Range vs Standard Deviation

The range measures spread as the distance between the two most extreme values. You compute it as $\text{range} = \text{maximum} - \text{minimum}$. For example, if test scores run from 62 to 98, the range is $98 - 62 = 36$ points. Because it uses only the two extreme values, the range is highly sensitive to outliers and ignores everything in between.

The standard deviation summarizes spread as the typical gap between a value and the mean. The sample standard deviation is $s = \sqrt{\frac{1}{n-1}\sum (x_i - \bar{x})^2}$, where $x_i$ are the values, $\bar{x}$ (x-bar) is the mean, and $n$ is the number of values. For example, a small $s$ means the data cluster tightly around the mean, while a large $s$ means they spread out widely. It is the square root of the variance, which returns the measure to the original units.