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I was studying for a test when I found the following formula for sample variance in my textbook:

$s^2\text{ can also be expressed in this way:}$ $$s^2 = \frac{1}{n-1}(\sum_{i=1}^n x_i^2 - n\overline{x})$$

I tried searching for this formula on the Internet, but I couldn't seem to find anything. I'm don't understand how that formula was derived from $s^2 = \frac{1}{n-1}\sum_{i=1}^n(x_i - \overline{x})^2$ either. Is the above formula correct at all?

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  • $\begingroup$ No. $s^2=\frac{1}{n-1}\sum (x_i-\bar x)^2=\frac{1}{n-1}(\sum x_i^2-n\bar x^2)$. $\endgroup$
    – StubbornAtom
    Jan 6, 2019 at 12:23
  • $\begingroup$ I see. How is the latter formula is derived? I'm still having some trouble understanding it. $\endgroup$
    – James
    Jan 6, 2019 at 12:42
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    $\begingroup$ Just expand the square. Nothing more. $\endgroup$
    – StubbornAtom
    Jan 6, 2019 at 12:49

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