# What are the mean and standard deviation of {2,3,3,5,1,5,4,4,2,6}?

Feb 17, 2016

Mean is $3.5$ and Standard Deviation is $1.83$

#### Explanation:

Sum of the terms is $35$, hence mean of $\left\{2 , 3 , 3 , 5 , 1 , 5 , 4 , 4 , 2 , 6\right\}$ is $\frac{35}{10} = 3.5$ as it simple average of the terms.

For Standard Deviation, one has to find average of squares the deviations of the terms from mean and then taking their square root.

The deviations are $\left\{- 3.5 , - 0.5 , - 0.5 , 1.5 , - 2.5 , 1.5 , 0.5 , 0.5 , - 1.5 , 2.5\right\}$
and sum of their squares is

$\frac{12.25 + 0.25 + 0.25 + 2.25 + 6.25 + 2.25 + 0.25 + 0.25 + 2.25 + 6.25}{10}$ or $\frac{33.50}{10}$ i.e. $3.35$.

Hence Standard Deviation is $\sqrt{3.35}$ i.e. $1.83$