# What is the standard deviation of {1, 2, 3, 4, 5}?

Nov 1, 2015

The answer is $6$.

#### Explanation:

Note that the formula of variance for calculation purpose is

$\frac{1}{n} {\sum}_{i = 1}^{n} {x}_{i}^{2} - {\left(\frac{1}{n} {\sum}_{i = 1}^{n} {x}_{i}\right)}^{2}$

where $n$ is the total number of values in the given data set.
In your given data we have $n = 5$ and the values of ${x}_{i}$'s are $\left\{1 , 2 , 3 , 4 , 5\right\}$ .

So, your variance $= \frac{1}{5} \left[{1}^{2} + {2}^{2} + {3}^{2} + {4}^{2} + {5}^{2}\right] - {\left(\frac{1}{5} \cdot \left[1 + 2 + 3 + 4 + 5\right]\right)}^{2}$
$= 11 - 9$
$= 6$