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Problem statment: What is the different between standard deviation and variance? What context should it be used for both of them?

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  • $\begingroup$ What's the difference between the side of a square and its area? $\endgroup$ – Glen_b Feb 23 '15 at 1:38
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standard deviation = square root of variance, hence standard deviation is usually written as $\sigma$ and variance as $\sigma^2$.

Here's a basic explanation comparing the two and how they can be used in basic situations.

In more complicated statistics, variance is used in a lot of ways, such as amount of variance explained (like to calculate $R^2$ or the Intra-Class Correlation coefficient (ICC), which is the amount of variance explained by each level in a multi-level experiment or model.

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