Quartile Calculator
This quartile calculator sorts your numbers and returns the lower quartile Q1, the median, the upper quartile Q3 and the interquartile range IQR. For 12 15 11 18 14 16 13 17 40, Q1 is 12.5 and Q3 is 17.5.
Source: Wikipedia – Quantil (Stochastik), calculation methods for quartiles. Updated: .
How it is calculated
Quartiles split a sorted list of numbers into four equal parts: the lower quartile Q1 cuts off the bottom quarter, the median Q2 sits in the middle, and the upper quartile Q3 cuts off the top quarter.
Four methods, four possible answers
There is no single definition of quartiles. The calculator offers the four common ones. The textbook median method removes the middle value from both halves when the count is odd, while Tukey's hinges keep it in both. Excel and R interpolate instead: QUARTILE.INC uses position (n − 1) × p + 1 and QUARTILE.EXC uses position (n + 1) × p. For small samples the results differ; for large ones they hardly do.
Interquartile range and outliers
The interquartile range IQR = Q3 − Q1 measures the spread of the middle half of the data. It gives the fences Q1 − 1.5 × IQR and Q3 + 1.5 × IQR used by Tukey's box plot: values outside them count as outliers, and the whiskers end at the smallest and largest value inside the fences.
- Separate numbers with spaces, commas, semicolons or line breaks.
- The exclusive method needs at least three values, the others at least two.
- Check which method your textbook or software uses before comparing results.
Frequently asked questions
How do you find quartiles for an even number of values?
Split the sorted list into two equal halves. Q1 is the median of the lower half and Q3 the median of the upper half. For 1 2 3 4 5 6 7 8, Q1 = 2.5 and Q3 = 6.5.
Why does Excel give different quartiles than my textbook?
QUARTILE.INC and QUARTILE.EXC interpolate between values, while the textbook method takes medians of the halves. Pick the matching method above and the numbers agree.
What counts as an outlier in a box plot?
A value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. In 12 15 11 18 14 16 13 17 40 the upper fence is 25, so 40 is an outlier.
Sources and legal basis
- Wikipedia – Quantil (Stochastik), calculation methods for quartiles
- Wikipedia – Quartile (Verfahren, Methods for computing quartiles)
- Hyndman & Fan (1996): Sample Quantiles in Statistical Packages, The American Statistician 50
- NIST/SEMATECH e-Handbook of Statistical Methods – Box Plot
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