This seems like such a straightforward question but, after googling the title of this question and variations thereof, I haven't been able to find an answer.
Please point me in the right direction if this has already been asked!
SampleA <- [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
STDEV.S(SampleA) -> 3.027
SampleB <- 1/SampleA ([1, 0.5, 0.33, 0.25, etc])
STDEV.S(SampleB) -> 0.277
What's the general theme here? More formally: If I know the standard deviation of sample $A$, what is the standard deviation of $A^{-1}$?
At first, I thought that the standard deviation after inverting all of the points would just be the inverse of the standard deviation, but 1/STDEV.S(SampleA) = 0.33, not 0.277.
You can not calculate the standard deviation of the inverse of the numbers in the set just from the standard deviation of of the set.
You can consider sets {1,2} and {2,3} their standard deviations are equal, but that of their inverses are not. That is enough to say that there is no direct relationship between standard deviation and the standard deviation of inverses.