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Although the range is easy to compute, it can provide a misleading impression of a distribution's variability when outliers are present. Because the range relies solely on the absolute highest and lowest values, a single extreme score will drastically inflate the range, giving the false appearance that the entire dataset is widely spread out.

Sensitivity of the Range to Outliers

To understand how outliers distort the range, consider an exam where most students score between $$90$$ and $$100$$, resulting in a narrow range of $$10$$. If a single student scores a $$20$$, the range suddenly jumps to $$80$$. This inflated value gives the false impression that the entire class's scores are highly variable, when in reality, only one student deviated significantly from the rest.

Example of the Range's Sensitivity to Outliers

What is the primary reason the range can provide a misleading impression of a distribution's variability when outliers are present?

A researcher collects reaction-time scores (in milliseconds) from 10 participants: 220, 230, 225, 240, 235, 228, 232, 226, 238, and 812. The last participant's unusually high score was caused by a distraction during testing. If the researcher computes the range for this dataset, the resulting value will accurately reflect how spread out the typical participants' scores are.

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