# How to calculate Variance?

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.

• What is the formula of variance? Why is information in the question incomplete to you? – StubbornAtom Sep 23 '18 at 13:50
• You can compute the sample variance. There are two common forms. One with 7 and the other with 8 in the denominator. – Michael Chernick Sep 24 '18 at 0:19

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.