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The proportion $x_i$ of $\sum_i x_i$ can be easily determined and interpreted using the formula $\frac{x_i}{\sum_i x_i}$ if all $x_i$ are positive.

But now I have positive as well as negative $x_i$. How to proceed then? How should the result be interpreted? For signed $x_i$ it can also happen that the denominator becomes zero. What would be the right approach?

Gilfoyle
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  • The same expression might be useful in some cases. What answer do you want? If you have $2,3,-1,-3$ what proportion is the $3$? – Ross Millikan Feb 09 '19 at 16:16
  • @RossMillikan Yes, I wonder if there is a better way to compute the proportion, or whatever it is, if positive and negative numbers are present. Would it make sense to separate positive and negative numbers or to use the absolute value to compute the sum? – Gilfoyle Feb 09 '19 at 16:40
  • I don't know what use you want to put this proportion to. It makes good sense for positive numbers, as you say. I don't see the point when negatives are there. You should define the purpose, then it may make sense to do some calculation of this sort. You certainly can separate the positives and negatives, then get the proportion of one positive out of all the positives. That could make sense in a business, where the negatives are costs and the positives are revenues. You can see which ones are important. – Ross Millikan Feb 09 '19 at 16:59
  • @RossMillikan I would like to be able to measure the contribution of a number (positive or negative) to the sum. I need this to interpret the result of a calculation I made. Therefore I need a suitable measure for this, but I have difficulties defining it. It is easy for positive numbers. Here for a sequence [1,2], the 1 contributes to 33% to the sum of both numbers. What is an appropriate way if there are also negative numbers? – Gilfoyle Feb 09 '19 at 18:51

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