# How to calculate standard deviation?

1. 84
Fritz Isaacsposted 9 years ago

How to calculate standard deviation?

How do you calculate the standard deviation of a sample or set of numbers?

2. 0
calculus-geometryposted 9 years ago

The mathematical explanation:
http://mathworld.wolfram.com/StandardDeviation.html

A more practical explanation using an example:
First take the average of your set. If you have {1, 1, 3, 6, 9} the average is 4.  Next, subtract the average from each data point in your set.  Using the same example set you get {-3, -3, -1, 2, 5}.  Now square each of these values. This gives you {9, 9, 1, 4, 25}.

Now take the average of those numbers. In this example, (9+9+1+4+25)/5 = 9.6.  And finally, take the square root of this number ... sqrt(9.6) = 3.098.  This is the standard deviation of your set.

If your set happens to be a sample taken from a larger population, the procedure is a little different.  The second time you take the average you would divide by 4 instead of 5, but not a big deal.  Anyway, it's easier to use an online calculator or program for the task rather than do it by hand.