Quartile Calculator
The median, the quartiles, the interquartile range and the values Tukey's rule flags as outliers.
Results
What this tool does
An average tells you where a set of numbers sits; the quartiles tell you how it is spread. Cut the ordered list into four and you get the five-number summary that a box plot draws: the smallest value, the quartile a quarter of the way up, the median, the quartile three quarters up, and the largest. The gap between the two quartiles is where the middle half of your data lives, and anything more than one and a half of those gaps outside them is flagged here as worth a second look.
Formula
quartiles by linear interpolation between positions (the Excel and R type 7 method) · the Tukey fences sit at one and a half times the interquartile range
Variables
| Symbol | Meaning | Unit |
|---|---|---|
numbers | Your numbers, one per line or separated by commas | — |
OUT | The five-number summary | — |
MD | Median | — |
Q1 | First quartile (Q1) | — |
Q3 | Third quartile (Q3) | — |
IQ | Middle half spans (IQR) | — |
MO | Mode | — |
MC | Times the mode appears | — |
LF | Anything below this is an outlier | — |
UF | Anything above this is an outlier | — |
OC | Outliers found | — |
OL | Which ones | — |
MN | Mean (average) | — |
CT | Count | — |
Worked example
- Your numbers, one per line or separated by commas12, 15, 11, 19, 22, 14, 17, 13, 25, 16, 18, 20, 48
- The five-number summarymin 11 Q1 14 median 17 Q3 20 max 48
- Median17.000
- First quartile (Q1)14.000
- Third quartile (Q3)20.000
- Middle half spans (IQR)6.000
- Mode11.000
- Times the mode appears1
- Anything below this is an outlier5.000
- Anything above this is an outlier29.000
- Outliers found1
- Which ones48
- Mean (average)19.2308
- Count13
Limitations
- The calculation runs entirely in your browser. The values you type are never sent to a server.
Frequently asked questions
Why does my spreadsheet give a different Q1?
Because there are at least nine published ways to work out a quartile and they disagree on small lists. This page uses linear interpolation between the ordered positions, which is what Excel's QUARTILE, Google Sheets and R's default type 7 all do — so it will match those. Minitab, SPSS and R type 6 use a different rule and will differ by a fraction on short lists. On anything with more than about fifty values the methods converge.
Should I delete the outliers it finds?
Almost never without knowing why they are there. Tukey's rule — one and a half interquartile ranges past the quartiles — is a flag, not a verdict: in a perfectly normal sample it marks roughly seven values in a thousand as outliers, so a long list will always have some. A point is worth removing when you can explain it, such as a typo or a broken instrument. Removing it because it is inconvenient is how a dataset stops being evidence.