How to find the margin of error of a value consisting of the sum of 5 values?

Question

I have a $X$ value that is the sum of 5 different $x1,x2,x3,x4$, and $x5$ values. Eacn $x_i$ has their error in same scale. I want to calculate the error of X. How can i do that? Basically, i tried to sum them. But it's not very scientific. Any ideas?

Answer 1

If you have some quantity $X$ which is a function of variables $x_i$ $$X = f(x_i)$$ And each $x_i$ has uncertainty $\sigma_i$, the uncertainty in $X$ is described by $$\sigma_X^2 = \sum_i \left(\frac{\partial f}{\partial x_i} \sigma_i\right)^2$$ Since your function $f$ is of the form $$f(x) = \sum_i c_i x_i$$ The partial derivative $ \frac{\partial f}{\partial x_i} $ is just the coefficient $c_i$. Note that this has the effect that different errors are weighted (in quadrature) by their respective variable’s contribution to the final value.