How Does Standard Error Change When Inverting a Variable?

[n0_3sc]

A quantity 'X' has a standard error 's' if 'X' is inverted ie. X^-1
what do I do with 's'?

 

[andrevdh]

The std error $s_Y$ in
$$Y=1/X$$
will be
$$s\frac{1}{X^2}$$

 

[kyle8921]

I would first clarify that the standard error of a quantity is a measure of the variability or uncertainty in the estimate of that quantity. In this case, the quantity 'X' has been inverted, meaning that it has been raised to the power of -1. This can also be thought of as finding the reciprocal of 'X'.

So, the standard error of X^-1 would represent the uncertainty in the estimate of the reciprocal or inverse of 'X'. In terms of what to do with 's', it would depend on the specific context and application of 'X'. If 'X' is a measurement or data point, then the standard error 's' would provide information about the accuracy and precision of the measurement or data. If 'X' is a parameter in a mathematical model, then the standard error 's' would indicate the variability in the estimate of that parameter. In either case, 's' would be an important factor to consider in interpreting and using the inverted quantity 'X^-1'.