Percentile

A percentile is the value below which a given percentage of observations falls. The 90th percentile is exceeded by only 10% of the data; the median is the 50th percentile; the interquartile range runs from the 25th to the 75th percentile.

ByHoang TruongUpdated July 2, 2026

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A test score at the 85th percentile means 85% of students scored lower and only 15% scored higher. The median is the 50th percentile, the lower quartile the 25th, and the upper quartile the 75th. Because percentiles rank position rather than distance from the mean, they stay meaningful even when a distribution is skewed or holds outliers.

Where it fits

TopicDescriptive StatisticsCoreSubjectData Analysis & StatisticsCore

The formula

LaTeX

\text{Location of } p\text{-th percentile} = \frac{p}{100} \times (n + 1)

Variables

$p$: Desired percentile (e.g. 25 for the lower quartile, 90 for the 90th percentile)
$n$: Number of observations in the ordered dataset

The result is a rank position in the ordered data. Non-integer results are resolved by linear interpolation between the two adjacent values.

Check yourself

PracticeCORE

A firm's invoice payment times have a median of 32 days. A report also states that the 90th percentile is 58 days. Which statement correctly interprets both figures together?

Select an answer to check your understanding.