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Mr.mean notes the time it takes for him (in minutes) to reach his place of work.

Information given in the question: $n = 8$

$∑x = 120 $
$∑x^2 = 1827$

from there, we are asked to find the variance. How can that be solved? It seems like incomplete information.

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    $\begingroup$ What is the formula of variance? Why is information in the question incomplete to you? $\endgroup$
    – StubbornAtom
    Commented Sep 23, 2018 at 13:50
  • $\begingroup$ You can compute the sample variance. There are two common forms. One with 7 and the other with 8 in the denominator. $\endgroup$
    – Michael R. Chernick
    Commented Sep 24, 2018 at 0:19

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You have all you need, even for unbiased estimation: $$S^2=\frac{1}{n-1}\sum_{i=1}^{n}{(x_i-\bar{x})^2}=\frac{1}{n-1}\sum_{i=1}^{n}{(x_i^2-2x_i\bar{x}+\bar{x}^2)}=\frac{\sum_{i=1}^{n}{x_i^2}-2n\bar{x}^2+n\bar{x}^2}{n-1}$$

You have $\sum{x}$, so $\bar{x}=\frac{\sum{x}}{n}$, and you have $\sum{x^2}$. Just substitute.

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