What is an IQ Percentile Rank?
A percentile rank indicates the proportion of the population that scores equal to or below a given score. If you score in the 98th percentile, it means you have outperformed 98% of people worldwide, and only 2% score higher.
Gaussian Bell Curve Normal Distribution
Standardized IQ tests follow the classic normal distribution function:
$$f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x - \mu)^2}{2\sigma^2}}$$
Approximately 68.2% of all humans fall within $\pm 1\sigma$ (IQ 85 to 115). Scores above 130 are rare and achieved by only 2.27% of people.