AP® Psychology · Unit 2 · Topic 2.8
IQ Scores and the Normal Curve
IQ scores form a bell-shaped normal curve centered on 100, where standard deviation tells you how far a score sits from average and translates directly into a percentile rank.
Most human traits that depend on many small genetic and environmental factors adding together end up distributed the same way: lots of people near the middle, fewer and fewer as you move toward either extreme. IQ is built this way on purpose. Test makers design the scale so the mean lands at 100 and the standard deviation is 15, then they fit the results to a normal curve. That curve has a fixed shape: about 68 percent of people fall within one standard deviation of the mean (between 85 and 115), about 95 percent fall within two standard deviations (between 70 and 130), and almost everyone falls within three.
Once you know where a score sits in terms of standard deviations, you know its percentile. An IQ of 130 is exactly two standard deviations above the mean. Since 95 percent of people fall within two standard deviations on either side, the remaining 5 percent split evenly between the two tails, leaving 2.5 percent above 130. That puts a 130 at roughly the 97.5th percentile. The same logic shows that 68 percent of people score between 85 and 115, because that range is exactly one standard deviation on either side of 100.
This connects to any bell-shaped data set measured by percentile: heights, blood pressure, standardized test results. The same rule applies everywhere a normal curve shows up, which is why psychologists lean on standard deviations instead of raw numbers to compare people across different scales and different studies.
Key terms
- Normal curve
- A symmetric, bell-shaped distribution where most scores cluster near the mean and fewer appear toward the extremes.
- Standard deviation
- A measure of how spread out scores are, used as the basic unit of distance from the mean on the curve.
- Z-score
- The number of standard deviations a score falls above or below the mean, found by subtracting the mean and dividing by the standard deviation.
- Percentile rank
- The percentage of people in a distribution who score at or below a given score.
- Interval scale
- A measurement scale with equal distances between values but no true zero point, so ratios between scores are not meaningful.
Watch it explained
- How it worksHow does the normal curve place 68 percent of scores within one standard deviation?
- Worked exampleFind the percentile of an IQ of 130 on a curve with mean 100 and standard deviation 15.
- Worked exampleFind what fraction of people score between 85 and 115 on that same curve.
- Common mistakeWhy isn't an IQ of 130 twice as intelligent as an IQ of 65?
- Ties togetherHow does an IQ distribution connect to percentile rank in any other research data?
Check yourself
End of topic.