percentile() — Percentiles

The value below which a given percentage of the data falls.

percentile(x, p)

Key idea

The p-th percentile is the value with about p% of the data at or below it. (e.g. P90 = 89 -> 90% scored 89 or less)
Being "in the 90th percentile" means 90% are below you — not that you scored 90%.
Quartiles (the four-way cut points) are special percentiles: Q1 = 25th, median = 50th, Q3 = 75th.
To find it, sort the data and read off the value at the p% position.

How to read a percentile

Sort the data from smallest to largest.
The p-th percentile sits at the p% position up the sorted list — roughly p% of values fall at or below it.
Example: the 90th percentile is the value that 90% of the data lies below, leaving the top 10% above it.
The 50th percentile is the median; the 25th and 75th are the quartiles Q1 and Q3 that define the IQR.

Definition

$P_{p} = the value with p % of the data at or below it$

$p$: the percentage you ask about (0–100)
$P_{p}$: the value at that percentile
$P_{50}$: the median

$P_{90} = 89.2 \Rightarrow 90% of values are at or below 89.2$

In plain words

Line everyone up shortest to tallest. The 90th percentile height is the spot where you’re taller than 9 out of every 10 people.

Where you'd use it

A baby is in the 75th percentile for weight — heavier than 75% of babies that age.
Engineers track p95 latency — the response time that 95% of requests come in under.
A test report says you’re in the 88th percentile: 88% of test-takers scored below you.

Frequently asked questions

What does the 90th percentile mean?: The value below which 90% of the data fall.
Why does my answer differ from a textbook?: There are several percentile definitions; R has 9 quantile "types".

Statistics Playground

An interactive playground for probability and statistics. Pick a function, edit its parameters, and see the distribution curve, the computed value, and a plain-English interpretation — all computed in your browser (no server, no install). The functions mirror familiar R syntax (for example pnorm, dbinom, t.test) and the numbers come from numpy running under Pyodide.

The normal distribution

pnorm(q, mean = 0, sd = 1) — Cumulative probability for the normal distribution.
dnorm(x, mean = 0, sd = 1) — Height of the bell curve at a point (the density).
qnorm(p, mean = 0, sd = 1) — The inverse of pnorm; turns a probability back into a value.
rnorm(n, mean = 0, sd = 1) — Draws random values from a normal distribution.
scale(x) — Re-expresses values as z-scores (mean 0, sd 1).

Binomial & Poisson distributions

dbinom(x, size, prob) — Probability of exactly x successes in n trials.
pbinom(q, size, prob) — Probability of q or fewer successes.
dpois(x, lambda) — Probability of exactly x events at rate λ.
ppois(q, lambda) — Probability of q or fewer events at rate λ.

The chi-square distribution & hypothesis testing

pchisq(q, df) — Cumulative probability for the χ² distribution.
t.test(x, mu = 0) — One-sample t-test against a hypothesised mean.

Correlation & regression

cor(x, y) — Strength of a linear relationship, −1 to +1.
lm(y ~ x) — Fits a least-squares straight line through the points.

Descriptive statistics

mean(x) — The arithmetic average.
median(x) — The middle value of the data.
sd(x) — Standard deviation; typical distance of a value from the mean.
var(x) — Variance; the mean squared deviation from the mean.
IQR(x) — Span of the middle 50% of the data.
range(x) — The minimum and maximum values.
quantile(x) — Sample quantiles that split the data into equal slices.
summary(x) — The five-number summary plus the mean.
weighted.mean(x, w) — An average where each value carries a weight.

Combinatorics, sampling & visualisation

factorial(x) — x!, the ways to arrange x distinct items in order.
choose(n, k) — Ways to choose k items from n, order ignored.
sample(x, size, replace = FALSE) — Draw a random sample.
hist(x, breaks) — A frequency histogram of the data.
boxplot(x) — A box-and-whisker summary of the spread.