Interquartile Range Calculator
The Interquartile Range Calculator sorts a numeric data set and calculates its first quartile, third quartile, and interquartile range. The IQR describes the spread of the middle half of the observations and is often used to assess variability and identify potential outliers.
How to use this calculator
- Enter at least four numeric observations separated by commas, spaces, or semicolons.
- The values are sorted from smallest to largest.
- Review Q1, Q3, and the difference between them.
- Keep in mind that quartile conventions may differ between textbooks and software.
Interquartile range formula
IQR = Q3 − Q1, where Q1 is the median of the lower half and Q3 is the median of the upper half.
- This calculator uses the median-of-halves method.
- When the data count is odd, the central observation is excluded from both halves.
- The IQR is resistant to extreme values compared with the full range.
Worked examples
Calculate IQR
For the ordered values 2, 4, 5, 7, 9, 10, 12, 15, Q1 is 4.5 and Q3 is 11.
IQR = 11 − 4.5 = 6.5.
The middle-half spread is 6.5 units.
Understanding the result
The interquartile range covers the middle 50% of a sorted data set.
A larger IQR indicates greater spread in the middle part of the observations.
Different quartile definitions may produce different answers for small data sets.
Important notes
Separate values clearly and enter only numeric observations.
Check the quartile convention required by your course, report, or statistics software.
Frequently asked questions
What does IQR measure?
The IQR measures the distance between the first quartile and third quartile, covering the middle half of the data.
Can IQR be used to identify outliers?
It is often used with the 1.5 × IQR rule as a screening convention, but context and the chosen method still matter.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- Standard Deviation — Understand standard deviation as a measure of spread and the difference between population and sample standard deviation.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.