Dear Jonathan,

> standard deviation "feels" a bit different from a mean, and a variance even 
> more so because of its different units, but I can't see a clear justification 
> for treating these two differently from mean, median, mode or other cell 
> methods - they are all statistics which characterise variation of a single 
> quantity over its dimensions

I have a hard time understanding how mean, median or mode can be used to 
characterise variation. For each of these statistics one can (in principle) use 
one data vaue to argue that it is the the best available estimate of the 
corresponding true unobserved value "out there". However, for standard 
deviation, variance and standard error this is clearly not possible. So, I 
would say that there is a fundamental difference. In the light of this issue, 
mean, median or mode do not (as far as I understand) give any information that 
can be related to uncertainty, which is contrary to standard deviation, 
variation or standard error.      

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