Clarifying Percentages vs. Percentage Points
Date: 11/21/2003 at 14:23:06 From: LMC Subject: Percentages vs. Percentage Points What is the difference between measuring using percentages versus measuring using percentage points? What is meant by a percentage point?
Date: 11/21/2003 at 16:44:38 From: Doctor Peterson Subject: Re: Percentages vs. Percentage Points Hi, LMC. The term "percentage point" is used to get around an ambiguity in English when we are comparing two different percentages. The problem is that "percent" implicitly refers to a relative change (some fraction of an original amount, like a salary increase of 10%) rather than an absolute change (some specified amount, like a salary increase of $1000). What do we say when we want to treat a percentage as an absolute amount? If, for example, the current tax rate were 10% and we increased it to 12%, we might say that we increased it by 2 percent. But that would be taken to mean that we increased it by 2% _of the original 10%_ (that is, by 2/100 of 10%, or 0.2%), to 10.2%. The question is, are we using "percent" to mean one of the units called percent, or a percentage of that percentage? To avoid this problem, we say instead that we are increasing the tax rate by "two percentage points". This unambiguously refers to the number 2% itself as a unit, rather than to 2% of something else. On the other hand, if we actually wanted to say that the tax increased to 10.2%, it would be a good idea to clarify that as well, perhaps by saying explicitly that it increased by 2% of its old rate, or by stating the old and new values. Technically, however, it is correct to say that it increased by 2%. Here are some pages I have found that discuss this: http://mathworld.wolfram.com/Percent.html http://en.wikipedia.org/wiki/Percent In summary, I wouldn't say that we "measure" using one or the other; rather, we use the one term to clarify our meaning where the other would be ambiguous, because we are switching perspective from thinking of a percentage as a fraction of something else, to treating it as a number that stands on its own. A percentage change is a difference divided by some base number, while a percentage _point_ change is a simple addition or subtraction. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 11/24/2003 at 08:32:09 From: LMC Subject: Thank you (Percentages vs. Percentage Points) Dr. Peterson, Thank you very much for such a speedy and useful clarification! LMC
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