Interquartile Range Calculator
Enter a data set to instantly calculate the first quartile (Q1), third quartile (Q3), and interquartile range (IQR) — a measure of statistical spread based on the middle 50% of the data.
Interquartile range
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Enter a data set to calculate.
How the Interquartile Range formula works
The interquartile range formula:
Q1 = median of the lower half of the sorted data Q3 = median of the upper half of the sorted data IQR = Q3 − Q1
Step-by-step calculation
- Sort the data set from smallest to largest.
- Find Q1, the median of the lower half of the data.
- Find Q3, the median of the upper half of the data.
- Subtract Q1 from Q3 to get the IQR.
Worked example
Data set: 4, 8, 15, 16, 23, 42. Lower half: 4, 8, 15 (Q1 = 8). Upper half: 16, 23, 42 (Q3 = 23). IQR = 23 − 8 = 15.
Frequently asked questions
Why use IQR instead of range?
IQR focuses on the middle 50% of the data, making it far less sensitive to extreme outliers than the full range (max − min), which can be heavily skewed by a single unusual value.
How is IQR used to detect outliers?
A common rule flags any value more than 1.5×IQR below Q1 or above Q3 as a statistical outlier — the Outlier Calculator applies this method directly if you need outlier detection rather than just the IQR itself.