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I have six scores as: Score 1 - Large value is better, i.e., 63 is better than 60. Score 2 - Small value is better, i.e. 5 is better than 6.7. Score 3 - Small value is better, i.e. 5 is better than 6.7. Score 4 - Small value is better, i.e. 5 is better than 6.7. Score 5 - Small value is better, i.e. 5 is better than 6.7. Score 6 - Small value is better, i.e. 5 is better than 6.7.

Now I want to calculate an aggregate score so that i will be able to compare the score of two persons P1 and P2 and decide which one is better.

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Just convert all the scores so that higher is better. Say each score x is out of some number y. Thus we can represent a score as $x/y$. Define a function $f$ which maps $x/y$ to $y - (x/y)$. Apply this function to all the scores in which lower is better. You can then either convert all scores to a like denominator, or compute their decimals to easily see which scores are higher.

Let us look at some examples. Say we want to compare 3/5 (higher better) to 1/20 (lower is better). Our function maps 1/20 to 20-1/20 = 19/20. Thus both our scores are now changed to higher is better, and are (3/5,19/20). Converting to like denominator, we have our scores are (12/20,19/20). Clearly 19/20 is greater.

If multiple scores belong to one person, after applying the transformation (ie the function) given above, just compute the average of that person's transformed scores to get an aggregate score.

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  • $\begingroup$ For score 1 range is 0-100. i.e. y can be set as 100. But i don't have any range for score 2- 5. They can vary ...??? $\endgroup$ – Peter Naughton IITM Jun 25 '17 at 6:46
  • $\begingroup$ @PeterNaughtonIITM the solution works for any positive integer $y$. $\endgroup$ – Evan Rosica Jun 25 '17 at 6:48
  • $\begingroup$ Thanks... Evan Rosica. $\endgroup$ – Peter Naughton IITM Jun 25 '17 at 6:52

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