One sample. One named convention.
Check the percentile.
See the interpolation.
Enter a small measurement sample and one chosen percentile. Quantilenote uses Type 7 linear interpolation and shows the rank, adjacent sorted observations and exact weight behind its answer.
Free · Browser local · Duplicates retainedEnter your sample
This is one Type 7 sample quantile. Other conventions can differ. It is not a population estimate or a guarantee that exactly the chosen fraction of observations is strictly below the answer.
Type 7 · Exact arithmetic
Chosen sample percentile
Reduced rational value:
- Sample observations
- Zero-based fractional rank
- Exact rank fraction
- Upper interpolation weight
Exact upper weight fraction: .
| Bracket | Order position | Exact value |
|---|---|---|
| Lower | ||
| Upper |
Notes include every input value in entered order, sorted values with duplicates and the chosen convention. Exact outputs may have more fractional places than inputs.
A convention you can inspect
For n observations and probability p, Type 7 uses zero-based rank(n-1)p. A fractional rank interpolates adjacent sorted values rather than selecting an unexplained nearest rank.
Exact small decimals
The50th percentile of0 and 0.000000000001 is exactly0.0000000000005. Extra output precision is retained, rather than rounded to the input's12-place limit.
Duplicates stay in the sample
The sample 0,0,100 has Type 7 median 0. Both zeros count. This does not mean exactly half of its observations are strictly below0.
Try the visible calculation
The starting sample 10,20,40,100 at 75 gives rank 2.25. Sorted positions3 and 4 contain40 and 100; upper weight 0.25 gives40+0.25(100-40)=55. That answer need not be one of the observations.
Use worked examples and the method to check the convention. The calculator does not remove missing values, choose among algorithms or infer a population distribution from the entered sample.