In Reply to Parent Post by Statisticale
I have an area of forest that has been stratified into 2, & I wish to calculate the +/- 3 standard deviation (sigma) distribution of tree heights in the combined area. The weighting of the first area is 0.73, & the second is 0.27. Means heights are 8.3 & 5.5 meters, with standard deviations of 1.2 & 0.9 meters.
If we make the assumption that co-variance can be ignored, can the combined result be calculated without going to partial derivitaves? If so, how?
If you assume independence, you can use the property of variances to solve the problem.
Var (X + Y) = Var(X) + Vary (Y)
Var (0.73X) = (0.73^2)Var(X)
Var (0.27Y) = (0.27^2)Var(Y)
Var (0.73X + 0.27Y) = (0.73^2)Var(X) + (0.27^2)Var(Y)
The calculation of the means is straightforward.
Overall Mean = ((n1*0.73*mean1) + (n2*0.27*mean2))/(n1+n2)
Does that make sense. Of course the assumnption of independence is CRITICAL here.