Interquartile Range (IQR) Calculator

Your Data

Separate values with commas, spaces, or new lines. Needs at least 3 values.

About This Tool

What Is the Interquartile Range?

The interquartile range (IQR) measures the spread of the middle 50% of your data. It's the distance between the first quartile (Q1, the 25th percentile) and the third quartile (Q3, the 75th percentile) — and unlike the standard deviation, it isn't thrown off by extreme outliers.

When to Use It

Measuring spread when your data has outliers or is skewed
Detecting outliers using the standard 1.5×IQR fence rule
Building the five-number summary behind every box plot

The Formula

\( IQR = Q_3 - Q_1 \) Outlier fences: \( [Q_1 - 1.5 \times IQR,\ Q_3 + 1.5 \times IQR] \)

Worked Example

10 values: 22, 25, 28, 30, 31, 33, 35, 36, 38, 90.

Q1 = 27.25, Q3 = 36.5, IQR = 9.25
Fences: 13.375 to 50.375
90 falls outside the upper fence, so it's flagged as an outlier — likely worth a second look before you trust it in further analysis.

Your Results

Interquartile Range (IQR)

Min

Median

Max

What This Means

Fences & Outliers

Q1 / Q3 Median Outlier

Perfect for students, researchers, and professionals looking to build real statistical skills.

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