Direct answer
A percentile locates a value within an ordered reference distribution, quartiles mark the 25th, 50th, and 75th percentiles, and the interquartile range is Q3−Q1 under a named quantile convention.
Visual explanation
Cumulative position and the middle half
What this calculation tells you
Quantiles divide ordered observations by cumulative position. They describe rank and distribution structure rather than a distance from the mean.
Before comparing percentiles, verify that both results use the same population, period, inclusion rules, weighting, and interpolation convention. A percentile is not a universal score detached from its reference.
Where it is used
Education
Explain relative standing within a stated assessment population.
Operations
Track service-time or latency distributions beyond one average.
Research
Report robust location and spread for skewed observations.
Quality
Define entered distribution positions without assuming normality.
Common situations
- Finding the position of one value in an ordered dataset.
- Comparing middle-half spread across groups.
- Reconciling different software quartiles.
- Communicating a service-time percentile with its reference period.
Start with the statistical question
Before comparing percentiles, verify that both results use the same population, period, inclusion rules, weighting, and interpolation convention. A percentile is not a universal score detached from its reference.
An ordered strip of observations is crossed by a movable cumulative-position marker. The middle 50% is shaded between Q1 and Q3, making the IQR a visible width rather than an abstract subtraction.
Worked example
Using linear interpolation at (n−1)p, the 25th percentile of 10, 20, 30, 40 lies at position 0.75 and equals 17.5. Another published convention may return a different quartile from the same four values.
Assumptions that carry the result
Observations must be orderable, and weighted quantiles require a separate explicit weighting convention. Small datasets make interpolation choices especially visible.
Interpret the result without overreaching
A percentile does not reveal absolute performance, causal importance, or uncertainty about a wider population. Report the raw value, reference group, date, and method when the comparison matters.
- Treating the 90th percentile as 90% correct.
- Comparing percentiles from different reference groups.
- Assuming all software calculates quartiles identically.
Practical questions
Frequently asked questions
Is the 75th percentile the same as 75%?
It is a position: roughly 75% of the reference observations are at or below the percentile under the chosen convention.
Why do calculators disagree on quartiles?
Software uses different rank and interpolation definitions, especially for small datasets.
Can I average percentiles?
Not generally. Percentiles are nonlinear positions and usually cannot be combined without underlying data or a justified model.
Further reading
Authoritative sources
Use these primary and professional resources to check definitions, conventions, or requirements that may extend beyond this guide.