What is a Percentile?
The Pth percentile is the value below which P% of observations fall. The 50th percentile is the median. The 25th and 75th percentiles are Q1 and Q3 (quartiles). Percentiles are widely used in standardized testing, growth charts, salary surveys, and quality control.
Percentile Formulas
Value at Pth percentile: L = (P/100) × N → round up to get position
Key Percentiles
| Percentile | Name | Meaning |
|---|---|---|
| P25 | First Quartile (Q1) | 25% of data below this value |
| P50 | Median (Q2) | 50% of data below; middle value |
| P75 | Third Quartile (Q3) | 75% of data below this value |
| P90 | 90th percentile | Top 10% threshold |
| P99 | 99th percentile | Top 1% threshold |
Frequently Asked Questions
What is the interquartile range (IQR)?
The IQR = Q3 − Q1 (P75 − P25). It measures the spread of the middle 50% of data and is robust to outliers. Values more than 1.5 × IQR below Q1 or above Q3 are commonly flagged as outliers (Tukey's fence).
Is the 50th percentile the same as the mean?
The 50th percentile is the median, not the mean. They are equal only in symmetric distributions. In skewed distributions (e.g., income), the mean is pulled toward the outliers while the median stays at the true midpoint of the data.
What does it mean to be in the 90th percentile for height?
It means you are taller than 90% of the reference population. Only 10% of the population is taller than you. Growth charts for children use percentiles this way — being in the 90th percentile for height simply means taller than 90% of same-age, same-sex children.