Question

What is the standard deviation for {1,3,4,6,8}?

Answer 1

`s=\sqrt{5.84}\approx 2.42`

Explanation:

First, we evaluate the mean:
`\bar{x}=\frac{x_1+x_2+\ldots+x_N}{N}=\frac{1+3+4+6+8}{5}=4.4`
Now, it's often easier to find the value of the variance, then the standard deviation is it's square root:
`s^2=\frac{(x_1-\bar{x})^2+(x_2-\bar{x})^2+\ldots+(x_N-\bar{x})^2}{N}=`
`=\frac{(1-4.4)^2+(3-4.4)^2+(4-4.4)^2+(6-4.4)^2+(8-4.4)^2}{5}=5.84`
`s=\sqrt{s^2}=\sqrt{5.84}\approx 2.42`

Note:
There'a also a simpler formula for the variance:
`s^2=\frac{x_1^2+x_2^2+\ldots+x_N^2}{N}-\bar{x}^2=\frac{1^2+3^2+4^2+6^2+8^2}{5}-4.4^2=5.84`