Quartile Calculator
Enter your numbers to get the lowest value, Q1, the median, Q3, the highest value, the interquartile range and any outliers. Choose the method to match your exam board or spreadsheet.
Worked examples
School method
1, 2, 3, 4, 5, 6, 7, 8, 9
Q1 2.5, median 5, Q3 7.5, IQR 5
The halves are 1 to 4 and 6 to 9.
Spreadsheet method
1, 2, 3, 4, 5, 6, 7, 8, 9
Q1 3, median 5, Q3 7, IQR 4
Interpolated, as QUARTILE.INC gives.
About Quartile Calculator
Quartiles cut an ordered list into four equal parts. The lower quartile, Q1, has a quarter of the values below it, the median has half, and the upper quartile, Q3, has three quarters. The interquartile range, Q3 minus Q1, is the spread of the middle half of the data, and unlike the range it is not thrown off by one extreme value. With the smallest and largest values, the quartiles make the five number summary used to draw a box plot.
There is no single agreed way to calculate quartiles, which is why different tools can give different answers for the same numbers. The common UK school method takes the median of the lower half and of the upper half, leaving out the middle value when there is an odd number of values. Others keep the middle value in both halves, or interpolate the way spreadsheets do. This page offers four methods so you can match your course or software. It also flags outliers: values more than 1.5 times the interquartile range below Q1 or above Q3.
How to use Quartile Calculator
- Type or paste your numbers, separated by commas, spaces or new lines.
- Choose the method that matches your course or spreadsheet.
- Read Q1, the median, Q3 and the interquartile range.
- Check the fences and any outliers, and the sorted data with its halves.
Common uses
- Drawing box plots in maths and science
- Finding the spread of exam results
- Spotting unusual values in a data set
- Matching the answers from a spreadsheet
Frequently asked questions
Why do different calculators give different quartiles?
Because there are several accepted methods, especially when the number of values is small. The page lets you pick the method so you can match your teacher or software.
What is the interquartile range?
It is Q3 minus Q1, the range of the middle half of the values. A small IQR means the middle of the data is tightly grouped.
How are outliers found?
A value is an outlier if it is more than 1.5 times the IQR below Q1 or above Q3. These limits are called fences.
Which method is used by spreadsheets?
QUARTILE and QUARTILE.INC use the interpolated method on the page, and QUARTILE.EXC uses the second interpolated method.
Should I remove outliers?
Not automatically. They may be mistakes, but they may also be real and important. Check where they came from before deleting anything.