Step 1: Understanding the Concept:
The concept of Intelligence Quotient (IQ) was introduced to provide a numerical value representing a person's intellectual standing relative to their age group.
William Stern, a German psychologist, originally devised the formula for IQ, which was later adopted and popularized by Lewis Terman in the Stanford-Binet scale.
The calculation involves two distinct ages: Chronological Age (the actual physical age) and Mental Age (the level of intellectual performance).
Step 2: Key Formula or Approach:
The formula used to calculate the ratio IQ is:
\[ IQ = \frac{MA}{CA} \times 100 \]
Where:
\( MA = \text{Mental Age} \)
\( CA = \text{Chronological Age} \)
The multiplication by 100 is done to eliminate decimals and create a scale where 100 is the average.
Step 3: Detailed Explanation:
Let's plug the values from the question into the formula:
The child's Chronological Age (\( CA \)) is 10 years.
The child's Mental Age (\( MA \)) is 12 years.
Using the formula:
\[ IQ = \frac{12}{10} \times 100 \]
Step-by-step calculation:
1. Divide the Mental Age by the Chronological Age: \( 12 / 10 = 1.2 \)
2. Multiply the result by 100: \( 1.2 \times 100 = 120 \)
An IQ score of 120 indicates that the child is performing significantly above their age level.
In standard IQ classification, a score of 100 is the mean (average).
Scores between 110 and 119 are considered "High Average," while scores from 120 to 129 are often classified as "Superior."
If the child had a mental age of 10, their IQ would be exactly 100.
If the mental age were lower than the actual age (e.g., MA = 8), the IQ would be 80, indicating a delay.
Since this child has a higher mental age, their score must be above 100.
Step 4: Final Answer:
Based on the formula \( IQ = (MA/CA) \times 100 \), a 10-year-old with a mental age of 12 has an IQ of 120.