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mathematical formula to calculate standard deviation is $SD = (\frac{SSD}{n-1})^{0.5}$

Would like to find SSD and how to write in r ?

SSD = ????

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  • $\begingroup$ Just rearrange: ssd <- (sd^2)*(n-1). $\endgroup$
    – ralph
    Commented Jun 5, 2021 at 10:55
  • $\begingroup$ @ralph thanks ralph! but can you show the working to convert that to sd^2? $\endgroup$
    – Learner
    Commented Jun 5, 2021 at 11:06
  • $\begingroup$ Square both sides (to remove the square root), then multiply both sides by $(n - 1)$. $\endgroup$
    – ralph
    Commented Jun 5, 2021 at 11:09

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I'll use $\sigma$ for SD to avoid confusion with SSD:

If $\sigma = (\frac{SSD}{n-1})^{0.5}$, then

$\sigma^2 = \frac{SSD}{n-1}$. Therefore:

$SSD = \sigma^2 (n-1)$

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    $\begingroup$ So sd(x)^2 * (length(x) - 1) in R (or var(x) * (length(x) - 1)) $\endgroup$
    – Dave
    Commented Jun 5, 2021 at 12:05

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