Geometric mean with logarithmically spaced data?
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This is partly a Matlab question, partly conceptual. I generated three vectors with logarithmically spaced numbers using logspace. If I want to average the first element in the three vectors, then separately the second element, and so on, should I take the arithmetic or geometric mean? If the latter, how do I do this?
1 Comment
Stephen23
on 12 Jul 2022
Edited: Stephen23
on 12 Jul 2022
"If I want to average the first element in the three vectors, then separately the second element, and so on, should I take the arithmetic or geometric mean?"
You gave no information in your question that helps us to understand what you need those means to achieve or how you will use them. In the absence of an such information, are you looking to understand different types of mean?:
Accepted Answer
DGM
on 12 Jul 2022
Edited: DGM
on 12 Jul 2022
"how do I do this?"
% three vectors:
A = logspace(0,2,10);
B = logspace(0,1.9,10);
C = logspace(0.2,2,10);
% put them in an array
allvecs = [A; B; C]
% take the arithmetic mean
avg = mean(allvecs,1)
% take the geometric mean
gmn = geomean(allvecs,1)
1 Comment
John D'Errico
on 12 Jul 2022
Edited: John D'Errico
on 12 Jul 2022
I'm confused as to the question. Is it asking if you should use a geometric mean or an arithmetic mean? Surely that is your choice? @DGM tells you how to compute either, but there is no truly correct way to do something that only you know why you are doing it.
Another simple way to form a set of several geometric sequences is::
S = 2.^([0;0;0] + [1;2;3].*linspace(0,1,10))
I'll let you figure out how I generated them..
Now, since I carefully chose the rate constants, a property of the geometric mean is that it will return the middle sequence.
geomean(S,1)
Do you see that the geometric mean here just reproduced the middle one?
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