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.

A researcher is examining three small datasets representing student stress levels (measured on a scale of 1 to 100). Match each dataset with the description that best captures the resulting range and its sensitivity to any outliers present.

Rank the following research scenarios from the least misleading use of the range to the most misleading use, based on the sensitivity of the range to outliers.

Suppose you are constructing a demonstration for a psychology lab to show how the range can provide a misleading impression of spread. Your goal is to design a dataset of five participants where the 'typical' spread (the range of the first four participants) is exactly $3$, but the inclusion of a fifth participant (an outlier) inflates the total range to exactly $30$. Which of the following datasets successfully meets these design criteria?

Match each conceptual aspect of the range ($Range = X_{max} - X_{min}$) to the explanation of why it can provide a misleading impression of a distribution's variability when outliers are present.

Although the range is easy to compute, it is often a misleading measure of spread because it is highly sensitive to _____, which can disproportionately inflate the result.

In a cognitive psychology experiment, a researcher records reaction times (in milliseconds) for two conditions. Condition A scores are {200, 205, 210, 215, 220} and Condition B scores are {200, 205, 210, 215, 400}, where the last value is an outlier caused by a distracted participant. The range for Condition B is _____ times larger than the range for Condition A.

A developmental psychologist measures the number of words spoken by two-year-olds in a 10-minute play session. Group A: {12, 15, 14, 16, 13} (Range = $4$ words). Group B: {12, 15, 14, 16, 84} (Range = $72$ words). True or False: Concluding that the enriched environment generally causes children's word counts to be widely spread out across a 72-word span is an analytical error because a single extreme outlier in Group B has inflated the range, giving a misleading impression of the distribution's typical variability.

A research methods class is evaluating how well the range reflects the overall variability of different datasets. Rank the following datasets from the one where the range provides the least misleading (most representative) reflection of the distribution's general variability to the one where it provides the most misleading (least representative) reflection.