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Why is standard deviation often easier to interpret than variance?

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sample space for a pair of dice — probability theory Sample space for a pair of dice.

In probability theory, standard deviation is often considered easier to interpret than variance because of the units in which they are measured.12

While variance is defined as the weighted average of the squared deviations from the mean, this calculation results in units that are the square of the original data's units. For example, if a random variable represents a measurement in meters, the variance would be expressed in square meters, which can be difficult to relate back to the original scale of the data.12

In contrast, the standard deviation is the positive square root of the variance. By taking the square root, the standard deviation returns the measure of dispersion to the same units as the original random variable. This allows for a more direct and intuitive interpretation of how the data is spread around the mean.12