Which of the following is correct formula to calculate IQ?

Intelligence Quotient (IQ) is a standardized score comparing a person's Mental Age (MA) — the age level at which their performance matches average scores on a cognitive test — to their Chronological Age (CA), their actual age in years. William Stern proposed expressing this comparison as a ratio scaled to a base of 100, later adopted by Lewis Terman in the Stanford-Binet scale, so that a person whose mental performance exactly matches their chronological age scores exactly 100.

1. Identify what each offered expression does with Mental Age (MA) and Chronological Age (CA): which age sits in the numerator, which sits in the denominator, and where the x100 scaling factor is applied.

2. The Stern ratio-IQ definition requires Mental Age in the numerator, Chronological Age in the denominator, and the entire ratio - not just one term - multiplied by 100.

3. Test each candidate against the baseline case where a person's Mental Age exactly equals their Chronological Age (MA = CA): a fair IQ formula must return exactly 100 for this case, since such a person is, by definition, performing at exactly the expected average level.

The baseline case alone is necessary but not sufficient to identify the formula, since an inverted ratio scaled by 100 also equals 100 when Mental Age equals Chronological Age; the deciding check is what happens as mental performance moves ahead of chronological age. Only the expression that places Mental Age over Chronological Age, with the whole ratio multiplied by 100, both matches the baseline AND rises above 100 as mental development outpaces chronological age - exactly the two properties required of a genuine intelligence-quotient score.

• CA/MA (no x100 scaling): places Chronological Age over Mental Age and applies no scaling at all; for the baseline MA = CA case this gives 1, not 100.

• CA/MA x100: keeps the same inverted ratio but does scale by 100; for the baseline MA = CA case it happens to give 100, but for anyone whose Mental Age runs ahead of Chronological Age the ratio falls below 1, driving the score below 100 - the opposite of the above-100 score expected for above-average mental development.

• MA/(CA x100): keeps Mental Age correctly in the numerator, but multiplies only the denominator by 100 instead of the whole ratio; for the baseline MA = CA case this returns 0.01, a hundredfold too small.