# How to calculate the variance/ standard deviation of a sum of ratios (X1+X2+X3+…)/Y?

I calculated the correlation matrixes between each variable and i found that some are correlated some are not ? what should i do to find out the variance of the sum of all random variables divided by a random variable (costs divided by cycle time which is also a random variable)

Here is the correlation matrix i generated thank you very much

• Edit: i found this but i don't know if it is related or solves my problem ?stat.cmu.edu/~hseltman/files/ratio.pdf – latrous Sep 11 at 8:04
• I'm guessing that the sum on top goes from $1$ to $Y$ and that $Y$ is an integer. In that case I would suggest you compute the conditional variance given $Y$ and then apply the usual formulas. – P. Quinton Sep 11 at 8:08
• @P.Quinton, thank you for your answer, but why conditional variance ? (the goal is to find the mean cost per time unit, so i am divding the total cost per time and all is random variables as they depend on simulation results using as entry random variables ) – latrous Sep 11 at 8:14
• If you have the conditional variance then you can find the variance using this en.wikipedia.org/wiki/… so all you have to know is $\mathrm{Var}[U|Y]$ and $\mathbb E[U|Y]$ where $U$ is your thing. – P. Quinton Sep 11 at 9:24