Which of the following is correct formula to calculate IQ?

Question

Accepted Answer

The correct formula to calculate IQ (Intelligence Quotient) is given by Option 1.

**Explanation for why Option 1 is correct:**

The formula for IQ was originally proposed by William Stern and later popularized by Lewis Terman for the Stanford-Binet Intelligence Scales. It is defined as:

$	ext{IQ} = \frac{	ext{Mental Age (MA)}}{	ext{Chronological Age (CA)}} 	imes 100$

*   **Mental Age (MA):** This refers to a person's intellectual level, expressed as the age at which an average individual reaches the same level of intellectual development. It is determined by performance on standardized intelligence tests. For example, if a 6-year-old child performs on an intelligence test at the level of an average 8-year-old, their mental age is 8.
*   **Chronological Age (CA):** This is the actual biological age of the individual, measured from birth.
*   **Multiplication by 100:** The ratio of MA to CA is multiplied by 100 to eliminate decimals and express the IQ as a whole number, making it easier to interpret. An average IQ score is 100, meaning the mental age is equal to the chronological age (MA/CA = 1). Scores above 100 indicate a mental age greater than the chronological age, and scores below 100 indicate a mental age less than the chronological age.

Therefore, Option 1, $\frac{MA}{CA} 	imes 100$, accurately represents the historical and widely accepted formula for calculating IQ.

**Explanation for why other options are incorrect:**

*   **Option 2: $\frac{CA}{MA}$**
    This formula reverses the mental age and chronological age. If used, a person with a mental age greater than their chronological age (indicating higher intelligence) would have an IQ less than 1, which is incorrect and not how IQ is scaled. For example, if MA=10 and CA=8, this formula would give 8/10 = 0.8, which is not an IQ score.

*   **Option 3: $\frac{CA}{MA} 	imes 100$**
    Similar to Option 2, this formula incorrectly places chronological age in the numerator and mental age in the denominator. If a child has a mental age of 10 and a chronological age of 8, this formula would yield $(8/10) 	imes 100 = 80$. While 80 is an IQ score, it would incorrectly suggest that the child is below average, when in fact, a mental age of 10 at a chronological age of 8 indicates above-average intelligence. The correct calculation would be $(10/8) 	imes 100 = 125$.

*   **Option 4: $\frac{MA}{CA 	imes 100}$**
    This formula incorrectly multiplies the chronological age by 100 in the denominator. This would result in an extremely small IQ value, far from the standard scale where 100 is average. For example, if MA=10 and CA=10, this formula would give $10 / (10 	imes 100) = 10 / 1000 = 0.01$, which is not a meaningful IQ score. The multiplication by 100 should be applied to the entire ratio, not just the denominator.