# How do you find the standard deviation of 5.6, 5.2, 4.6, 4.9, 5.7, 6.4?

May 22, 2017

$.5859$

#### Explanation:

First, find the mean:

$\frac{5.6 + 5.2 + 4.6 + 4.9 + 5.7 + 6.4}{6} = 5.4$

Now find the sum of the differences between the mean and all the points. Square those results:

${\left(5.6 - 5.4\right)}^{2} = .04$
${\left(5.2 - 5.4\right)}^{2} = .04$
${\left(4.6 - 5.4\right)}^{2} = .64$
${\left(4.9 - 5.4\right)}^{2} = .25$
${\left(5.7 - 5.4\right)}^{2} = .09$
${\left(6.4 - 5.4\right)}^{2} = 1$

Find the average of the differences:

$\frac{.04 + .04 + .64 + .25 + .09 + 1}{6} = .343$

Now square root the result:

$\sqrt{2.06} = .5859$

May 22, 2017

Using graphing calculator

#### Explanation:

You can do this problem very easily using a graphing calculator.

First, put the data set in a list. Go to stat, then edit, and then put in your numbers in one column.

Then, go to stat, then calc, then 1 var stats. Plug in your list and press calculate. Your result is $\sigma x$