Measures of Distribution

Range, IQR, and standard deviation each describe how spread out data is, with different sensitivity to outliers.
Range (max − min) is the simplest but most outlier-sensitive; IQR (Q3 − Q1) captures the middle 50% and ignores extremes.
Standard deviation measures typical distance from the mean and underlies the 68-95-99.7 rule.
Only confirmed measurement errors should be automatically excluded as outliers — true anomalies and skew require judgment.

Range = Xmax − Xmin, IQR = Q3 − Q1, σ = √( Σ(xᵢ − μ)² / N )

Outlier rule: flag values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR.
If n is odd, Q1/Q3 positions are (n+1)/4 and 3(n+1)/4; if n is even, average the two nearest values.

Measure	What it captures / outlier sensitivity
Range	Spread of entire dataset (max − min) — very high sensitivity
IQR	Spread of middle 50% of data — low sensitivity, ignores extremes
Standard deviation	Typical distance from the mean — moderate to high sensitivity

True statistical anomaly: A genuine extreme value (e.g., someone over 7 feet tall) — not automatically excluded, requires judgment.
Measurement error: A mistake in recording/reading data (e.g., misreading a tape measure) — should be excluded from analysis.
Non-normal distribution: A skewed distribution with a long tail producing extreme-looking values — not automatically excluded, requires judgment.

Don't assume every outlier should be removed — only a confirmed measurement error is automatically excluded; true anomalies and skew-driven extremes need case-by-case judgment.
IQR describes only the middle 50% of data — it deliberately ignores the extremes that range and standard deviation are sensitive to.

Which spread measure is least affected by a single extreme outlier: range, IQR, or standard deviation?

A recorded height of 720 cm turns out to be a tape-measure misread. Should it be excluded?

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