Hi I am wondering how to calculate the standard deviation from sample data when you are just given the sum of $X^2$, the sum of $X$ and a value for $n$. Every formula I try gives me a error as it ends up with a negative root. For example here is a question im stuck on: $n=90, \sum X^2 = 353.1916, \sum X= 177.9$ and then they got a result of $0.132$ for the standard deviation.
Any help would be greatly appreciated.
$$V(X) = E[X^2] - (E[X])^2$$ $E[X^2] = \frac{1}{n}\sum X^2$ and $E[X] = \frac{1}{n}\sum X$ So the variance is $$\frac{353.1916}{90}-\Big(\frac{177.9}{90}\Big)^2$$ and the sample standard deviation is the square root of the variance: 0.1309, slightly different from the claimed answer, which could be rounding issues.