# The sum of all X's is 3780. The sum of all X^2 is 80000. The sample N = 180. How can I calculate the variance?

Jan 20, 2017

The variance is $= 442$

#### Explanation:

$\sum x = 3780$

$\sum {x}^{2} = 80000$

$n = 180$

$\overline{x} = \frac{\sum x}{n} = \frac{3780}{180} = 21$

$V \left(x\right) = \frac{\sum {x}^{2} - {\overline{x}}^{2}}{180}$

$= \frac{80000 - {21}^{2}}{180} = \frac{79559}{180} = 442$