Descriptive statistics Updated November 2026

Percentile

The kth percentile is the value below which k percent of the data falls. To find it, sort the data, compute the position (k / 100) * (n - 1) + 1, and interpolate between the two neighboring values. The percentile rank of a value is the share of values below it.

Syntax

position = (k / 100) * (n - 1) + 1  (Excel PERCENTILE.INC method)

Part	What it is
`k`	the percentile wanted, 0 to 100
`n`	the number of sorted values

Examples

Data sorted: 10, 20, 30, 40, 50  (n = 5)
40th percentile: position = 0.4 * 4 + 1 = 2.6
value = 20 + 0.6 * (30 - 20)

Result: 26

Excel: =PERCENTILE.INC(A1:A5, 0.4)

Same data, 50th percentile (median): position = 0.5 * 4 + 1 = 3

Result: 30

Percentile rank of 40 in 10, 20, 30, 40, 50
values below 40: 3 of 5

Result: 60th percentile

Excel: =PERCENTRANK.INC(A1:A5, 40) returns 0.75 because it interpolates over n - 1; the simple count-below method gives 0.6

Common mistakes

Mixing PERCENTILE.INC and PERCENTILE.EXC; they use different positions and give different answers on small data sets, so state which one you used.
Reading a percentile as a percent score; the 90th percentile means 90% of values are below it, not that the value is 90.
Computing a percentile on unsorted data; sort first.

Practice Percentile

These drills check your answer on live data, free, no account needed.

Percentile (inclusive method)A training team scored 9 trainees on a skills check: 98, 75, 61, 52, 57, 39, 64, 78, 40. Find the 10th percentile using the inclusive method: sort the data, find the rank 1 + p(n - 1), and interpolate linearly between the two neighboring values. Round to 2 decimal places.

Questions

What is the difference between percentile and percentile rank?

A percentile is a value (the 90th percentile is a height, a score, a time). A percentile rank is a position for a given value (your score sits at the 90th percentile).

Which percentile is the median?

The 50th percentile. The 25th and 75th percentiles are the first and third quartiles.

Why do calculators give different percentiles for the same data?

There are several interpolation methods. Excel PERCENTILE.INC, PERCENTILE.EXC, R's default and textbook nearest-rank methods can all differ by a little on small samples; they agree closely on large ones.

Range and interquartile rangeThe range is max minus min; the interquartile range is Q3 minus Q1. Worked examples with exact numbers, Excel QUARTILE.INC and why methods differ.
Mean, median and modeHow to calculate the mean, median and mode of a data set by hand and in Excel, when each average is the right one, and the mistakes that give a wrong answer.
z-scoreThe z-score formula z = (x - mean) / sd, worked examples, how to read a z-score as a percentile with the normal table, and the Excel function STANDARDIZE.
Normal distributionHow to find normal distribution probabilities with z-scores, read the standard normal table, find a percentile cutoff, and use NORM.DIST and NORM.INV.