I want to calculate the standard deviation of the following numbers:
30, 45, 45, 60, 75, 80, 90, 100, 110, 120.
As far as I know, that would be
$\sqrt{\frac{1}{10}((30-75.5)^2+(45-75.5)^2+(45-75.5)^2+(60-75.5)^2+(75-75.5)^2+(80-75.5)^2+(90-75.5)^2+(100-75.5)^2+(110-75.5)^2+(120-75.5)^2)}$ = 28.587585
This site: http://de.numberempire.com/statisticscalculator.php got it right, but according to my book and this site: http://rechneronline.de/durchschnitt/ the result it 30.134.
So what's the right result and how come it differs?
As I mentioned in the comments, there are two different types of standard deviation. You are calculating the bias estimate. Your book most probably wants the unbiased estimate. $s_{n-1}=\sqrt{\frac{n}{n-1}}s_{n}$ Use n=10 for the number of values. You can see where the difference comes from