Quartile and percentile calculator
Quartiles, interquartile range, whisker bounds and outliers from a list of numbers.
Fill in the fields and the result will appear here automatically.
Quartiles locate the 25th, 50th and 75th percentiles of an ordered data set. The interquartile range IQR = Q3−Q1 describes its central portion and complements standard deviation rather than being universally better. With ties, more than half the observations may lie between Q1 and Q3. Several definitions exist; this page uses type 7 linear interpolation at position (n−1)·p. It also reports the theoretical fences Q1−1.5·IQR and Q3+1.5·IQR for flagging unusual values.
How it works
Formula and logic
Percentile position (n−1)·p with linear interpolation between neighbours, as in PERCENTILE.INC; whiskers at Q1 − 1.5·IQR and Q3 + 1.5·IQR. The result label “whisker bounds” refers to these calculated fences. Actual box-plot whiskers normally end at the most extreme observations inside them and may therefore differ. A value strictly beyond a fence is flagged for review, not proved erroneous. This tool accepts 4–10000 finite numbers and at most 1000000 characters. Four is its product minimum; quartiles can be mathematically defined for smaller sets.
Example
For the sample 2 4 4 5 7 9 11 12 the first quartile is 4, the median 6 and the third quartile 9.5.
Fields and units
- Numbers separated by spaces or new lines — data unit
How to use
- — Separate numbers with spaces, new lines or semicolons; a comma before a space also counts as a separator.
- — Write decimals with a comma: 2,5 is two and a half, not two values.
- — This form accepts at least four values. This is a calculator input limit: the chosen interpolation rule can also define quartiles for three numbers.
- — A value beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR counts as an outlier — the usual box-plot convention.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- R: type 7 quantile interpolation and alternative definitions R: whisker ends are observations within fences; hinges can differ from type 7
- Limitation
- Several definitions exist; this page uses type 7 linear interpolation at position (n−1)·p. A value strictly beyond a fence is flagged for review, not proved erroneous.
FAQ
Why do different tools give different quartiles?
Because several definitions exist: some exclude the median when splitting the sample, others include it, others interpolate differently. This page uses linear interpolation by position (n−1)·p — the same as PERCENTILE.INC and NumPy by default.
Why is the interquartile range better than the plain range?
It depends less on extreme observations because it uses the central quartiles. It is not the best measure for every task: the range describes extremes, while standard deviation describes squared deviations. How one changed value affects quartiles depends on the data size and ordering.
Why one and a half ranges for an outlier?
This is a rule for flagging unusual values, not a universal error test. For a theoretical normal population, its own quartiles place less than 1% probability beyond these fences. Fences estimated from a small data set need not flag the same proportion of observations.
What if every number is the same?
Then the quartiles coincide, the interquartile range is zero and the whiskers collapse to a point. There are no outliers: no value falls outside the bounds.