I have the following chart. How do I calculate the standard deviation? I've tried to do that:
$x=$ $[2^2*30+6^2*35+(9.5)^2*10+13.5^2*20+18^2*5)] \over 100 $ $-(7.25)^2$= 22.912 -> wrong answer. what did I do wrong?

I have the following chart. How do I calculate the standard deviation? I've tried to do that:
$x=$ $[2^2*30+6^2*35+(9.5)^2*10+13.5^2*20+18^2*5)] \over 100 $ $-(7.25)^2$= 22.912 -> wrong answer. what did I do wrong?

Since this is a table of samples, we should use the corrected sample standard deviation whose square is divided by $n-1$ instead of $n$. This gives the square of the standard deviation to be $23.1439$ instead of $22.9125$.