standard deviation for an equation


I am trying to figure out how to get the standard deviation for two equations.

The first one is quite simple; it's just how to find the SD for a part of an average value. I have the SD for an average amount of element in 4 values
e.g. average = 118 mg/kg and SD = 48 mg/kg
I am multiplying 118 mg/kg by 0.2 kg to get total element amount in 200 g. How do I calculate the SD for the 200g? Is it simple multiplication there as well?

The second part involves calculating a percent element transfer using the average values from above, as well as average amounts of an element in another medium

i.e. percent = (avg total amount in filtrate/avg total amount in ash) * 100

The avg in filtrate is from 2 values and avg in ash is from 4 values; do I use the relative errors calculation with the answers given from the first question? Does it matter that the number of samples is different?

Thanks for any and all help!
I can answer the first question: Multiplying a set of numbers by a constant will multiply the SD by that value. Consider what happens to the range if you multiply all numbers by a value -- it will increase by that value (5 to 15, multiply by 4 --> 20 to 60 and the range goes from 10 to 40).

Not quite sure what you are doing with ratios -- an example might flesh it out. It sounds like you want some kind of SD -- but this is a ratio of averages. What would the sd be for? I doubt there is a truly simple way to get an error measure like an SEM from this situation.


New Member
yeah, I'm not sure about your 2nd question either, but maybe this helps: to get var of a ratio take the var of the second-order taylor series approximation