system
Given the following post, respond as if you're commenting on Reddit:
human
What actually is standard deviation and variance?

I know they're measures of spread but i don't get what it's actually showing, google and my teacher is no use. Also what's the difference, to me variance is just standard deviation squared making it seem sort of redundant?
gpt
The variance is the average squared distance from the mean, and is in some sense the more "primary" of the two, and so if either one of them is redundant it would be the standard deviation. That said, the variance is difficult to interpret (being in squared units), and so it's common to take its square root to put it back onto the original scale of the variable. The SD is -- not exactly, but this is a reasonably good intuitive approximation -- the average distance from the mean. Despite being easier to interpret, variances are much easier to work with mathematically, and so which one you use will generally depend on your purpose.