Q.(a) Find out the IQ of a 14-year-old child with a mental age of 16.

Intelligence Quotient Classification

The Intuition

Imagine you give a test to a thousand 10-year-olds. Some will answer more questions correctly, some fewer. The raw score — "35 out of 50" — tells you something, but not enough. Did that child do better than most? Worse? How much better?

That's the problem IQ classification solves. It takes a person's test score and tells you where they stand relative to everyone else their age. The key idea is the bell curve — most people cluster near the middle, and the further you go from the middle, the fewer people you find.

The Precise Statement

IQ scores are designed to follow a normal distribution (the bell curve) with a mean of 100 and a standard deviation of 15 (on most modern tests like the Wechsler scales).

The classification system divides this bell curve into ranges. Here is the standard classification table:

What the Numbers Actually Mean

The average range (90–109) covers half the population. If you score 100, you performed exactly at the median — better than half your peers, worse than the other half.

Each 15-point step represents one standard deviation. A score of 115 means you performed better than about 84% of people your age. A score of 130 means better than about 98% — roughly 1 in 50 people. …

The Verbal Performance Distinction

Imagine you meet someone who can argue brilliantly about politics, quote poetry, and tell you the capital of every country — but when you ask them to tie their shoelaces, they fumble. Or the opposite: a person who can fix a car engine blindfolded, paint a landscape, and dance gracefully, yet struggles to find the right words in a conversation.

That gap — between what you can say and what you can do — is the heart of the Verbal Performance Distinction.

The Intuition

Your brain has two broad kinds of ability:

• Verbal knowledge — things you can state, explain, or describe in words. Facts, definitions, rules, theories. "The capital of France is Paris." "Water boils at 100°C at sea level."
• Performance ability — things you can actually do, often without being able to explain how. Riding a bicycle, catching a ball, recognising a friend's face, speaking your native language fluently.

The key insight: these two can come apart. You can know something verbally but fail to perform it. You can perform something smoothly but be unable to describe how.

The Precise Statement

This is not a minor curiosity. It is a foundational idea in cognitive science, education, and artificial intelligence. It tells us that "knowing" is not a single thing — there are different kinds of knowing, stored and accessed differently in the brain.

Why It Matters

In learning: A student who can recite Newton's laws (verbal) may still be unable to solve a problem using them (performance). Teaching that only tests verbal recall misses this gap. Real mastery requires bridging the two — turning verbal knowledge into fluid performance.

In skill acquisition: When you first learn to drive, you think through every step verbally ("clutch in, gear up, clutch out slowly"). With practice, the performance becomes automatic — you no longer need the verbal script. The distinction explains why experts often cannot explain how they do what they do. …