# What does $14.2 \pm 0.1$ mean?

I need to experimentally determine some value $Z = 3X+Y$ where $X$ and $Y$ are measurements. I was given the value for $X$, let's say $X = 14.2\pm 0.1$.

Up to now I thought that if I read something like $X=14.2 \pm 0.1$, it was assumed that the measurements were normally distributed with a mean of $14.2$ and a standard deviation of $0.1$.

Is this correct?

My measurements of $Y$ resulted in a mean of let's say $9.5$ and a standard deviation of $0.2$.

I proceeded as follows: I assumed $X$ and $Y$ are both normally distributed and independent with the given means and standarddeviations. So $Z$ is the sum of two normally distributed values, so it must be normally distributed as well with the mean $3\cdot 14.2 + 9.5 = 52.1$ and a standard deviation of $\sqrt{ 3^2 \cdot 0.1^2+0.2^2} = 0.36$ So I could write $Z=52.1 \pm 0.36$.

Again is this the correct way to do this, or is my understanding of this notation wrong?

Unless stated otherwise, the $\pm$ refers to the standard error which is indeed the standard deviation of the measurement.