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I've heard from different sources that, standard deviation measures how spread out the numbers are. But I've also heard the same for variance.

Is it technically correct to say this statement for both std and var?

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  • $\begingroup$ how spread out the numbers are ? This wording is incorrect for a site which impleads statistics as a major component. The term variance has an origin in mathematics. $\endgroup$
    – Subhash C. Davar
    Commented Mar 16, 2020 at 14:06

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Yes it is. Standard deviation is a square root of variance. Square root is a monotonic transformation, meaning that it preserves the order, e.g, if a > b then sqrt(a) > sqrt(b), assuming a and b are non-negative and they always are for variance.

Standard deviation is easier to interpret and is more commonly used, when we calculate variance we square every term, taking a square root in standard deviation, we undo that.

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  • $\begingroup$ I think that variance tells the area that supports +/-. It does not express "spread out" or dispersion. $\endgroup$
    – Subhash C. Davar
    Commented Sep 18, 2023 at 15:12

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