Quartile Calculator: Q1, Median, Q3, IQR, Five-Number Summary and Outliers
Paste your numbers and pick a quartile method. You get Q1, the median, Q3, the IQR, outliers and a box plot, with the positions used.
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Interquartile range (IQR)
28
- Q1 (lower quartile)
- 15
- Q2 (median)
- 40
- Q3 (upper quartile)
- 43
- Outliers (1.5 × IQR)
- —
Method: Tukey hinges, medians of the lower and upper halves (median excluded when n is odd).
Show working
- n = 11, sorted: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49
- Q1 = median of lower 5, Q3 = median of upper 5
- Q1 = 15, Q2 = 40, Q3 = 43
- IQR = Q3 − Q1 = 43 − 15 = 28
- Q1 − 1.5·IQR = −27, Q3 + 1.5·IQR = 85
Five-number summary
| Min | Q1 | Median | Q3 | Max |
|---|---|---|---|---|
| 6 | 15 | 40 | 43 | 49 |
How to use
- Type or paste your data.
- Choose the quartile method (your textbook or software may specify one).
- Read Q1, Q2, Q3, the IQR and any outliers.
Good to know
Methods give slightly different answers for small data sets. Tukey (halves): Q1 and Q3 are the medians of the lower and upper halves, excluding the median when n is odd (used by many school books and TI calculators). (n + 1)p: Q1 at position (n + 1)/4, with interpolation (Excel QUARTILE.EXC, Minitab). Linear: position (n − 1)p + 1 (Excel QUARTILE.INC, Google Sheets).
IQR = Q3 − Q1 is the spread of the middle half of the data. Values below Q1 − 1.5·IQR or above Q3 + 1.5·IQR are flagged as possible outliers; the box plot whiskers stop at the last non-outlier values.
Example: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49 gives Q1 = 15, median = 40, Q3 = 43 (Tukey and (n + 1)p) but Q1 = 25.5, Q3 = 42.5 by the linear method.
Questions
Why do different calculators give different quartiles?
There are several accepted definitions. Pick the method your course or software uses; the median is the same in all of them.
What is the interquartile range?
Q3 − Q1, the range covered by the middle 50% of the values. It is not affected by extreme values.
How are outliers found?
Any value more than 1.5 × IQR below Q1 or above Q3 (Tukey’s fences).
What is the five-number summary?
Minimum, Q1, median, Q3 and maximum, the five numbers a box plot is drawn from.
Is my data stored or sent anywhere?
No. The calculation runs entirely in your browser; nothing you type leaves your device.