Percent Change, Increase, DifferenceDate: 07/15/97 at 08:24:03 From: Allistair Subject: Percent difference I haven't had math in years and I need a little help here. Say you have two numbers 5 and 7. You want to know what is the difference in percent between the two numbers. Below is an real example of the problem I'm working on. 1991 = $2346.80 1992 = $3608.29 Percent change 91-92 = ? Date: 07/15/97 at 09:02:14 From: Doctor Rob Subject: Re: Percent difference First you need to compute the difference between the two amounts. Then you make a fraction of that difference over the first of the two amounts. Finally you convert the fraction to a percentage by dividing the denominator into 100 times the numerator. In your example, dropping the dollar signs, the difference is 3608.29 - 2346.80 = 1261.49. The fraction is 1261.49/2346.80, and the percentage comes from dividing 2346.80 into 126149. The result is 53.75, and since the sign is positive, this is a 53.75 percent increase from 1991 to 1992. In the other example, 5 and 7, the difference is 2, the fraction is 2/5, and the percentage is 5 divided into 200, or 40. Thus 7 is 40 percent larger than 5. On the other hand, if you take 7 and 5, the difference is -2, the fraction is -2/7, and the percentage is 7 divided into -200, or -28.57. Thus 5 is 28.57 percent smaller than 7. It may seem paradoxical that if we start with 5 and add 40 percent, we get 7, but to get back to 5 we have to subtract only 28.57 percent. The reason these percentages are different is that they are percentages of different amounts: 40 percent of 5, and 28.57 percent of 7 - both are equal to 2. For more about percentages and fractions, see the Dr. Math FAQ: http://mathforum.org/dr.math/faq/faq.fractions.html -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 05/05/2003 at 18:01:25 From: Jerone Anderson Subject: Percent difference The above explanation defines percent difference as ((q1-q2)/q2)*100, which is used in many calculations for percent error rather than percent difference. Percent difference is defined as (|q1-12|/((1/2)*(q1+q2)))*100 for comparing values. I am confused, as the terms percent difference and percent error are not consistent with what is expected in many classes. Date: 05/05/2003 at 22:57:56 From: Doctor Peterson Subject: Re: Percent difference Hi, Jerone. The above is really about "percent change" or "percent increase," rather than "percent difference," since there is an "old" and a "new" value. In that case, you take the percentage of the old value. When there is no directionality to the difference, so you can't distinguish an "old" value from a "new" value, you have to use the average of the two as the standard of comparison, as in your formula. This is one of many cases where terms are used differently in various contexts, and what is a minor error of terminology in one question can lead to major confusion for people coming at it from a different direction. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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