Which of the following is the correct formula to calculate I. Q. ?

Question

Accepted Answer

The correct formula to calculate I.Q. (Intelligence Quotient) is given by Option 2: Μ.Α. / C.A. × 100. Here's a detailed explanation of why this is the correct formula and why the other options are incorrect:

1. **Explanation of Option 2 (Correct Answer):**
   - **Μ.Α. / C.A. × 100**: This formula stands for Mental Age (Μ.Α.) divided by Chronological Age (C.A.), multiplied by 100. The concept of I.Q. was developed to assess an individual's cognitive abilities relative to their age group. Mental Age refers to the age level at which an individual performs intellectually, while Chronological Age is the actual age of the individual. By dividing Μ.Α. by C.A. and multiplying by 100, the formula provides a standardized score that indicates how an individual's cognitive abilities compare to the average for their age. This is why Option 2 is the correct formula for calculating I.Q.

2. **Explanation of why other options are incorrect:**
   - **Option 1: C.A. / Μ.Α. × 100**: This formula incorrectly places Chronological Age in the numerator and Mental Age in the denominator. If used, it would result in a score that does not accurately reflect the individual's cognitive abilities relative to their age. It would inversely relate age and mental performance, which is not the intended purpose of the I.Q. calculation.
   
   - **Option 3: C.A. / Μ.Α. × 100**: This option is identical to Option 1 and suffers from the same flaw. It incorrectly reverses the roles of Chronological Age and Mental Age, leading to an inaccurate assessment of intelligence.
   
   - **Option 4: 100 C.A. × Μ.Α.**: This formula is mathematically incorrect for calculating I.Q. as it does not involve division, which is essential for comparing Mental Age to Chronological Age. Multiplying 100 by C.A. and Μ.Α. does not provide a meaningful measure of intelligence.

In conclusion, Option 2 is the correct formula for calculating I.Q. because it accurately compares an individual's Mental Age to their Chronological Age, providing a standardized score that reflects their cognitive abilities relative to their age group. The other options fail to achieve this due to incorrect mathematical operations or arrangement of variables.