# Propagation of error vs. direct computation

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?