How does standard deviation differ from variance?

In probability theory and statistics, both variance and standard deviation are measures of the dispersion or spread of a set of values or a random variable about its mean ($\mu$).12

The primary differences between them are:

• Mathematical Relationship: The standard deviation ($\sigma$) is defined as the positive square root of the variance (${\sigma }^2$). Conversely, variance is the square of the standard deviation.123
• Units of Measurement: Variance is expressed in squared units of the original data, which can make it difficult to interpret directly. Because the standard deviation is the square root of the variance, it is expressed in the same units as the original random variable.2

Due to this consistency in units, the standard deviation is often the preferred measure for describing the variability of a data set or probability distribution.2