Quartile calculator
Paste a list of numbers to get the quartiles, the interquartile range and any outliers beyond the 1.5 × IQR fences. Quartile methods differ slightly, so the one you choose is named under the results.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Paste or type your numbers.
- Pick the quartile method. The default is the median of the halves, excluding the middle value.
- Read Q1, Q2, Q3, the IQR, the fences and any outliers.
How it works
The data is sorted. Q2 is the median. Depending on the method Q1 and Q3 are the medians of the lower and upper halves, or interpolated positions in the sorted list. The IQR is Q3 − Q1, and the fences are Q1 − 1.5 × IQR and Q3 + 1.5 × IQR.
Worked example
Data: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49 (11 values).
- Median (Q2) is the 6th value, 40.
- Lower half without the median: 6, 7, 15, 36, 39, so Q1 = 15.
- Upper half: 41, 42, 43, 47, 49, so Q3 = 43.
- IQR = 43 − 15 = 28, fences are −27 and 85, so there are no outliers.
With the inclusive method Q1 becomes 25.5 and Q3 becomes 42.5.
Tips
- Always quote the method when you report quartiles.
- Outliers are flagged, not removed; check them before you decide what to do.
- Small samples (under 8 values) are very sensitive to the method.
Frequently asked questions
What are quartiles?
Quartiles split sorted data into four parts with the same number of values. Q1 has a quarter of the values below it, Q2 is the median and Q3 has a quarter above it. The IQR is Q3 minus Q1, the spread of the middle half.
Why do different tools give different quartiles?
There is no single agreed definition. Textbooks usually take the median of each half, either leaving out the middle value or keeping it, and spreadsheets interpolate. Results agree for some data sets and differ slightly for others, so this tool lets you pick the method.
How are outliers found?
With Tukey's rule. A value is an outlier when it is below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. These fences are the ones drawn as whiskers in a box plot.
Which method should I use for homework?
Use the one your course teaches. Many intro statistics books and the TI-83/84 calculators use the median-of-halves method that excludes the middle value, which is the default here. Excel's QUARTILE.INC matches the interpolated option.
Do I need to sort the numbers first?
No. The list is sorted for you, and the order you type does not change the result.