Interquartile Range Calculator
Paste or type your data values below (comma, space, semicolon, or line break separated), then click Calculate IQR.
What is the interquartile range (IQR)?
The interquartile range is a measure of spread that tells you how wide the middle 50% of your data is. Instead of using the smallest and largest values (which can be heavily influenced by extreme outliers), IQR focuses on the center of the distribution.
Where:
- Q1 (first quartile) is the 25th percentile.
- Q3 (third quartile) is the 75th percentile.
Why people use IQR
IQR is popular in statistics, analytics, and quality control because it is robust and easy to interpret. If your dataset has unusual highs or lows, the IQR usually remains stable while range and even standard deviation can move a lot.
- Great for skewed data distributions
- Useful for box plots and outlier detection
- Simple to explain to non-technical audiences
How this calculator works
1) Sort the data
All values are arranged in ascending order.
2) Find quartiles
The calculator computes Q1, Q2 (median), and Q3 using your selected quartile method:
- Exclusive median: if the dataset has an odd count, the middle value is excluded from both halves.
- Inclusive median: if the dataset has an odd count, the middle value is included in both halves.
3) Compute IQR and fences
It then calculates:
- IQR = Q3 − Q1
- Lower fence = Q1 − 1.5 × IQR
- Upper fence = Q3 + 1.5 × IQR
Values outside these fences are flagged as potential outliers.
Quick interpretation guide
- Small IQR: the middle 50% of values are tightly clustered.
- Large IQR: the middle 50% are more spread out.
- Outliers present: investigate unusual observations before making decisions.
IQR vs. other spread measures
IQR vs Range
Range uses only min and max, so one extreme value can change it dramatically. IQR ignores extremes and focuses on central spread.
IQR vs Standard Deviation
Standard deviation is powerful and common, especially for normally distributed data. But if data are skewed or contaminated with outliers, IQR often provides a more resistant summary.
Common mistakes to avoid
- Mixing numbers with text (for example, including units like “12kg” in the input).
- Forgetting that quartile definitions can differ across software tools.
- Using too few data points to draw strong conclusions.
- Treating all outliers as errors without investigation.
FAQ
Can I use decimals and negative values?
Yes. The calculator accepts integers, decimals, and negative numbers.
How many values do I need?
You need at least two values to compute quartiles and IQR meaningfully, though larger samples are better for analysis.
Why are my quartiles different from another tool?
Different platforms can use different quartile conventions. Try switching between exclusive and inclusive methods to match your source.