Interquartile Range Calculator
Calculate the first quartile, third quartile and interquartile range from an entered numeric sample.
How to use this calculator
- Enter at least four numeric values separated by semicolons or new lines.
- Check that all inputs use the same units, time period and population scope.
- Change one assumption at a time when comparing scenarios.
Formula used by interquartile range calculator calculator
IQR = Q3 − Q1, using the median-of-halves convention for this calculator.
- IQR = Q3 − Q1, using the median-of-halves convention for this calculator.
- Different software can use different quartile interpolation conventions, especially with odd sample sizes. This tool uses the median of each half, excluding the overall median for odd-sized data.
- The tool validates entered values and formats results for readability; it does not verify assumptions against external records.
Worked examples
Worked example
Values 5, 7, 8, 9, 10, 12, 13, 15.
Lower-half median Q1 = 7.5; upper-half median Q3 = 12.5; IQR = 5.
The middle 50% of the sample spans 5 units under the stated quartile convention.
Understanding the result
Calculate the first quartile, third quartile and interquartile range from an entered numeric sample.
Different software can use different quartile interpolation conventions, especially with odd sample sizes. This tool uses the median of each half, excluding the overall median for odd-sized data.
Important notes
Different software can use different quartile interpolation conventions, especially with odd sample sizes. This tool uses the median of each half, excluding the overall median for odd-sized data.
Treat the result as an estimate based on the entered inputs. For regulated, engineering, employment, tax or business decisions, check applicable official rules, specifications and professional guidance.
Frequently asked questions
How is IQR used?
It describes the spread of the middle half of the sample and is often used in box plots and outlier rules.
Does IQR identify every outlier?
No. An outlier rule usually compares values with Q1 − 1.5×IQR and Q3 + 1.5×IQR; the choice of rule is contextual.
How should I use the result?
Different software can use different quartile interpolation conventions, especially with odd sample sizes. This tool uses the median of each half, excluding the overall median for odd-sized data.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- Percent Difference — Understand percent difference, when it is appropriate, and how it differs from percentage change and percent error.
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.