Could someobdy explain me briefly why standard deviation is so widely used in statistics? I just wonder, what is standard deviation needed for when we have variance? Wouldn't it give the same result if we just interpreted the variance instead of standard deviation? So basically, what makes standard deviation better than variance? Thanks!
2026-04-02 01:39:59.1775093999
Standard deviation versus variance
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This is a good question.
For me, the reason to prefer standard deviation is because it shares the same dimensions as the quantity of interest.
For example, if a random variable $X$ is measured in meters (m), then the variance will be measured in $m^2$, while the standard deviation will also be measured in meters.
Since most often I can approximate the distribution of $X$ by a normal distribution, this means I can say things like 'X is likely to be within $\pm2$ standard deviations of the mean.'
For the variance this does not make sense, since I cannot just add together meters and meters squared.