I have 3 values and each of them have some random error to them. These values have no correlation with each other and neither do the errors. I want to find the mean of these values and the standard error of the mean value.
Example data: x= 1 +- 0.03 y= 2 +- 0.54 z= 4 +- 0.22 mean= ? +- ?
I am not very experienced in statistics so please keep the answer simple to understand. I have been told that the mean is just not arithmetic mean i.e (x+y+z)/3. We need to consider the errors as some weighting.
This is what my professor told me:
To compute the mean value of the 3 independent projections, you want to use not just the values of the shear (1,2,4 in this example) but also their associated error bars. That is, you have 3 sets of data points with error bars, so you should be computing a weighted mean and deriving the final error bars using the weights in the standard fashion.
I am not sure what exactly she means by standard fashion or how to get the weighted average.