# What is the best approximation of the standard deviation of {10,15,20,25,30} - 5,7.5 or 10?

Sep 23, 2016

Standard deviation can be best approximated by $7.5$.

#### Explanation:

The mean of $\left\{10 , 15 , 20 , 25 , 30\right\}$ is

$\frac{10 + 15 + 20 + 25 + 30}{5} = \frac{100}{5} = 20$.

The deviations from mean are $\left\{- 10 , - 5 , 0 , 5 , 10\right\}$ and

square of deviations are $\left\{100 , 25.0 , 25 , 100\right\}$ and

average deviation is $\frac{100 + 25 + 0 + 25 + 100}{5} = 50$

and standard deviation is $\sqrt{50} = 7.071$

Hence, standard deviation can be best approximated by $7.5$.