Suppose I have a set $\{x_i\}_{i = \overline{1,N}}$ of data that characterizes some parameter $X$, and I want to compute the standard deviation of some parameter $Y = f(X)$.

I can think of two methods for doing this:

  1. propagation of errors
  2. direct computation of $\{y_i = f(x_i)\}_{i = \overline{1,N}}$ followed by the computation of the standard deviation for $\{y_i\}$

Are these approaches the same?


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