Interpolated percentile
For 1,2,3,4, linear P25 has index 0.75 and value 1.75.
Find percentile values or percentile ranks, compare calculation conventions, and inspect quartiles, IQR, deciles, and sorted data.
A percentile value is a point associated with a specified position in sorted data. Percentile rank instead describes a query value's relative position in a dataset.
Percentiles are not percentages of the data values themselves. Multiple legitimate conventions exist, so results from different tools may differ.
CalcRocket sorts values ascending and interpolates between neighboring zero-based positions. This is the type 7 convention described in R's quantile documentation; P0 and P100 return the minimum and maximum.
index=(p/100)(n−1); value=xₗ+fraction(xᵤ−xₗ)Uses a one-based rank after sorting, with P0 explicitly returning the minimum and P100 the maximum.
rank=ceil((p/100)n)A separate midrank convention for a queried value; it is not the inverse of every percentile-value method.
rank=(below+0.5×equal)/n×100IQR=Q3−Q1For 1,2,3,4, linear P25 has index 0.75 and value 1.75.
For 1,2,3,4,5, P50 is 3.
For query 3 in 1,2,3,4,5, two values are below and one equals it, giving 50%.
Can return a value between observed data points.
Always returns an observed value and uses a one-based ceiling rank.
Comparisons are meaningful only when the same percentile definition is used.
Q1, Q2, and Q3 are the 25th, 50th, and 75th percentiles. Q2 is the median. IQR measures the distance from Q1 to Q3.
The rank convention gives tied values half credit: values below plus half the values equal to the query, divided by the dataset count.
It is a data value associated with a specified cumulative percentage under a stated convention.
This calculator sorts the data and supports type 7 linear interpolation and a ceiling-based nearest rank.
It estimates the percentage position of a query value within a dataset.
A percentage is a proportion; a percentile describes position in ordered data.
Multiple accepted percentile conventions use different index and interpolation rules.
The 50th percentile is the median under these methods.
Q1, Q2, and Q3 are P25, P50, and P75.
It is Q3 minus Q1.
Yes. Linear interpolation can return a value between adjacent observations.
Each tied value receives half weight in this calculator's percentile-rank convention.