# Percentage difference in normalized number set

Let's say I have two numbers that I know to have been normalized- 39, 12. How do I calculate the percentage difference between them? Is it the same as if they hadn't been normalized? ie: (12/39) * 100

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Shouldn't the percentage difference be [(12-39)/39]*100 or [(39-12)/12]*100? Note that you get different answers, not just the negative-when the two numbers are unequal the percentage difference depends upon which you regard as the base.

Whether normalization changes the percentage depends upon what you mean by normalization. Sometimes it is multiplication by a constant to bring the range to something you like. This will not impact the percentage difference-try multiplying 39 and 12 by a and note that it divides out of the expression. Sometimes it involves adding or subtracting a constant-that will make a difference. Compare [(39-12)/39]*100 to [(30-3)/30]*100. The answer is different. Sometimes it is a more complicated expression, which will almost always change the percentages.

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