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'[WOT] Almost memoryless average?'
1999\04\26@172524 by Richard Martin

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For a distribution symetrical about the mean the mean
and the median are the same. In fact that's a fairly good
'cheap' test of the assumption of symetry.

Sorting on a small memory machine isn't 'easy'. Particularly
with a very crude index register. But you get what you pay for.
Meaning (among other things) sometimes the median is more
relevant to what you want to do.

The  'one byte of memory'  algorithm computes 7.25 , but of course
the sample is highly skewed to the high end. But the 'normal'
average calculation for this sample fits into one byte anyway.

We used techniques like these to 'average' biological waveforms
when 'memory' cost real $$. I remember a $70 '7474 equivalent.

I think there is a simple ("intuitive") proof that the 'box' average
is equivalent to 'gaussian' or any other for symmetric distrib.

Dick M.

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