Finding the standard deviation of a set of angles. My question is given a set of angles in the form of degrees minutes and seconds once finding the mean how do you find the standard deviation.

I know how to find the average or mean of a set (see below) but i'm not sure how to find the standard deviation.

For example say we have the following set of angles:

$$39^\circ 15'01''$$
$$39^\circ 14'15''$$
$$39^\circ 14'32''$$

The average is $39^\circ 14'36''$.  Now, how do I find the standard deviation.

I looked at the wiki page, but can't make since of it using degrees minutes seconds instead..
Your first number is $39 + \dfrac{15}{60} + \dfrac{1}{60^2} = 39.250277777\ldots$.  Deal similarly with the others.

And remember to do as little rounding as possible at least until the last step.  Rounding should always wait until the last step except when you know how much effect it will have on the bottom line.  One way to do avoid it is to work with exact fractions.  (Except that the seconds are of course probably rounded&nbsp;.&nbsp;.&nbsp;.&nbsp;.
This is a link to the Standard Deviation formula of a sample, applying it to your example:

√(((15′01″ - 14′36″)^2+(14′15″ - 14′36″)^2+(14′32″ - 14′36″)^2)/3-1)

= 23.26″