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I have some confusion here. If some random variable is measured in some units, say $kg$ then clearly it's variance is measured in $kg^2$. But if the variable is dimensionless and measured say in $\%$ or base points in what unit the variance is measured? $\%^2$? Does it make sense?. It seems for me a bit weird.

Alexander Vigodner
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I think it is not always useful to think of variance in units, since it can get confusing at some point. You have to remember variance is a measure that tells you how far a set of numbers is spread out, and by numbers it means we can practically use it on anything even if they don´t have dimensions ( a % is still number ). So rather than seeing it as a squared percentage try to visualize it as how far the %´s you get on your experiment are from each other.

Pablo Estrada
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  • I understood your point. However, we do need remember about units using variance in some formulas to avoid senseless results and adjust certain parameters accordingly. – Alexander Vigodner Aug 29 '14 at 19:32