Interquartile Range Calculator
Calculate the Interquartile Range (IQR)—the statistical spread of the middle 50% of your data. Serves as the primary measure of dispersion in box plots and Tukey’s outlier detection rules.
List of numbers in any order; sorted automatically
Spread of the central 50% (Q3 − Q1)
How to Use This Calculator
- Enter your dataset separated by commas or spaces.
- View the computed IQR at the top.
- Inspect individual quartiles (Q1, Q2/Median, Q3) below.
Formula & Calculation Methodology
The IQR subtracts the 25th percentile (Q1) from the 75th percentile (Q3). John Tukey’s rule identifies values outside 1.5 × IQR beyond quartiles as potential outliers.
Worked Example
Evaluating 7, 8, 12, 14, 15, 18, 19, 20, 22, 24, 26, 30
Evaluating 10, 20, 30, 40, 50
Frequently Asked Questions
Why is IQR preferred over range for skewed data?↓
The full range (Max − Min) is heavily distorted by extreme outliers. The IQR focuses exclusively on the central 50%, remaining completely immune to extreme boundary extremes.
How does IQR detect outliers in box plots?↓
Any point falling below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is flagged as an outlier and plotted as an individual point outside the box plot whiskers.
What is the semi-interquartile range?↓
The semi-interquartile range (or quartile deviation) is half of the IQR: (Q3 − Q1) / 2.
What is a limitation of the IQR?↓
The IQR ignores the specific values within the lower 25% and upper 25%, meaning it cannot convey total sample variance.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.