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How to use
Sample percentiles do not have one universal convention, so this tool exposes its assumption instead of hiding it: inclusive linear interpolation (Type 7) or nearest rank. The selected method is also used for quartiles and IQR.
- Paste values separated by commas, spaces, semicolons or line breaks.
- Enter a percentile from 0 to 100.
- Choose linear interpolation or nearest rank.
- Review the percentile, quartiles, median, IQR and data range.
How it is calculated
Example
For 10,20,30,40 using Type 7, P75 lies at position 2.25 between 30 and 40, giving 32.5.
Important notes
Software and textbooks can differ slightly because percentile-position conventions vary. Match the method when comparing results, and do not confuse a statistical percentile with an ordinary percentage.
Worked examples and interpreting results
For the 75th percentile of 10, 20, 30, 40, sort the values and interpolate between the third and fourth positions using the linear convention.
| Case | Calculation | Result |
|---|---|---|
| Linear 75th percentile | 30 + 0.25 × (40 − 30) | 32.5 |
| Linear median | 20 + 0.5 × (30 − 20) | 25 |
| Linear first quartile | 10 + 0.75 × (20 − 10) | 17.5 |
How to check the result
Linear interpolation and nearest-rank methods can return different values. Compare percentiles only when the same definition and dataset are used.
Frequently asked questions
What is Type 7?
Linear interpolation at h=(n−1)p, a widely used statistical convention.
What is IQR?
Q3−Q1, the spread of the middle 50% of the data.
Why can two percentile calculators disagree?
Several valid conventions locate the percentile rank and interpolate between observations, especially in small samples. Software may use different definitions, so document the method when comparing formal results.