Calculating and Classifying the Child's IQ Score

This solution explains how to calculate the Intelligence Quotient (IQ) for a child based on their chronological age (CA) and mental age (MA), and then determines the classification of the calculated IQ score. The child's chronological age is $9$ years and $6$ months, and their mental age is $12$ years.

Understanding IQ Calculation

The Intelligence Quotient (IQ) was historically calculated using a ratio derived from a child's performance on an intelligence test. The formula used is:

$$ \text{IQ} = \frac{\text{Mental Age (MA)}}{\text{Chronological Age (CA)}} \times 100 $$

Where:

• Mental Age (MA): Represents the intellectual level at which the child is functioning, as measured by the test.
• Chronological Age (CA): Represents the child's actual age in years and months.

Step-by-Step IQ Calculation

To calculate the IQ, we first need to ensure both ages are in the same units, typically years.

1. Convert Chronological Age (CA) to Years: The child's chronological age is $9$ years and $6$ months. Since there are $12$ months in a year, $6$ months is equal to $\frac{6}{12} = 0.5$ years. So, the CA in years is $9 + 0.5 = 9.5$ years.
2. Apply the IQ Formula: Using the formula with MA = $12$ years and CA = $9.5$ years: $$ \text{IQ} = \frac{12}{9.5} \times 100 $$
3. Perform the Calculation: $$ \text{IQ} = 1.263157... \times 100 $$ $$ \text{IQ} \approx 126.3 $$

Classifying the IQ Score

The calculated IQ score of approximately $126.3$ needs to be classified according to standard IQ score interpretations. These classifications help understand where the individual's cognitive abilities fall relative to the general population.

Based on the standard classifications, an IQ score of $126.3$ falls within the range of $120 - 129$. Therefore, the child's IQ is classified as Superior.

Conclusion

The calculation shows the child's IQ is approximately $126.3$. This score is typically classified as Superior in standard psychological assessments.