Interquartile Range (IQR) Calculator
Calculate the interquartile range of up to 8 numbers and check for outliers using the standard 1.5×IQR fence rule.
Only the first this-many values below are included.
Your results
No values fall outside the 1.5×IQR outlier fences.
Calculation breakdown
- IQR
- IQR = Q3 − Q1
- Outlier fences
- lower = Q1 − 1.5×IQR, upper = Q3 + 1.5×IQR
Worked example
For the values 41, 47, 52, 55, 58, 63, 66 and 70, Q1 is about 51 and Q3 about 64.75, giving an IQR of roughly 13.75, a measure of the spread of the middle 50% of the data.
Assumptions
- The IQR describes the spread of the middle 50% of the data and is less affected by outliers than the range.
- The 1.5×IQR outlier rule is a common convention, not a strict statistical law.
How this calculator works
Enter up to 8 numeric values to find Q1, Q3 and the interquartile range (Q3 minus Q1), a robust measure of spread. The calculator also flags any values that fall outside the standard 1.5×IQR outlier fences.
How the interquartile range is calculated
First sort the data from smallest to largest. The lower quartile (Q1) marks the 25th percentile and the upper quartile (Q3) marks the 75th percentile. The interquartile range is Q3 minus Q1, so it describes the spread of the middle half of the observations.
For the ordered data 2, 4, 6, 8, 10, 12, 14 and 16, Q1 is 5 and Q3 is 13 using the median-of-halves method. The IQR is therefore 13 − 5 = 8.
- IQR = Q3 − Q1
- Sort the values before finding quartiles
- A larger IQR means the middle 50% is more spread out
Quartile methods and possible outliers
Statistical packages can use different interpolation rules, especially for short data sets, so a textbook or software result may vary slightly. Use the same quartile convention when comparing two sets of results.
A common screening rule flags values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR as possible outliers. A flagged value is not automatically an error; it is a prompt to investigate the observation and the context.
Frequently asked questions
Why use IQR instead of the full range?
IQR only measures the middle 50% of the data, so it is far less affected by a single very high or low outlier than the full range.
What is the 1.5×IQR rule?
It's a common convention that flags any value more than 1.5 times the IQR below Q1 or above Q3 as a potential outlier.
Is the 1.5×IQR rule always correct?
No, it's a useful default but not a strict law — some genuinely valid data points will fall outside the fences, especially in skewed datasets.
Editorial review and responsibility
Reviewed by the CalcAussie editorial team on 21 September 2026. Review scope: Method, Australian terminology, material assumptions, source links and user-facing limitations.
Calculator results remain estimates based on the figures entered. Check material decisions against current official information and report a suspected error so it can be reproduced and corrected.