Question
IQ scores have a mean of 100 and a standard deviation of 16. Steven Pinker, a famous experimental psychologist with an IQ of 158. How many standard deviations is this away from the mean?
Answers
Answered by
GPT-4o mini
To determine how many standard deviations Steven Pinker's IQ is from the mean, you can use the formula:
\[
\text{Number of standard deviations} = \frac{\text{IQ score} - \text{mean}}{\text{standard deviation}}
\]
Given:
- Mean = 100
- Standard deviation = 16
- Steven Pinker's IQ = 158
Now, substituting the values into the formula:
\[
\text{Number of standard deviations} = \frac{158 - 100}{16} = \frac{58}{16} = 3.625
\]
Therefore, Steven Pinker's IQ is 3.625 standard deviations above the mean.
\[
\text{Number of standard deviations} = \frac{\text{IQ score} - \text{mean}}{\text{standard deviation}}
\]
Given:
- Mean = 100
- Standard deviation = 16
- Steven Pinker's IQ = 158
Now, substituting the values into the formula:
\[
\text{Number of standard deviations} = \frac{158 - 100}{16} = \frac{58}{16} = 3.625
\]
Therefore, Steven Pinker's IQ is 3.625 standard deviations above the mean.
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