# Can you find the standard deviation of negative numbers?

Nov 1, 2015

Yes.

#### Explanation:

Yes. Why not?!!

Consider the data sets $\left\{- 1 , - 2 , - 3 , - 4 , - 5\right\}$. Note that all are negative numbers.

So, variance of the data set will be $\frac{1}{n} {\sum}_{i = 1}^{n} {x}_{i}^{2} - {\left(\frac{1}{n} {\sum}_{i = 1}^{n} {x}_{i}\right)}^{2}$
$= \frac{1}{5} \left[{\left(- 1\right)}^{2} + {\left(- 2\right)}^{2} + {\left(- 3\right)}^{2} + {\left(- 4\right)}^{2} + {\left(- 5\right)}^{2}\right] - {\left(\frac{1}{5} \cdot \left[- 1 - 2 - 3 - 4 - 5\right]\right)}^{2}$
$= 11 - 9$
$= 6$