Which of the following best explains why the $\mathrm{range}$ is less desirable than the $\mathrm{standard\; deviation}$ as a measure of dispersion?

• A. The $\mathrm{range}$ is always smaller than the $\mathrm{standard\; deviation}$ for any data set.
• B. The $\mathrm{range}$ can only be used for data sets with an even number of observations.
• C. The $\mathrm{range}$ only considers the smallest and largest values, ignoring all other data points.
• D. The $\mathrm{range}$ is unaffected by outliers, while the $\mathrm{standard\; deviation}$ is sensitive to them.

Answer: (C)

Verified step by step guidance

1. Understand what the range measures: it is the difference between the maximum and minimum values in a data set, calculated as \(\text{Range} = \text{Max} - \text{Min}\).
2. Recognize that the range only uses two data points (the smallest and largest), and ignores all other values in the data set, which means it does not reflect the overall variability of the data.
3. Recall that the standard deviation measures the average amount by which each data point deviates from the mean, taking into account all values in the data set, providing a more comprehensive measure of dispersion.
4. Consider the effect of outliers: the range is highly sensitive to extreme values since it depends solely on the minimum and maximum, while the standard deviation also reflects how data points are spread around the mean, making it more informative.
5. Conclude that the range is less desirable because it ignores the distribution of all intermediate data points, whereas the standard deviation incorporates all data points, giving a fuller picture of variability.