I have a some datasets that I want to take an average of - a typical dataset might look something like this:
0 0 0 1 100 100 10000 30 10 10 0 0 0 0 0
Ordinarily I would use the geometric mean for something like this - but unfortunately I have a lot of zeros in there. I don't want to use the median because the truly extreme values (~10,000) are quite rare and I want them to be included when they do appear.
So I was wondering if a valid approach might be to first take the geometric mean of the nonzero values, then take the weighted arithmetic mean of the geometric mean together with the zero values.
So for the above dataset:
Geometric mean of nonzero values = Geom(1,100,100,10000,30,10,10) = 43.6
Weighted arithmetic mean = (7*43.6 + 8*0)/15 = 19.075.
I think this seems better than the simple arithmetic mean, which returns 683, and better than the median, which returns 0.
Is there anything wrong with doing this, and if so could anyone suggest an alternative. Any advice on how to calculate an error for this would also be appreciated.
EDIT: I realised that my plan clearly doesn't work, as if I had a dataset consisting of 10000 from the above dataset but all other values replaced with 0, I would still end up with a mean of 666 - which is a much higher number than 19.075, despite the actual data going into it being lower. So now I have no idea how to approach this problem, and would appreciate any insight!