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 $\mathrm{range}$ only considers the smallest and largest values, ignoring all other data points.
• B. The $\mathrm{range}$ is unaffected by outliers, while the $\mathrm{standard\; deviation}$ is sensitive to them.
• C. The $\mathrm{range}$ is always smaller than the $\mathrm{standard\; deviation}$ for any data set.
• D. The $\mathrm{range}$ requires the data to be $\mathrm{normally\; distributed}$, while the $\mathrm{standard\; deviation}$ does not.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand what the range measures. The range is the difference between the maximum and minimum values in a data set, calculated as \(\text{Range} = \text{Max} - \text{Min}\).
2. Step 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. Step 3: Understand what the standard deviation measures. The standard deviation considers how each data point deviates from the mean, providing a measure of spread that incorporates all data points.
4. Step 4: Compare sensitivity to outliers. The range is highly sensitive to outliers because it depends solely on the extreme values, while the standard deviation also reflects the spread of the entire data set but is influenced by all values, including outliers.
5. Step 5: Conclude why the range is less desirable: because it ignores the distribution of all intermediate data points and only focuses on extremes, it can give a misleading picture of variability compared to the standard deviation, which provides a more comprehensive measure of dispersion.