What is the interquartile range (IQR)?

The interquartile range (IQR) is a measure of statistical dispersion and is defined as the difference between the third quartile (Q3) and the first quartile (Q1). It describes the spread of the middle 50% of the data.

How do you detect outliers with IQR?

Using Tukey's rule, values below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR are considered outliers.

Why use IQR instead of range?

The IQR is robust to extreme values, while the range depends only on the smallest and largest observations and can be distorted by outliers.

Interquartile Range (IQR) Calculator

Paste your dataset, and this tool will sort it, calculate Q1, median, Q3, the IQR, and show the usual Tukey outlier fences.

1. Enter your data

You can separate values with commas, spaces, or line breaks. Example: 12, 15, 15, 18, 21, 22, 26

2. Results

Q1 (25%)

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Median (Q2)

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Q3 (75%)

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IQR (Q3 − Q1)

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Count (n)

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Outlier fences (Tukey)

Lower fence: —

Upper fence: —

Any value < lower fence or > upper fence is a potential outlier.

Detected outliers

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3. Sorted data

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What is the IQR?

The interquartile range (IQR) is a robust measure of variability. It tells you how spread out the middle 50% of your values are. Because it ignores the lowest 25% and highest 25% of data, it is much less sensitive to outliers than the full range.

How we computed your quartiles

This tool uses the classic “median-of-halves” method (Tukey style):

Sort the data.
Find the median (Q2).
If n is odd, exclude the median from both halves.
Q1 = median of the lower half, Q3 = median of the upper half.

IQR = Q3 − Q1
Lower fence = Q1 − 1.5 × IQR
Upper fence = Q3 + 1.5 × IQR

Why IQR is useful

It’s used in boxplots.
It’s a good default for outlier detection.
It’s robust and easy to explain.

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

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Formula (extracted text)

IQR = Q3 − Q1 Lower fence = Q1 − 1.5 × IQR Upper fence = Q3 + 1.5 × IQR

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
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