# What is the standard deviation of {4, 5, 8, 3, 6, 2, 1, 5, 9, 5, 4, 2}?

##### 1 Answer
Feb 21, 2016

Standard Deviation is 2.2913

#### Explanation:

Set of numbers are $\left\{4 , 5 , 8 , 3 , 6 , 2 , 1 , 5 , 9 , 5 , 4 , 2\right\}$. As there are 12 terms whose sum is 54, mean is $\frac{54}{12}$ or $4.5$.

Hence deviations from mean are $\left\{- 0.5 , 0.5 , 3.5 , - 1.5 , 1.5 , - 2.5 , - 3.5 , 0.5 , 4.5 , 0.5 , - 0.5 , - 2.5\right\}$ and sum of there squares is

$0.25 + 0.25 + 12.25 + 2.25 + 2.25 + 6.25 + 12.25 + 0.25 + 20.25 + 0.25 + 0.25 + 6.25 = 63$

Hence Standard Deviation is $\sqrt{\frac{63}{12}} = \sqrt{\frac{21}{4}} = \frac{1}{2} \sqrt{21} = \frac{4.5826}{2}$ i.e. $2.2913$