Why is the range not considered a stable measurement of variability?

The range is not considered a stable measurement of variability primarily because it can change greatly with a single score change. The range is defined as the difference between the highest and lowest values in a data set. Therefore, if either the maximum or minimum value changes, the range can fluctuate significantly. This sensitivity to extreme values means that the range does not provide a reliable measure of variability across different data sets.

For instance, in a small sample size where one score is particularly high or low, if that score is adjusted, it may dramatically alter the range, making it an unstable measure. In practical applications, relying solely on range could lead to misleading conclusions about the dispersion of values in a data set, especially in cases where outliers are present. Such characteristics highlight why the range is less preferred compared to other measures of variability, like the standard deviation or interquartile range, which consider the distribution of all data points more comprehensively.