What makes the range less desirable than the standard deviation as a measure of dispersion?

Verified step by step guidance

1. Understand that both range and standard deviation are measures of dispersion, which describe how spread out the data values are in a dataset.
2. Recall that the range is calculated as the difference between the maximum and minimum values in the dataset: \(\text{Range} = \text{Max} - \text{Min}\).
3. Recognize that the range only considers the two extreme values and ignores all other data points, making it sensitive to outliers or extreme values.
4. Know that the standard deviation takes into account all data points by measuring the average distance of each data point from the mean, providing a more comprehensive measure of spread.
5. Conclude that because the standard deviation incorporates all values and is less affected by outliers, it is generally a more reliable and informative measure of dispersion than the range.

Key Concepts

Range

The range is the difference between the maximum and minimum values in a data set. It provides a simple measure of spread but only considers the two extreme values, ignoring the distribution of all other data points.

Standard Deviation

Standard deviation measures the average distance of each data point from the mean, reflecting the overall variability in the data. It accounts for all values, providing a more comprehensive and reliable measure of dispersion.

Sensitivity to Outliers

The range is highly sensitive to outliers because it depends solely on extreme values, which can distort the perceived spread. In contrast, standard deviation, while also affected by outliers, incorporates all data points, making it a more stable and informative measure.