# Summing standard deviations? or summing variances?

I have a method for making measurements. Within this method there are four separate variables that can influence the measurement (i.e. variation). I have individually tested each variable (by making changes) to ascertain the level to which they will affect the measurement.

For each variable I make say five changes, and get 5 measurements. I work out the mean measurement value and then calculate the difference between the mean measurement value and the each of the five measurements I made. What I get is a mean difference of 0 and a standard deviation that essentially tells me how variable the measurement is as a result of the changing individual variable.

So I have four standard deviation (s.d) values, that relate to each of the variables. Now I want to consider what would happen if I changed all four variables and what the cumulative effect on the measurement would be, i.e. how much would the measurement vary if all four variables changed.

I thought I should just add the standard deviations, but I'm reading about having to add the variances not the s.d? and am now confused. What I want is an overall variation value in some form, I'm guessing a s.d.

Do I add the variances and then sqrt them to get an overall s.d. that represents the variation? The variables are independent (do not affect one another) but I'm not sure about their distributions, I'm assuming normal.

Thanks!!!

• Yes, you add the variances, then sqrt them to get the std deviation of a sum. If you're curious why...if you grab any probability book, it's gonna be shown pretty early on as a standard example. Jul 6, 2014 at 14:43