About this calculator
IQR Calculator helps users measuring the spread of the middle half of a dataset and checking outliers. Use it when you need a clear numerical result, the formula behind the result, and enough context to explain the answer in homework, a report, a spreadsheet, or a practical data check. It is designed for educational and analytical use, so it should support your reasoning rather than replace judgement about the data source, sampling method, or assumptions.
IQR Calculator methodology
The calculator sorts the data, estimates Q1 and Q3, subtracts Q1 from Q3, then calculates optional outlier fences using 1.5 x IQR.
- IQR = Q3 - Q1
- lower fence = Q1 - 1.5 x IQR
- upper fence = Q3 + 1.5 x IQR
How to use the IQR Calculator
- Enter the data, counts, or parameters requested by the calculator.
- Remove labels, currency symbols, blank cells, and non-numeric notes before calculating.
- Check whether the problem asks for a sample result, population result, one-tail result, or two-tail result.
- Review the formula and make sure it matches the convention used by your course, worksheet, or report.
- Compare the result with the worked examples if you are learning the method.
- Round only at the final step unless your instructions require a specific precision.
- Keep a copy of the input data if the result needs to be checked later.
Worked examples
Basic IQR
Input: Q1 = 15, Q3 = 27
Calculation: IQR = 27 - 15.
Result: IQR = 12.
Outlier fences
Input: Q1 = 15, Q3 = 27
Calculation: IQR = 12, fences = 15 - 18 and 27 + 18.
Result: Fences are -3 and 45.
What the result helps you decide
IQR helps you understand spread without being as sensitive to extreme values as range or standard deviation.
For school and university work, the result is often only one part of the answer. You may still need to state assumptions, show working, define variables, and interpret the result in words.
Why IQR is robust
IQR focuses on the middle 50% of values, so one very large or very small value does not directly control it.
IQR and box plots
Box plots use IQR to show the box width and to flag possible outliers beyond the fences.
Common mistakes to avoid
- Mistake 1
- Quartile definitions can vary.
- Mistake 2
- IQR ignores the exact size of extreme values.
- Mistake 3
- A flagged outlier is not automatically an error.
Edge cases
- Very small datasets can produce unstable summaries and wide uncertainty.
- Rounded inputs can slightly change final answers, especially in multi-step calculations.
- Different textbooks and software packages may use different percentile or quartile conventions.
- A statistically valid calculation can still be misleading if the data is biased or measured poorly.
Limitations
This calculator is for general educational information only. It does not prove that a statistical model is appropriate, that a sample is representative, or that a result is practically important.
- Check the formula convention required by your teacher, exam board, software package, or research method.
- For professional research, engineering, clinical, legal, or financial decisions, verify results with a qualified person.
- Use the calculator as a transparent estimate and keep the original data available for audit.
Frequently asked questions
What is IQR?
It is the interquartile range: Q3 minus Q1.
Why use IQR instead of range?
IQR is less affected by extreme values.
What are Q1 and Q3?
Q1 is the 25th percentile and Q3 is the 75th percentile.
How are outlier fences calculated?
They are Q1 - 1.5 x IQR and Q3 + 1.5 x IQR.
Can IQR be zero?
Yes, if the middle half of values are the same or very tightly clustered.
Related calculators
- Box Plot Calculator
- Percentile Calculator
- Mean, Median, Mode and Range Calculator