system
Given the following post, respond as if you're commenting on Reddit:
human
When and why is variance sometimes used instead of standard deviation?

Standard deviation (sigma) is the average distance from the mean, so if you are describing the spread of a distribution, doesn't reporting it as sigma squared (i.e., variance) exaggerate that spread? I understand that variance is computed the way it is because E[(X-mu)] = 0, so we need to square the difference (and people like avoiding the absolute value function). But when does it actually make sense to report or use sigma^2 over sigma?
gpt
Both variance and standard deviation are measures of spread.

The reason that standard deviation is useful is that its units are the same as the units of the original data set, so it's meaningful to interpret it in the context of the original data (that is why we talk about "X standard deviations from the mean").

The reason that variance is useful is that it's more convenient to work with when you're dealing with the underlying math, rather than dealing with actual data. 

If you are doing data analysis, it (almost) never makes sense to report variance. If you are doing theoretical work, it almost never makes sense to use standard deviation.