Quartile IQR Calculator

Compute quartiles and the IQR of a dataset, with fences that flag outliers.

Quartile IQR Calculator

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Data

Result

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Median

Formula: Tukey hinges: Q1 is the median of the lower half, Q3 of the upper half. IQR = Q3 - Q1; fences at Q1 - 1.5 IQR and Q3 + 1.5 IQR.

Tukey's hinges

Quartiles split sorted data into quarters. The tool uses Tukey's hinge method: Q1 is the median of the lower half, Q3 the median of the upper half, and the median itself is Q2. The interquartile range, Q3 - Q1, covers the middle 50% of values.

Fences catch outliers

Values beyond Q1 - 1.5 x IQR or Q3 + 1.5 x IQR are flagged as outliers. This is the rule behind box-plot whiskers, and unlike the range it resists being stretched by a single wild value.

Quartile IQR Calc FAQs

What are the quartiles of 4, 7, 9, 11, 12, 15, 19, 22, 33?

Q1 = 8, median = 12, Q3 = 20.5, IQR = 12.5. The data is preloaded; with fences at -10.75 and 39.25 there are no outliers.

What is the IQR?

The interquartile range: Q3 minus Q1. It measures the spread of the middle half of the data and ignores outliers.

How are outliers detected?

Any value below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR is flagged. These are Tukey's fences, the box-plot standard.

Why use IQR instead of range?

The range is set by the two most extreme values, so one outlier distorts it. The IQR describes typical spread robustly.

Is my data sent to a server?

No. All sorting and quartile math runs in your browser.