119	high average
90–109	average
80–89	low average
70–79	borderline
below about 70	may indicate intellectual disability (diagnosis also requires assessment of adaptive functioning)

Exact labels and cut-offs vary between textbooks and tests, so learn the general pattern: about 90–110 is average, and very high or very low scores need specialist interpretation.

Types of intelligence tests

History

Binet-Simon scale (1905): the first practical intelligence test, developed by Alfred Binet and Théodore Simon in France to identify children who needed extra help in school.
Stanford-Binet (1916): Terman’s revision at Stanford University, which used IQ.
Wechsler scales: David Wechsler developed tests such as the WISC (for children) and WAIS (for adults), giving verbal and performance scores.
Raven’s Progressive Matrices: a non-verbal test using patterns, designed to reduce dependence on language.

Classification

Basis	Types	Notes
Number tested	individual tests (one person at a time) and group tests (many at once)	individual tests are more detailed; group tests are quicker
Language	verbal tests (need reading and language) and non-verbal or performance tests (pictures, blocks, puzzles)	non-verbal tests suit young children, people with low literacy and speakers of other languages

Cautions in using tests

Tests can be culturally biased, favouring children familiar with the test’s language and content.
An IQ score is one sample of performance on one day; it does not measure creativity, motivation, character or every kind of talent.
Teachers should never label children by IQ in front of others.

Individual differences

Individual differences are the ways people differ from each other in intelligence, aptitude, interests, attitudes, learning pace, personality, physical abilities and background. They arise from the interaction of heredity and environment.

Teaching for individual differences

Differentiated instruction: varying content, process and products for different learners
Flexible grouping, peer tutoring and remedial or enrichment activities
Multiple ways for children to show learning
Special attention to gifted learners (enrichment, challenge) and slow learners (more time, concrete materials, encouragement)

Example

A Class 5 teacher notices that some pupils finish maths problems quickly while others need more time. She prepares three levels of worksheets on the same concept, lets fast finishers create their own problems, and works with a small group using bundle sticks. Every child works on the same concept at a suitable level of challenge.

Exam focus

IQ = MA ÷ CA × 100. Practise finding IQ, MA or CA.
Binet-Simon (1905) = first practical test; Stanford-Binet (1916, Terman) introduced IQ use.
Raven’s Progressive Matrices = non-verbal; WISC = Wechsler test for children.
Average IQ is around 100, roughly 90–110.

Key takeaways

IQ = (mental age ÷ chronological age) × 100.
Modern tests use deviation IQ with an average of 100.
Binet and Simon created the first practical intelligence test in 1905.
Tests can be individual or group, verbal or non-verbal.
Teachers should respond to individual differences with differentiated teaching, not labels.

Practice

A child has a mental age of 12 and a chronological age of 10. The IQ is:
- (A) 83
- (B) 100
- (C) 120
- (D) 112
An IQ of 100 means:
- (A) mental age equals chronological age
- (B) the child is gifted
- (C) the child has a disability
- (D) mental age is double chronological age
The first practical intelligence test was developed by:
- (A) Wechsler
- (B) Raven
- (C) Spearman
- (D) Binet and Simon
A child aged 8 has an IQ of 125. Their mental age is:
- (A) 9 years
- (B) 10 years
- (C) 12 years
- (D) 6.4 years
Raven’s Progressive Matrices is an example of a:
- (A) verbal individual test
- (B) projective test
- (C) non-verbal test
- (D) personality inventory
Which test is designed for children by Wechsler?
- (A) WISC
- (B) TAT
- (C) MMPI
- (D) Rorschach
A major caution about intelligence tests is that they:
- (A) measure every human talent perfectly
- (B) may be culturally biased
- (C) never change
- (D) are only for adults
The best response to individual differences in a class is:
- (A) one identical task for all with no support
- (B) public ranking by IQ
- (C) differentiated instruction with varied levels and supports
- (D) separating slow learners permanently

Answers and explanations (tap to show)

(C) IQ = (12 ÷ 10) × 100 = 120.
(A) When mental age equals chronological age, IQ = 100.
(D) Binet and Simon developed the first practical intelligence scale in 1905.
(B) Mental age = (125 × 8) ÷ 100 = 10 years.
(C) Raven’s test uses patterns, not words, so it is non-verbal.
(A) The Wechsler Intelligence Scale for Children is the WISC; TAT, MMPI and Rorschach are personality measures.
(B) Tests may favour children familiar with their language and content.
(C) Differentiated instruction adapts teaching to different learners without labelling them.

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IQ, Intelligence Tests and Individual Differences

This lesson is for members

IQ, Intelligence Tests and Individual Differences

Calculating IQ

Worked examples

Finding a missing value

Deviation IQ

Interpreting IQ

Types of intelligence tests

History

Classification

Cautions in using tests

Individual differences

Teaching for individual differences

Example

Exam focus

Key takeaways

Practice