# Calculating standard deviation from two averages?

• Nov 1st 2012, 08:57 AM
Bwts
Calculating standard deviation from two averages?
Hi,

I have 2 sets of measurements of equal number. Each set is associated with a different set of markers, a top set and a bottom set.

I have the average position of each set of markers with the associated standard deviations.

Now I want to subtract the two averages to get an average distance, what do I do about the standard deviations?

Further information: there is no clear one to one correspondence between elements of one set to another, so calculating the difference between elements of one set to another is meaningless. This is due the manner that the experiment was set up.

Thanks for any help

B
• Nov 1st 2012, 05:45 PM
chiro
Re: Calculating standard deviation from two averages?
Hey Bwts.

When you subtract means you get the mean is E[X-Y] = E[X] - E[Y] with Var[(X_bar-Y_bar)] = Var[X_bar] + Var[Y_bar] so the standard deviation of the difference of the means is given by SQRT(Var[X_bar] + Var[Y_bar]). So you add the two standard deviations of the mean (estimated or given) and take the square root.