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That is, the sum of squares of some numbers divided by the sum of the numbers. The term "anti-harmonic mean" has been coined for this quantity. I'm hoping there is a better name.

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closed as too localized by Simon Thomas, Daniel Moskovich, Mark Sapir, Chandan Singh Dalawat, José Figueroa-O'Farrill Nov 30 '10 at 3:40

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Do you like "contraharmonic mean" better? See for details and references. – Doug Chatham Nov 30 '10 at 0:33
Yes, I do. At least it has some history. Thanks! – tdnoe Nov 30 '10 at 0:46
Five people vote to close a question, and not one of them leaves a comment indicating a reason. This leaves me with no idea as to what could be the objection to this question. – Gerry Myerson Nov 30 '10 at 10:04
+1 on Gerry Myerson's comment. But seeing that Doug Chatham has already provided what is possibly a satisfactory answer in the comments above, I won't vote to re-open. – Willie Wong Nov 30 '10 at 11:08
@Willie Wong, I agree. I am, however, sorely tempted to bring it up in meta. – Gerry Myerson Dec 1 '10 at 23:28