# Carrying over the standard deviation across calculations

I have conducted a measurement of sample on an instrument. I thus have the value of my samples, of a blank, and the standard deviation of said blank. I would like to execute operations on the value of my sample and need help understanding how standard deviation carries over across these operations. Here,± designates SD. Sample-1 and sample-2 are replicates.

Starting data:

Blank = 136 ± 1.37
Sample-1 = 374
Sample-2 = 394


I then take into account the blank and standard deviation by doing Adjusted sample = Blank - Sample. I get:

Sample-1 = 238 ± 1.37
Sample-2 = 258 ± 1.37


I then do a linear operation (e.g. multiply by k) to convert to different units on both the value and standard deviation (to account for sample volume, which is equal in this case).

Sample-1 = 24 ± 0.09
Sample-2 = 26 ± 0.09


Now I'd like to get to the true measurement of my sample, so I average the two replicates. In terms of SD, I do SD(Sample) = SD(Sample-1, Sample,2) + AVERAGE(SD(Sample-1) + SD(Sample-2). I get:

Sample = AV(24, 26) ± SD(24, 26) + AV(0.09, 0.09)
Sample = 25 ± 1.5


I then convert the sample to a different unit again by a linear operation applied to the value and SD but lets disregard that here.

Now, I have a different measurement with its own standard deviation let's call it Count = 2.86 ± 6.76.

I would like to divide Sample/Count, here is where I think I make a mistake as I simply do SD(SAMPLE)/SD(Count). Is that correct?

Sample and Count are not technically independent but I think can be considered as such here.