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    <pre><code>from __future__ import division from itertools import izip, repeat import math def weighted_mean(values, weights=None): total = 0 number = 0 if weights is None: weights = repeat(1) for weight, value in izip(weights, values): total += weight * value number += weight return number and total / number xa = [1, 2, 3, 10, 1383, 0, 12, 9229, 2, 494, 10, 49] xb = [1, 1, 4, 12, 1100, 43, 9, 4848, 2, 454, 6, 9] print "Option 1, if you want bigger numbers to have a bigger effect on the score" weights = (math.sqrt(abs(a) * abs(b)) for a, b in izip(xa, xb)) scores = (abs(a) + abs(b) and abs(a - b) / (abs(a) + abs(b)) for a, b in izip(xa, xb)) final_score = weighted_mean(scores, weights) print "%.02f%%" % (final_score * 100) print "Option 2, if you want to have all numbers have the same effect on the score" scores = (abs(a) + abs(b) and abs(a - b) / (abs(a) + abs(b)) for a, b in izip(xa, xb)) final_score = weighted_mean(scores) print "%.02f%%" % (final_score * 100) </code></pre> <p>Of course, you can also use other kinds of weights, such as <code>(abs(a) + abs(b)) / 2</code>, depending on how you want to interpret a given difference.</p> <p>Loopless version of the second one:</p> <pre><code>xan = numpy.array(xa) xbn = numpy.array(xb) error_threshold = 0.000001 final_score = numpy.mean((abs(xan - xbn) + error_threshold) / (abs(xan) + abs(xbn) + error_threshold)) </code></pre> <p>Or the first:</p> <pre><code>scores = (abs(xan - xbn) + error_threshold) / (abs(xan) + abs(xbn) + error_threshold) weights = numpy.sqrt(abs(xan) * abs(xbn)) final_score = numpy.sum(scores * weights) / numpy.sum(weights) </code></pre>
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    1. CO@ Rosh Oxymoron: What was that in OP's question that makes you to suggest this approach?
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    2. COHis question? DominiCane wants the difference in percent between two lists of numbers, the mean of the difference between each pair of numbers seems to be a quite possible options, depending on the requirements. Weighted with the arithmetic mean of the two values, it will yield exactly the area difference suggested in the OP which is good if an exact quantity difference is expected, unweighted it will yield something good for input that's not normalized or the change is expected to be proportional to the value (average salary in different countries), etc.
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