Outlier Detection Lab: Tukey's IQR Fences

Dataset

Sample size (n) 80

Outlier injection rate 6%

Tukey Fence

Fence multiplier k 1.5

Live Statistics

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Median

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IQR (Q3−Q1)

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Outliers flagged

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Lower fence

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Upper fence

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How it works

This lab draws n samples from a normal-ish distribution (a handful are deliberately injected far into the tails), sorts them, and computes the three quartiles by linear interpolation between order statistics — the same method spreadsheets and NumPy use by default.

IQR = Q3 − Q1
Lower fence = Q1 − k · IQR
Upper fence = Q3 + k · IQR
Outlier ⇔ value < lower fence  OR  value > upper fence

Sample size / outlier rate — regenerates the underlying dataset. A higher rate seeds more points far in the tails.
Fence multiplier k — the classic Tukey box plot uses k = 1.5 (mild outliers) or k = 3.0 (extreme outliers only); dragging it live re-classifies the same dataset without regenerating it, so you can watch points cross the fence.
The teal box spans [Q1, Q3], the whiskers reach to the most extreme point still inside the fences, and any point beyond a fence turns red and floats outside the whisker.

Real-world relevance: this exact 1.5×IQR rule is the default outlier rule in pandas' .describe()-adjacent tooling, most BI box-plot widgets, and is often the first, cheapest anomaly filter run before a heavier ML-based detector.

Normal point Outlier (beyond fence) IQR box (Q1–Q3)

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