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What is the difference between standard deviation and variance in how we interpret it, not just in their mathematical formulas? I know that standard deviation

What is the difference between standard deviation and variance in how we interpret it, not just in their mathematical formulas?

I know that standard deviation is how much on average numbers differ from the mean, and that variance is the average degree to which each data point differ from the mean. The definitions seem to denote the same thing, so what is the difference?

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