Percentile Calculator

Percentile: relative position in the data

A percentile is the value below which a given percentage of the data falls. P50 is the median, P25 = Q1, P75 = Q3, and P75 − P25 is the interquartile range (IQR). Interpolation method: sort the data and compute position k = (P/100) · (n + 1). Example: for [2, 4, 4, 4, 5, 5, 7, 9], P75 = 5.75. Percentile vs percentage: percentage is a proportion of the whole; percentile is a relative position in the distribution. A child at the 85th percentile on a WHO growth curve is taller than 85% of children the same age — pediatricians watch curve consistency, not the absolute value.

Applications

ENEM scoring (percentile of candidates), salary surveys (P50 median ≠ mean, P90 used for ceilings), server latency SLAs (P95 and P99 — long tails matter more than the average), income distribution (related to the Gini coefficient), pediatric growth curves (P3, P15, P50, P85, P97).

FAQ

Why do different tools return slightly different percentiles? There are several formulas (linear interpolation, nearest rank, exclusive/inclusive). Excel uses PERCENTILE.INC; NumPy defaults to linear interpolation; small samples make the differences visible.

Median or mean? The median (P50) resists outliers; the mean is pulled by extreme values. For salaries and house prices, the median is more representative.

What is P99 in an SLA? 99% of requests are at or below that latency — only 1% are slower. Web services commonly target P95 and P99 because long tails (a few slow requests) ruin user experience even when the average is fine.