Sensitivity of the Range to Outliers

Example of Calculating the Range

Which measure of variability is calculated as the difference between the highest and lowest scores in a distribution?

A researcher is studying the variability in the number of social interactions participants have in a single day. Match each participant's set of scores with its calculated range.

A researcher finds that a sample of social anxiety scores ranges from $30$ to $80$. After discovering a technical glitch that added $5$ points to every participant's score, the researcher subtracts $5$ points from each score to correct the data. The range of the corrected anxiety scores will be smaller than the range of the original, uncorrected scores.

An undergraduate researcher is evaluating how effectively the range describes the variability of different datasets. Rank the following research scenarios from the one where the range is the most misleading (least representative of the typical spread) to the one where the range is the most accurate (most representative of the spread).

Match each term related to the range with its correct definition in the context of psychological data analysis.

A clinical psychologist compares the number of panic attacks experienced by patients in two different treatment groups over a month. If Group A has a range of $4$ and Group B has a range of $12$, how should the researcher interpret the difference between these two groups?

A psychologist records the reaction times of five participants: 250ms, 280ms, 310ms, 350ms, and 420ms. The value 170ms represents the _____ of this dataset.

A developmental psychologist records the ages (in years) of a sample of toddlers: $2$, $3$, $2$, $4$, and $5$. Applying the calculation for the range as the difference between the highest and lowest scores in the distribution, the researcher determines the range of toddler ages to be $3$ years.

A cognitive psychologist studies participant reaction times and obtains the following scores: $200$ ms, $220$ ms, $250$ ms, and $290$ ms. After adding a new participant with a reaction time of $450$ ms to this distribution, the range increases by _____ ms.

A researcher is evaluating the stability of the range as a measure of variability across different participant groups. Rank the following reaction-time distributions (in milliseconds) from the one where the range is the most stable and representative measure of variability to the one where it is the least stable and representative (most heavily distorted by a single outlier).