IQ test classification

Question

For IQ tests with a mean of 100 and a standard deviation of 15, a score of 73 would represent a classification of what?

Answer 1

a score of 73 is almost 2 standard deviations below the mean, so that would typically be classified as "borderline" or "below average"

Answer 2

For IQ tests with a mean (average) of 100 and a standard deviation of 15, a score of 73 would be classified as below average or in the lower part of the distribution.

Here's how it's determined:

1.Understanding IQ Scores: IQ scores are typically distributed with a mean of 100 and a standard deviation of 15 in a normal distribution.

2. Calculating Z-score: To find out where a score of 73 falls on this distribution:

\[

Z = \frac{X - \mu}{\sigma}

\]

where:

- \( X \) is the score (73 in this case),

- \( \mu \) is the mean (100),

- \( \sigma \) is the standard deviation (15).

Calculate the Z-score:

\[

Z = \frac{73 - 100}{15} = \frac{-27}{15} \approx -1.8

\]

3. Interpreting the Z-score: A Z-score of -1.8 indicates that the score of 73 is 1.8 standard deviations below the mean.

4. Classification: According to standard IQ classifications based on normal distribution:

- Scores below 90 are often considered below average,

- Scores around 73 would generally be in the lower percentile range of IQ scores.

Therefore, a score of 73 on an IQ test with a mean of 100 and a standard deviation of 15 would be classified as below average.