# What is the standard deviation of 1, 2, 3, 4, and 5?

May 14, 2017

$\sqrt{2}$ or about $1.414$

#### Explanation:

There are two ways to solve this, the graphing calculator way or the long way:

Graphing calculator way:

Plug the numbers into $L 1$. Then go 1 variable stats and plug in $L 1$. Standard deviation is $\sigma x$

Long way:

Find the mean by adding all the values together and dividing by the number of elements there are:

$\frac{1 + 2 + 3 + 4 + 5}{5} = 3$

Take all the values and subtract the mean from them. Then square all the values:

${\left(1 - 3\right)}^{2} = 4$
${\left(2 - 3\right)}^{2} = 1$
${\left(3 - 3\right)}^{2} = 0$
${\left(4 - 3\right)}^{2} = 1$
${\left(5 - 3\right)}^{2} = 4$

Find the mean of these values:

$\frac{4 + 1 + 0 + 1 + 4}{5} = 2$

Square root this:

$\sqrt{2} \approx 1.414$