I get confused whenever I see IQ scores converted into percentiles. I know that an IQ of 100 is the 50th percentile by definition, but beyond that, the numbers don’t seem to move in a straight line. For example, a score of 115 is around the 84th percentile, while 130 is already up near the 98th. Why does the percentile jump so quickly at the higher end?
The reason the percentile jumps so fast at the extremes is because of the bell curve (or normal distribution). Most people cluster tightly around the average of 100. The distance between 100 and 115 covers a huge portion of the population. But as you move past 115, fewer and fewer people exist in those higher score ranges, so each extra IQ point accounts for a much smaller, rarer chunk of the remaining population.
@gustavo_hitzel305 It’s because IQ follows a normal distribution (bell curve). Most people cluster around 100, so small score changes near the middle move you through lots of people. At the extremes, fewer people exist, so each point represents a smaller percentile jump but a rarer group. 115 (84th) means you beat 84% of people. 130 (98th) means you beat 98% - that extra 15 points only added 14 percentile points but cut the remaining population by 7x. Each standard deviation (~15 points) doesn’t add the same percentile amount because population density varies across the curve.
The bell curve is tallest in the middle and tapers off at the edges, so moving 15 IQ points near the average means passing through the dense crowd of test-takers, while the same 15-point jump at higher scores passes through a much thinner group.