# What is the standard deviation of {2, 5, 9, 1, 1, 1, 3, 2, 7}?

$\sigma = \sqrt{\frac{1}{9} \cdot \left(\frac{614}{9}\right)} = 2.753224821$

#### Explanation:

The formula for standard deviation $\sigma$ is

$\sigma = \sqrt{\frac{1}{n} \cdot {\sum}_{i = 1}^{n} {\left({x}_{i} - \mu\right)}^{2}} \text{ }$ where $\mu =$mean
$\text{ }$ $n =$number of items

Solve for the mean first

$\mu = \frac{2 + 5 + 9 + 1 + 1 + 1 + 3 + 2 + 7}{9} = \frac{31}{9} = 3.44444$

Compute the standard deviation $\sigma$

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

sigma=sqrt(1/9*((2-31/9)^2+(5-31/9)^2+(9-31/9)^2+(1-31/9)^2+(1-31/9)^2+(1-31/9)^2+(3-31/9)^2+(2-31/9)^2+(7-31/9)^2)

$\sigma = \sqrt{\frac{1}{9} \cdot \left(\frac{614}{9}\right)} = 2.753224821$

God bless....I hope the explanation is useful.