1. What is the IQ Formula?

The IQ formula converts a raw test score into an intelligence quotient (IQ) score with a mean of 100 and standard deviation of 15. This allows comparison of scores across different tests and populations.

2. How Does the Calculator Work?

The calculator uses the IQ formula:

Where:

• \( Score \) — Raw test score
• \( Mean \) — Average score in the reference population
• \( SD \) — Standard deviation of scores in the reference population

Explanation: The formula calculates how many standard deviations the raw score is from the mean, then scales this to the IQ scale (mean=100, SD=15).

3. Importance of IQ Calculation

Details: Standardized IQ scores allow comparison of cognitive abilities across individuals and populations, and are used in educational, clinical, and research settings.

4. Using the Calculator

Tips: Enter the raw test score, the mean score for the reference population, and the standard deviation. All values must be valid (SD > 0).

5. Frequently Asked Questions (FAQ)

Q1: Why is 100 used as the mean IQ?
A: 100 is the standard mean for most modern IQ tests, allowing easy interpretation of scores (above 100 is above average).

Q2: What does the standard deviation represent?
A: The SD (typically 15) shows how spread out the scores are. About 68% of people score within 1 SD (85-115) of the mean.

Q3: Can this formula be used for any test?
A: Only if the test's scores follow a normal distribution and you have the proper mean and SD for the reference population.

Q4: What are limitations of IQ scores?
A: IQ tests measure specific cognitive abilities and may not capture all aspects of intelligence or potential.

Q5: How often do IQ scores change?
A: While relatively stable in adults, IQ scores can change with education, environment, and brain development in children.